Voting is like donating thousands of dollars to charity
Summary: People often say that voting is irrational, because the probability of affecting the outcome is so small. But the outcome itself is extremely large when you consider its impact on other people. I estimate that for most people, voting is worth a charitable donation of somewhere between $100 and $1.5 million. For me, the value came out to around $56,000. So I figure something on the order of $1000 is a reasonable evaluation (after all, I’m writing this post because the number turned out to be large according to this method, so regression to the mean suggests I err on the conservative side), and that’s be enough to make me do it.
Moreover, in swing states the value is much higher, so taking a 10% chance at convincing a friend in a swing state to vote similarly to you is probably worth thousands of expected donation dollars, too.
I find this much more compelling than the typical attempts to justify voting purely in terms of signal value or the resulting sense of pride in fulfilling a civic duty. And voting for selfish reasons is still almost completely worthless, in terms of direct effect. If you’re on the way to the polls only to vote for the party that will benefit you the most, you’re better off using that time to earn $5 mowing someone’s lawn. But if you’re even a little altruistic… vote away!
Time for a Fermi estimate
Below is an example Fermi calculation for the value of voting in the USA. Of course, the estimates are all rough and fuzzy, so I’ll be conservative, and we can adjust upward based on your opinion.
I’ll be estimating the value of voting in marginal expected altruistic dollars, the expected number of dollars being spent in a way that is in line with your altruistic preferences.1 If you don’t like measuring the altruistic value of the outcome in dollars, please consider making up your own measure, and keep reading. Perhaps use the number of smiles per year, or number of lives saved. Your measure doesn’t have to be total or average utilitarian, either; as long as it’s roughly commensurate with the size of the country, it will lead you to a similar conclusion in terms of orders of magnitude.
Component estimates:
At least 1/(100 million) = probability estimate that my vote would affect the outcome. This is the most interesting thing to estimate. There are approximately 100 million voters in the USA, and if you assume a naive fair coin-flip model of other voters, and a naive majority-rule voting system (i.e. not the electoral college), with a fair coin deciding ties, then the probability of a vote being decisive is around √(2/(pi*100 million)) = 8⁄10,000.
But this is too big, considering the way voters cluster: we are not independent coin flips. As well, the USA uses the electoral college system, not majority rule. So I found this paper by Gelman, King, and Boscardin (1998), where they simulate the electoral college using models fit to previous US elections, and find that the probability of a decisive vote came out between 1/(3 million) and 1/(100 million) for voters in most states in most elections, with most states lying very close to 1/(10 million).
At least 55% = my subjective credence that I know which candidate is “better”, where I’m using the word “better” subjectively to mean which candidate would turn out to do the most good for others, in my view, if elected. If you don’t like this, please make up your own definition of better and keep reading :) In any case, 55% is pretty conservative; it means I consider myself to have almost no information.
At least $100 billion = the approximate marginal altruistic value of the “better” candidate. I think this is also very conservative. The annual federal budget is around $3 trillion right now, making $12 trillion over a 4-year term, and Barack Obama and Mitt Romney differ on trillions of dollars in their proposed budgets. It would be pretty strange to me if, given a perfect understanding of what they’d both do, I would only care altruistically about 100 billion of those dollars, marginally speaking.
Result
I don’t know which candidate would turn out “better for the world” in my estimation, but I’d consider myself as having at least a 55%*1/(100 million) chance of affecting the outcome in the better-for-the-world direction, and a 45%*1/(100 million) chance of affecting it in the worse-for-the-world direction, so in expectation I’m donating at least around
(55%-45%)*1/(100 million)*($100 billion) = $100
Again, this was pretty conservative:
I’m more like 70% sure,
Being in California, Gelman et al. put my probability of a decisive vote around 1/(5 million).
To me, the outcome matters more on the order of a $700 billion donation, given that Obama and Romney’s budgets differ on around $7 trillion, and I figure at least 10% of that is stuff that I’d care about relative to other shifts in money I could imagine.
That makes (70%-30%)*1/(5 million)*($700 billion) = $56,000. Going further, if you’re
90% sure,
voting in Virginia -- 1/(3.5 million), and
care about the whole $7 trillion dollar difference in budgets,
you get (90%-30%)*1/(3.5 million)*($7 trillion) = $1.2 million. This is so large, it becomes a valuable use of my time to take 1% chances at convincing other people to vote… which I’m hopefully doing by writing this post.
Discussion
Now, I’m sure all these values are quite wrong in the sense that taking account everything we know about the current election would give very different answers. If anyone has a more nuanced model of the electoral college than Gelman et al, or a way of helping me better estimate how much the outcome matters to me, please post it! My $700 billion outcome value still feels a bit out-of-a-hat-ish.
But the intuition to take away here is that a country is a very large operation, much larger than the number of people in it, and that’s what makes voting worth it… if you care about other people. If you don’t care about others, voting is probably not worth it to you. That expected $100 - $1,500,000 is going to get spread around to 300 million people… you’re not expecting much of it yourself! That’s a nice conclusion, isn’t it? Nice people should vote, and selfish people shouldn’t?
Of course, politics is the mind killer, and there are debates to be had about whether voting in the current system is immoral because the right thing to do is abstain in silent protest that we aren’t using approval voting, which has better properties than the current system… but I don’t think that’s how to get a new voting system. I think while we’re making whatever efforts we can to build a better global community, it’s no sacrifice to vote in the current system if it’s really worth that much in expected donations.
So if you weren’t going to vote already, give some thought to this expected donation angle, and maybe you’ll start. Maybe you’ll start telling your swing state friends to vote, too. And if you do vote to experience a sense of pride in doing your civic duty, I say go ahead and keep feeling it!
Related reading
I’ve found a couple of papers by authors with similar thoughts to these:
Jankowski (2002), “Buying a Lottery Ticket to Help the Poor: Altruism, Civic Duty, and Self-interest in the Decision to Vote”, and
Edlin, Gelman and Kaplan (2007), “Voting as a Rational Choice: Why and How People Vote To Improve the Well-Being of Others.
Also, just today I found this this interesting Overcoming Bias post, by Andrew Gelman as well.
1 A nitpick, for people like me who are very particular about what they mean by utility: in this post, I’m calculating expected altruistic dollars, not expected utility. However, while our personal utility functions are (or would be, if we managed to have them!) certainly non-linear in the amount of money we spend on ourselves, there is a compelling argument for having the altruistic part of your utility function be approximately linear in altruistic dollars: there are just so many dollars in the world, and it’s reasonable to assume utility is approximately differentiable in commodities. So on the scale of the world, your affect on how altruistic dollars are spent is small enough that you should value them approximately linearly.
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Obviously you are willing to extend this sort of cost benefit analysis to all kinds of influencing government?
If me grabbing a nanoslice of power in the form of casting a vote is like donating a thousand dollars to charity, me grabbing more than a nanoslice even by illegal means shouldn’t be dismissed out of hand and deserves even handed analysis. The value of such information seems to be pretty high.
You have, in a nutshell, just explained why lobbyists exist.
Yes, this. I’d like to see the author of the article give a similar analysis on whether or not we should quit our jobs and become lobbyists.
I would argue it is easier to pull sideways by lobbying than voting or campaigning.
Do you own any stock in Diebold?
Are you a candidate this election for local supervisor of elections?
I shudder to think of what a small group of dedicated rational thinkers could do to subvert democracy to serve the needs of the people...
It’s worth pointing out that the $100 you “donate” probably goes much, much less far than a $100 donation to an effective charity. So it might be better to think in terms of shifting $100 in federal funds. That makes it seem like a lot less of a slam dunk to me. Would I take half an hour out of my day to move $100 from an ineffective government agency to an effective one? Meh. Feels like my other attempts at altruism probably have a much higher expected impact.
I’m also worried about getting called up for jury duty if I re-register to vote now that I’m living in a different county.
On the whole though, fairly persuasive.
What would you consider an effective government agency?
Yes, this is a very good point, and should be part of the $100 billion dollar estimate at the election outcome value… How much do you think the difference of candidates is worth, in MED$? (marginal effective donation dollars)
Some interesting comparisons (I don’t claim these are the most interesting, they’re just off the top of my head):
$100 billion = 1⁄3 (100 million) ($1000) = 1⁄3 (population of the USA) (marginal cost of saving lives with mosquito nets) and also
$100 billion = 1⁄70 (population of the world) (marginal cost of saving lives with mosquito nets)
It’s actually not obvious to me that the difference in candidates would be much less valuable than these things, but these comparisons do make me personally not want to call MED$100 billion a conservative lower bound.
Does anyone have any interesting estimates for the difference of election outcomes in MED$?
You might want to specify that when you talk about “donations” you are referring to charitable donations rather than campaign donations. It might just be me, but the political priming made this distinction less obvious than it probably should have been.
Wow, thanks for this! I just changed the title.
Ah! Yeah, I didn’t get this distinction on an admittedly casual readthrough, and was trying to figure out why the 55% confidence even factored in, since presumably if I’m wrong about who the best candidate is when I vote I would counterfactually be equally wrong when I donate, so the 55% factor would apply equally to both sides of the inequality.
But this makes more sense.
Of course, my confidence that my charitable donation is going to somewhere valuable is similarly a factor, and might be less than 55%. (Though I do realize that by local social convention this is a solved problem.)
As the paper says:
And as it turns out, conditional on polls and other information from right before the election, one would have to assign a very low probability that California will (almost) vote Republican. Also, conditional on California (almost) voting Republican, one would have to assign a very high probability that enough other states will vote Republican to make California’s outcome not matter.
It seems to me that a reasonable probability estimate here would be multiple orders of magnitude lower than the cited estimate; and it seems to me that together with the optimal philanthropy point made by user:theduffman and user:dankane and user:JohnMaxwellIV elsewhere in the thread, this makes voting in states like California not worthwhile based on the calculation presented in the original post.
Similarly, California’s Senate race isn’t significantly likely to shift. But at the House of Representatives level, the probabilities could be more significant—depending where you live. State representatives, mayors, plebiscites, etc.: there are many opportunities.
Irrespective of California, many people even in swing states think voting is silly, so I would hope that they read this post… but regarding California,
Thumbs up, except that conclusion here is not to not vote… it’s to either
1) watch the polls and vote based on proximity to a tie at both the state and federal level,
or if the time watching the polls is more of a sacrifice to you than the time spent on late-stage voting (can’t vote by mail),
2) just vote without the poll information.
Reason: supposing that (a) without the poll information, the EV of voting is high, and (b) finding out the poll results can change your decision, (a+b) implies that the poll results have high VOI. More precisely,
1/ (5 million) = Pr(decisive | no info) = Pr(decisive | close poll) Pr(close poll) + Pr(decisive | not-close poll) Pr(not-close poll)
Since Pr(decisive | not-close poll) is many orders of magnitude closer to 0 than 1/(5 million), and Pr(close poll) is quite small, say 1/N, Pr(decisive | close poll) must be on the order of N 1/(5 million), so the payoff would be N whatever is reported in the post, which would be huge.
So the conclusion here is that “Voting without poll results is like donating to charity, but adopting the policy of watching the polls and deciding to vote based on proximity to a tie is like donating almost as much to charity, and saves you time, unless you spend more time watching the polls that you would spend to vote.”
The problem is that letting polls influence voting decisions is subject to Goodhart’s law.
On the other hand, if you want to strictly adhere to utilitarian principles, you would probably have to note that the “altruistic dollars” obtained through selection of the better candidate probably produce much less utility per dollar than a dollar donated to one of givewell.org’s top rated charities. Standards of living in the US are already so high that a marginal dollar is worth much less than a marginal dollar in a less developed country. Then again, if you really followed this philosophy and lived in the US, you should probably actually devoting essentially all of your time to earning money to donate to such charities, which is not something that many people are actually willing to do.
US policy and wars have a large effect on people in poor countries. They are presumably considered in the $100 billion “better for the world” sum.
Unless they would be earning fabulous sums in that hour, an altruist would probably be justified in considering the expected value of their vote higher than the expected value of whatever else they would do with that one hour per year.
On the other hand, it seems to me like the differences between the foreign policies of the two candidates don’t seem nearly as significant as the differences in their domestic policies. Furthermore, problems like malaria would be best dealt with through foreign aid budgets, which really aren’t that big to begin with. In any case, I think my point stands that the value of an “altruistic dollar” in this context is significantly less than the value of an actual dollar donated to an optimal charity.
I agree with you, and while I agree that the values of “charity” versus “well-directed US spending” are at least one order of magnitude different, but I’m not convinced that they are more than three orders of magnitude different and most people do not even make $56/hour with total time fungibility.
Gelman, Silver, and Edlin have a more recent paper looking at the 2008 election, which estimated that California voters had a 1 in 1 billion chance of being decisive and that 1 in 10 million was the maximum probability of being decisive (for voters in the four swingiest states).
I think the polls are closer in 2012 than 2008.
Voting is more like stealing thousands of dollars to donate to an ok charity.
The problem is that the thousands of dollars are being stolen anyway and you need to vote to have any say in which charity, or to reduce the amount of money being stolen.
Just like no candidate really supports peace, no candidate really supports not-stealing.
Also, by taking part in a system of violence & theft, you are granting it some amount of legitimacy.
Stealing?
Taxes are an involuntary transfer of wealth made under threat of coercive violence. Theft is an an involuntary transfer of wealth made under threat of coercive violence.
Saying that does not mean much until one defines the proper scope of legitimate violence in society. Max Weber made the analytically useful point that one definitional aspect of modern government is its monopoly on legitimate violence.
Americans sometimes have this silly idea I like to call the “Holy Divine Right Of Tiny XML Tags Assigning Exclusive Ownership” or the “Principle of You-Can’t-Have-It-’Caus-It’s-MINE”.
For those who do, the idea that a government would forcibly, without giving you a choice retract from your possession a number of Game Points, which everyone agrees to hold as representative of value under the assumption that this very same government will enforce continuous acceptance of the value of these Game Points, is very evil and a violation of the above principles that are in their mind inviolable and necessary and ontological and what-have-you.
Nevermind all the complicating factors, such as the fact that you can choose not to give them points simply by not acquiring more than a set amount of points per year (hell, in many cases if you do this they will give you points).
You are pattern matching to a straw-man version of a belief which is not even the one I was relying on.
All the relevant part of my argument requires is for
Taking an action (voting) to reduce the amount of money one person who is not you has (whether they be an ex-recipient of state funding or a new taxpayer) and increases the amount another has (whether they be an ex-taxpayer or a new recipient of spending)
to be more similar to
Taking an action (stealing and donating) to reduce the amount of money one person who is not you has (the victim) and increases the amount another has (the beneficiary of the charity)
than to
Taking an action (donating to charity) to reduce the amount of money you have and increases the amount another has (the beneficiary of the charity)
which is I think clearly true.
edit: formatting. Also I’m not American
It was indeed very strawman, of that I was aware. The strawman version is easier to get across and requires crossing less inferential distance in most cases I’ve experienced.
Thanks for straight-up telling me that I was pattern matching to the wrong belief. Upon reconsideration, this is clearly true. The grandparent deserves the downvotes.
I’ve never found that to be true. It’s an absence of evidence issue—if the best you can do is explain a faulty version of your opponent’s argument, maybe you can’t actually explain the real argument. Thus, there’s no reason to trust the accuracy of your explanation.
Hmm, that’s something I hadn’t considered. Yes, maybe the real factor was that I wasn’t explaining the real arguments as well, even after multiple attempts (which is probably because I don’t understand them well, if true, because the lack of this common cause would imply statistical weirdness and that I should expect my next attempt at explanation to go remarkably well, right?).
These figures seem implausibly high if we are comparing to the best donations you can pick out. Trivially, the campaigns spend only a few billion dollars, with $700 billion you could use the interest alone to spend ludicrously on voter turnout and advertising in every election, state, local, and national going forward, for an expected impact greater than winning one election.
That is to say, voting yourself can’t be be worth more than $n if you can generate more than one vote with political spending of $n. And randomized trials find voter-turnout costs per voter in the hundreds of dollars. Even adjusting those estimates upward for various complications, there’s just no way that you wouldn’t be able to turn out or persuade one more vote for $56,000.
It’s just trivial that if voting is rational, political spending is even more rational. It’s not germane to use political contributions in proxy for charitable contributions.
“It’s just trivial that if voting is rational, political spending is even more rational.”
I clearly explained why this is wrong directly above. If your opportunity cost of time is $50 per hour, voting would take an hour, and it would cost you $400 to elicit a marginal vote of equal expected impact, then you are getting an eightfold multiplier on effort spent voting as opposed to earning money to influence other votes. You need to spend one hour instead of eight hours worth of effort to get the same result.
If your opportunity cost of time is lower, or the impact of money on elections is lower, the effect gets more extreme. If your breakeven point is anywhere in that range then voting can make sense for you even while political donation does not.
This seems to actually underestimate the value of voting, in that it assumes that a vote is only significant if it flips the winner of the election. But as Eliezer wrote:
Also, rationalists are supposed to win. If we end up doing a fancy expected utility calculation and then neglect voting, all the while supposedly irrational voters ignore all of that and vote for their favored candidates and get them elected while ours lose… then that’s, well, losing.
I recently heard an argument to the contrary: Viewing voter preferences along one dimension for simplicity, if a small percentage on the left breaks away and votes for an extreme-left candidate, the mainstream left candidate may actually move further to the right—since the majority of undecided voters are in the middle, not along the boundary between left and extreme-left.
This may not generalize to a hyperplane separating a particular non-mainstream candidate from other candidates in n-dimensional policy-space, but I don’t know if presidential campaigns are set up to do that level of analysis.
You were right when you described “along one dimension” as being simplistic. There are other options than extreme-left, left, centrist, right, and extreme-right (for instance). Engaging in false dilemma reasoning as an excuse to vote for a mainstream candidate with no interest in sending political messages encouraging reform is not particularly rational.
One might argue that you could send a better message by writing about an issue for 1 hr rather than waiting 1 hr in line at the polls.
Laptops! Do both.
If irrational voters are the supermajority, and elect their candidate, then you lose, yes. If you waste your time voting for someone rational who can’t win, you lose more.
Rational voters never being large enough of a block to influence the outcome of any election seems quite unlikely, especially so if we don’t require the rationalists’ favored candidates to necessarily win. I don’t know about the US, but at least in Finland, even a candidate who doesn’t get elected but does get a considerable amount of votes will still have more influence within his party (and with the actual elected candidates) than somebody who got close to no votes.
My claim isn’t that this can never be the case but that it’s not the case now, and in general it’s the most important factor in whether a rational voter can win by voting.
Don’t forget to take the long game into account.
? The long game makes voting when you can’t make a decent impact even less rational compared to anything else you could be doing that would give you long term gains. Making money you can invest, taking time to learn a skill or network, getting more information on almost anything, convincing people to follow your beliefs or teaching others about information, donating to x-risk or other charities, working on inventing. Each of these are “long game” activities.
Of course almost no one spends all their time doing this sort of thing, and I don’t care if you take 20 minutes out of one day to go vote because it gives you fuzzies. But don’t pretend it’s a great thing you do.
I won’t pretend it’s a great thing to vote if you promise you’ll stop pretending I pretended any such thing, or that I was talking about anything other than comparisons of voting strategies.
The US suffers from a major problem with institutionalizing false dilemmas in politics. Playing the long game as a voter might well involve actions intended to lead to eventual disillusionment in that regard. Whether your time is better spent, in the long run, doing something other than voting (and learning about your voting options) is a somewhat distinct matter.
In short, you suggested that at this time rational voters cannot win by voting, which I took to mean you meant they could not get a winning result in the election in which they vote right now. My response was meant to convey the idea that there are voting strategies which could lead to a win several elections down the line (as part of a larger strategy). You then replied, for some reason, by suggesting that voting is not as useful in general as inventing something—which may be true without in any way contradicting my point.
It’s ridiculous to condemn me for trying to interpret actual meaning out of your vague one sentence reply and then respond with 2 paragraphs of what you “meant to convey”, none of which was any more obviously implied than what I read into your comment.
To respond to THIS point: So what? Each vote is a distinct event. It can easily make sense that you can influence elections positively in the future without you having that ability in any relevant way today.
I fail to see how not knowing what someone meant somehow compels you to make up elaborate fantasies about what the person meant, or even excuses it.
. . . and of course nobody ever does anything other than actually cast a vote when strategizing for the future. There’s no way anyone could possibly, say, make the voting part of a grander strategy.
. . . and I suppose you probably think that I think voting is a winning strategy in some way, basically because I pointed out some possible strategies that might seem like a good idea to someone, somewhere, as part of an attempt to remind you that the one-vote-right-now tactic may not be the only reason someone casts a vote.
In short, you assume far too much, then blame me. Good job. That’s certainly rational.
But that point can still be subject to the same (invalid, IMHO) argument against voting: your vote alone is not going to change the poll’s percentages by any noticeable extent, hence you could as well not vote and nobody will notice the difference.
I’ll explain why I think this line of argument is invalid in another comment. EDIT: here
That’s actually a better point, but it opens a can of worms: ideally, istrumentally rational agents should always win (or maximize their chance of winning, if uncertainty is involved), but does a consistent form of rationality that allows that actually exist?
Consider two pairs of players playing a standard one-shot prisoner’s dilemma, where the players are not allowed to credibly commit or communicate in any way.
In one case the players are both CooperateBots: they always cooperate because they think that God will punish them if they defect, or they feel a sense of tribal loyalty towards each other, or whatever else. These players win.
In the other case, the players are both utility maximizing rational agents. What outcome do they obtain?
By having two agents play the same game against different opposition, you compare two scenarios that may seem similar on the surface but are fundamentally different. Obviously, making sure your opponent cooperates is not part of PD, so you can’t call this winning. And as soon as you delve into the depths of meta-PD, where players can influence other players’ decisions beforehand and/or hand out additional punishment afterwards, like for example in most real life situations, the rational agents will devise methods by which mutual cooperation can be assured much better than by loyalty or altruism or whatever. Anyone moderately rational will cooperate if the PD matrix is “cooperate and get [whatever] or defect and have all your winnings taken away by the player community and given to the other player”, and accordingly win against irrational players, while any non-playing rationalist would support such kind of convention; although, depending on how/why PD games happen in the first place, this may evolve into “cooperate and have all winnings taken away by the player community or defect and additionally get punished in an unpleasant way”.
By the way, the term CooperateBot only really makes sense when talking about iterated PD, where it refers to an agent always cooperating regardless of the results of any previous rounds.
Amount of money spent is a radically different thing from amount of good done. Even among charities effectiveness can differ by about 1000x. Government spending is likely to fall more in line with the least effective charities because it is biased by political motives. Most spending is not even in areas that are likely to be effective like global health, or rationality outreach. The money that is spent on global health is politically directed, going largely to local neighbours and sites of war and terrorism, not to those most in need.
As the most effective charities are likely 100-10000x more effective than government spending, the calculation should be adjusted down by 3-5 orders of magnitude. We’re looking at more like $0.01 - $15,000 as the equivalent impact.
GiveWell disagrees with the conclusions you suggest in drawing on that link, arguing that saving lives in rich countries is worth substantially more than saving lives in poor countries, since these contribute more to economic growth, scientific progress, donate to charity and pay taxes for foreign aid themselves, have a higher standard of living, and so forth. They think that this attenuates greatly the gap among charities. ETA: foreign aid still comes out ahead of most rich country charity in their view, because it is SO cheap as to offset the reduced impacts of saving a life there.
I would expect considerable differences in effectiveness among charities to remain. Even after these social and economic effects are taken into account, donating to charities that save lives in rich countries will either still be worth significantly less, per dollar donated, than saving lives in poor countries, or it will be worth significantly more. It would be surprising if the innate human tendency to favour the near and dear, which disregards causal information about how the economy and society operate, could produce results equal or very similar to those that a rational, impartial donor would want to produce.
Yes, there are differences, but the QALY numbers in the link will usually overestimate the differences in long-term QALYs between rich and poor country activities.
Hmm… The calculations work, but somehow it seems against our intuitions. Thinking about it, it seems that the problem is one of scope insensitivity. $100 billion, $700 billion, $7 trillion. They all feel more or less the same, which of course, is absolutely insane. When I look at the numbers, it just feels like “a lot”. Ultimately, what this post is saying is to simply shut up and multiply, which is a very good and and very relevant point.
Think of “billion” as being just the name of a unit, like an inch, or a light-year. You have 100, 700, or 7000 units. Do they still feel the same?
Yeah, of course, I understand about the problem of scope insensitivity and how to try to avoid it. My point was that before reading this article, I did not think of it like that, but rather just looked at that number and thought “a lot”. Reading this article made me understand that I was being scope insensitive, and that let me put everything into perspective, in a similar manner to the method you stated. The big problem with biases like this isn’t compensating for them once you identify them, but rather identifying them in the first place.
This was a post well worth making, particularly because of how much rhetorical support the superficial arguments against voting get
So… what you’re telling me here is that, in America, different people’s votes count for different amounts. If I have Tom, whose vote has a one-in-a-hundred-million chance of affecting the election; and John, who lives in a different state and whose vote has a one-in-three-million chance of affecting the election, then won’t the average politician completely ignore Tom’s state in order to concentrate more on influencing John’s vote?
This seems backwards.
It also implies that Tom’s state is going to end up with any messy industries that have to go somewhere, but that no voter wants in their back yard.
Yes, that does happen to some extent.
There are a number of factors influencing these decisions, but the main counterpoint to the idea of popular vote for President is to consider states to be relevant entities. The Federal government was originally conceived similarly to the EU government—an association of states. And some would say that France should have just as much say as Germany in how the EU is run, even if Germany has twice the population. Thus, the German voters in that scenario would each have half as much say as the French.
The way it actually pans out, the US House of Representatives roughly corresponds to equal representation by population, while the Senate has 2 senators per state regardless of population, and then the Electoral College has one Elector for each Representative and Senator, making it a compromise between the two approaches.
Okay, if the states are considered separate entities, then that doesn’t look too unfair. (Though I do think that that premise is no longer valid). Given the technological limits on long-distance communication that were present at the time that America was founded, it’s quite a sensible system—for that time. With modern technology, and considering what America has become in the meantime (more like one country than a collection of individual states), I don’t think that the system still remains as valid today.
Ideally, the Electors should then spend their votes in the same proportion as the voters: if 53% of voters vote for candidate A, then 53% of Electors (or as close as rounding errors will allow) should vote for candidate A. Having done a bit of research, though, I find that it does not appear to work that way—it seems that a state tends to spend all its electors on the candidate that got most of the vote, even if it’s only 53% of that vote. Fixing that would seem to me, naively, to result in a choice that more closely represents the choice of the American people in aggregate.
In principle, electors are able to vote for whoever they want. In practice, their behavior is governed by state law, which for about half of the states basically requires the electors to vote for whichever candidate won the majority of the vote.
Maine and Nebraska split their electors similarly to your suggestion.
One quirk of the electoral system means that states have strong incentives not to split their electors: a state that allows a split electoral slate will likely be swinging only a fraction of the electoral votes that a state with a unified slate would. The number of electoral votes a candidate is expected to get per unit campaign effort, therefore, is much lower in such a state. Since there’s an element of competition in the electoral system (states want attention to their citizens’ unique needs, and if possible promises to address them), it’s in their interests to avoid such a situation.
...so the actions of the Electors seem to be a 50-way Prisoner’s Dilemma, with a few strange little quirks.
Consider. The President, and the overall U.S. government, has a certain amount of attention (and budget) to give to each of the 50 states. In general, being politicians, we can assume that they will give the greatest consideration to those states which are most likely to affect the next election.
If all the states cooperate by splitting their Electors, then the President’s attention and budget will need to be split reasonably evenly; a few more votes in any single state could give him an additional Elector, and decide the next election.
However, any state can choose to defect, by putting all their Electors behind the majority candidate. Now the President will spend more budget on, and pay more attention to, that state, because if he loses votes there he could lose a lot of Electors. So it’s to the individual benefit of each state to defect. Since the President is paying more attention to the defecting states, however, the cooperating states get less attention.
But if they all defect in such a way, or even if a majority of them do, then the end result is that the voting within each state is only considered between the two leading parties; third- or lower candidates have no chance of getting Electors, and people may vote for one party entirely to keep the other party out. This feeds into the two-party swindle as well, which is bad for everyone. Another effect of everyone defecting is that, suddenly, the “swing states”, where the voting could go either way, become dramatically more important; for those states, the “everyone-defects” case is actually preferable (in terms of attention given) to the “everyone-cooperates” case, so they have even more cause to defect. (Note that the swing states still suffer from the two-party swindle).
Hmmmm. I don’t think America is going to be able to escape the two-party swindle until it gets rid of the electoral college—and I don’t think that’s going to happen, because the people who can get rid of it are in the position of gaining the greatest advantage from not getting rid of it.
Indeed, it seems we have a 50-way Prisoner’s Dilemma. May I interest you in a conditional public precommitment solution?
That would solve a lot of the problem, yes. If it gets the 50%-of-the-Electors that it needs, of course.
...
Come to think of it, that looks like a simple change that seems likely to have far-reaching beneficial effects on the future, at least in the medium term. Is there anything I (or anyone else reading the replies to this comment) could do to make it more likely that it would be more widely adopted?
And does the answer to the above question change when I add the data point that I am not American?
Well, everything I said in the grandparent would still apply if there were more than two major political parties in the US, or if electoral votes were tabulated in a different way (a ranked-preference voting system, say). There seems to be a loose consensus that first-past-the-post election schemes tend to lead to two-party systems, but I’d expect the presence of an electoral college to have a minor if any effect.
(The last time this was significant relative to the two-party system was probably the election of 1992, when Ross Perot swung just under 20% of the popular vote as an independent but carried no states.)
Thinking about it, I think that the main effect of the electoral college is to amplify the two-party-ism of the first-past-the-post voting system (by making it that a person with less than 50% of the votes can beat a person with more than 50% of the votes).
I also think that, from the outside, removing the electoral college looks like an easier fix than changing the first-past-the-post nature of the vote.
Yes, first-past-the-post is a strange system for implementing a national preference. But it functions to preserve the power of “swing” states—and states generally. And preserving the power of the states is the purpose behind a lot of the structure of the US Constitution—otherwise, two Senators per state regardless of state population makes very little sense.
Diminishing returns come into play. There’s only so much effort it’s worth putting into the most important state before the next most important becomes marginally equal.
That does look armchair-likely. Does it happen?
...true. One should probably expect thirty-three times as much effort going to John’s state as to Tom’s state.
I don’t know, I live on the wrong side of the Atlantic to have personal experience.
Yep, you read right, and yeah, it’s nuts.
Congressional elections work much differently than presidential elections. My vague impression is that nuts-and-bolts level concerns like what industries go in what state are handled by Congress, not the president.
No, actually, the federal government doesn’t do all that much to determine what industries go into which states. Mostly its private decision making. Businesses are generally free to locate their operations or management wherever they want to. Of course, some businesses, like gambling, are illegal in some localities or they can get more favorable treatment in certain locations rather than others, but typically the federal government doesn’t make those decisions.
Yep, I was being facetious.
While that’s true in most cases, federal contracts can make a pretty big difference in some industries, particularly those connected with infrastructure or defense. (All those highway projects with signs saying “Funded by the American Recovery and Reinvestment Act” form a recent and salient example.) This is a semi-adversarial process, since allocation of contracts is zero-sum and Congresscritters have incentives to funnel them to their own states or districts; “should” isn’t the only concern and may not even be a primary one.
On the other hand, these incentives are tied more to regions than to parties, so choice of candidate isn’t likely to make a big difference in how they’re executed.
Scott Aaronson and Peter Norvig make similar arguments.
Contrast with my analysis of the “voting” phenomenon.
Let X = the amount of money such that you are indifferent between being given X and getting to choose who wins the election.
Let P = the probability your vote would decide the election.
XP = the rough expected value of voting.
Say we need XP>$10 to make it worth voting. If P = 1/20M then you need X>$200M, which seems way too big.
Of course risk aversion would complicate this.
If you had a choice between getting large amount of money and personally deciding the election, what would you do?
I would prefer to get the $200 million since I think using this money to fight existential risk would more than offset the 70% or so (as of now) chance that my preferred candidate will lose the election.
So, your preferred candidate (EY?) would be expected to provide less than about $285M delta to fight existential risk?
I was stepping somewhat outside the box set by the previous box- for me, X is greater than the amount of wealth on the planet, but P is so small for a non-mainstream candidate that XP is negligible.
I don’t believe you. Compare your level of happiness/sadness over the election results to how you would feel if Bill Gates decided to give you $30 billion to spend however you see fit. Given that the House and Senate are controlled by different political parties (so each party has the ability to block any new law from going into effect) the election wasn’t as important as you are making it out to be.
Contrast “Being able to select one of two candidates” with “Being able to select from all people meeting constitutional requirements.”
$30B isn’t nearly enough to enact reform in the military (something the CiC can do without Congressional approval), nor in the rest of the executive branch alphabet soup. Decisions regarding what laws to focus on enforcing are nearly as effective as decisions to repeal laws. The tricky part would be implementing reform in such a manner as to outlive the single expected term of office.
I agree that I would rather have a large sum of money than personally deciding the election. An interesting question would be how much money would it take? There’s also the bias that I would take a small sum of money because it would benefit me. Perhaps a better way of framing this would be a choice between an effective charity or a random LW getting a sum of money or personally deciding the election.
If one Virginia voter does an expected 1/(3.5 million)*($7 trillion) = $2 million good by voting for candidate X, then there is another Virginia voter that does an expected $2 million of damage by voting for candidate Y. It seems that either
Roughly half of the population is misinformed about which alternative is objectively better. In that case, how do I justify a belief that I have a greater than 50% chance of being right, when everyone else has access to the same information?
There are real differences in values, and by my vote I direct the outcome towards my preference instead of the other Virginia voter’s. In that case, sure I want to vote, but should we really call it altruism?
Non-meta calculations, like usual. If someone else thinks the indefinite integral of x^2 is 3x^3, I don’t say “well, if we have the same information, I must have a 50% chance of being wrong.” Instead, I check the result using boring, ordinary math, and go “nope, looks like it’s x^3 / 3.”
Yes.
I agree with your approach to solving disagreements about integrals. I do not see how it applies to politics, where disagreements are far more diverse, including factual, moral, and unconscious conflicts.
Well, people do differ in values, but it seems like more often some people are just wrong. Viz: global warming as a factual disagreement.
So what do you do if half the population disagrees with you about a factual issue? (Copy and paste time!) I don’t say ‘well, if we have the same information, I must have a 50% chance of being wrong.’ Instead, I check the result using boring, ordinary scholarship, and go ‘nope, looks like there’s a mechanism for CO2 to cause the atmosphere to warm up.’
Note that a key part of this process is that if you’re wrong, you should notice sometimes—there’s no “checking” otherwise, just pretend-checking. So that’s a good skill to work on.
That some people are “just wrong” is not at issue. Even mistaken people agree that some people are wrong. (They just think it’s the right-thinking folks who are in error.)
Of course you don’t. If half the population disagrees with you about an issue, you should interpret that as evidence that you are incorrect. How strong the evidence is, depends on how likely they are to possess information you don’t, to be misled by things you’ve prepared yourself for, etc.
Agreed. I guess what makes checking the math work in the integral case is just that the better you are at checking the arguments, the less you have to worry about what other people think.
In other words, people who are convinced by this argument are more likely than the average person to be correct about the objectively better candidate it convinces them to vote for?
How are you measuring ‘objectively better’?
Roughly half the population is paperclip maximizers.
That situation is alternative 2.
Well, you can replace “which alternative is objectively better” with any other belief on which opinions differ and the same argument applies.
“any other belief”
This invites us to look at why beliefs differ. First we have to acknowledge that we are talking about differences between people with comparable levels of expertise, so this isn’t the same as the disagreements that exist between experts and novices.
For elections, I think we can say that people disagree in large part because the situation is incredibly complicated. It it hard to know how government policies will affect human welfare, and it is hard to know how elected officials will shape government policy.
The only interesting factor that I can think of is differences in our scope of altruism—one voter may feel altruistic towards their city, while another focuses on the nation, and a third focuses on all of humanity.
“First we have to acknowledge that we are talking about differences between people with comparable levels of expertise”
The assertion that the vast majority of voters have done a sizeable amount of research, rather than simply voting “along party lines” or “like mom always did” or “because dad was overcontrolling and I’m not going to support HIS party” strikes me as the sort of assertion that would require quite a lot of evidence.
One can reasonably conclude that in politics, as with math, the “average person” is ignorant and their opinion is not based on any sort of expertise.
“One can reasonably conclude that in politics, as with math, the “average person” is ignorant and their opinion is not based on any sort of expertise.”
Even if you limit the population to those who are well informed, that population is still rather evenly split and so his points still hold.
On some issues, probably. On others, you have the well-informed, educated, cares-about-facts types versus the religious fanatics who want to push their religious agenda, or their personal agenda, or support pork-barrel funding of pet projects, or want to waste extravagant amounts on feel-good charity that accomplishes nothing in the end.
I don’t think either political party in the US has a monopoly on educated—it’s easier for me to demonize and strawman Republicans since I was raised Democratic. Apologies if my examples thus seem biased in that direction.
So, yes, sometimes, it’s clear my opponent has a genuine, reasoned stance. Sometimes, it’s equally clear that they don’t. It’s important to be aware that sometimes the opposing side doesn’t have any rational objections because they’re wrong.
“Voting is irrational unless you are arrogant?”
You can still call it altruism, and it can be helpful to distinguish “selfishness” in the sense usually considered for decision problems from “altruism”. The example I like to propose for illustration is the Codependent Prisoner’s Dillema, which has Romeo and Juliet as the prisoners who are each obsessed with the other’s wellbeing and the jailers use this fact when manipulating them. So when Romeo is “selfishly maximising his own preferences” and picking the option that puts him away for 10 years but lets Juliet go free he is also being “altruistic” towards Juliet while brutally ignoring her preference that she be the one who gets to be the martyr.
The whole point of democracy is the results should equal the will of the people. If a significant percentage of the population doesn’t get involved, the results can be skewed and show the preferences of the people who voted instead of the whole population. My understanding of this post is that with more people voting, this is less likely to happen. The right decision for you may not be the right decision for everyone else, and the point of voting is to figure out the majority of the country’s preferences.
My issue with elections is how many people make decisions almost solely on campaign ads, with little to no actual research on candidate’s actual positions and how it will effect them. If people behaved more intelligently instead of voting based on attack ads, I wouldn’t have to sit through half an hour worth of them trying to watch a football game.
“In any case, 55% is pretty conservative; it means I consider myself to have almost no information.” I’m wondering what evidence there is for a probability above 50. That’s what I would consider “conservative”. It’s not literally “no information”, it’s “no more information than the median voter”. That’s what it would mean for your vote to affect the outcome in a positive manner. Conditional on your vote affecting the outcome, there must be as many people (in your area) for one candidate as the other. The more lopsided the outcome, the more plausible it is that a random voter (such as yourself) is making a “correct” decision in light of philosophical majoritarianism. The more divided it is the less it seems likely.
Steve Randy Waldmann has an interesting argument for voting, going from a tribalist to greater-good scenario.
The probabilities of deciding the election by state given in that paper are for 1992. If we assume that on average, a vote has a 1 in 10 million chance of deciding the election, and that 538 accurately forecasts the probabilities of each state being decisive, then a vote in California has a (1/10^7)*9*(<1/10^3) = less than 1 in 1 billion chance of deciding the election (since about 1⁄9 of voters live in California, and California has a less than 0.1% chance of casting the decisive electoral votes).
Only if the propositions “your vote is decisive for California” and “the outcome in California is decisive for the election” are independent. They aren’t.
Consider a possible world in which a Californian’s vote is decisive. That’s one in which California splits almost exactly 50:50, which means that either something very unusual has happened in California or else something very unusual has happened in the country as a whole.
Then the outcome in California decides the whole election if the overall results outside California are close enough. In the “something very unusual in the country as a whole” case, they probably won’t be. In the “something very unusual in California” case, though, they might well be. At present 538 is predicting an Obama win by about 80 EVs, or about 25 without California. It doesn’t have to be far wrong for a hypothetically-upset California to become decisive.
(Actually, of course, those “something very unusual in …” options are just two ends of a continuum. The point is that there’s a non-negligible region of that continuum in which, conditional on your vote being decisive in California, California is quite likely to be decisive overall.)
If my understanding of how 538 defines the decisive state is correct, then “probability of a single vote anywhere deciding the election” is the same as “probability of a single vote in California deciding the election conditional on California being the decisive state”. It’s possible that he does not [Edit: he doesn’t] conditionalize on close electoral college outcomes when giving the probability that each state is decisive, and that this would cause those 2 probabilities to be a little different, but probably not by very much. If we assume that they will be within a factor of 3 of each other, which seems reasonable, then the probability of a vote in California being decisive is still less than 1 in 300 million.
Why? (In any case, that might be true with 538′s model but not with that of Gelman et al. It wouldn’t be that surprising to find that combining bits of one model with bits of another leads to wrong conclusions.)
Gelman et al got a range of Pr(your vote is decisive), with a figure of about 1 in 100M for the “worst” state. Perhaps indeed the least-evenly-poised states now are more unbalanced than then.
By the way: It’s not clear to me what point you’re making. “Things have changed since the paper by Gelman et al, and voting is less reasonable now for Californians than it was then for anyone”? “Gelman et al must be wrong because their figures are inconsistent with 538′s”? “538 must be wrong because their figures are inconsistent with those of Gelman et al”? Or what? The first of those might be right, though I haven’t yet fully grasped your reasoning. The second and third don’t seem like reasonable conclusions; at most you could say “The two models can’t both be right in every detail” which is surely true and not very surprising.
Gelman et al didn’t have a definition of “the decisive state”. The only thing I got from the Gelman et al model is that the a priori probability of a randomly selected vote being decisive is 1 in 10 million. I don’t see any opportunity for error due to differences between the models there.
Gelman et al may have been right about the 1992 election (although I am a little suspicious about the fact that the spread between states is so narrow), but I am suggesting that Academian was wrong to use their results in the context of the 2012 election. So yes, the first of those 3 points that you suggested is what I mean.
Intuitively, Gelman et al say that a vote in California is more likely to swing the whole election than a randomly selected vote. This may have been true in 1992, but it can’t possibly be true now, as shown by the fact that neither campaign has made a serious effort to increase their vote totals in California, and no one considers it a swing state.
Gelman et al do have a definition of decisive state (though not exactly of “the decisive state):
This isn’t quite the same as the 538 definition, which applies even when a state is not tied .
Gelman et al only got to the conclusion that the probability of a random vote being decisive is about 10^-7 by having a model of how different states’ votes relate to one another. They give a not-terribly-complete description of their model: each state’s vote is a linear function of a bunch of predictors, plus a per-state error, a per-region error, and a national error. This isn’t a million miles away from the 538 model, but it certainly isn’t identical. So the relationship between (e.g.) the probability of California being decisive, and the probability of California being evenly split, might be quite different in the Gelman et al and 538 models.
In Gelman et al’s model (see Figure 3 in their paper), states less likely to be tied are more likely to be decisive if tied. (Because the states that are less likely to be tied are the larger ones, with more electoral votes.) Roughly, these factors cancel out, which is why they don’t see huge variations in Pr(your vote matters) according to state. Accordingly, they have California as very unlikely to be tied, and really quite likely to be decisive if tied. I repeat: this is not at all the same as saying that it’s at all likely actually to be decisive.
The following toy example may help. There are exactly three states. One is solidly Red and has 2EV, one is solidly Blue and has 2EV, one is a slightly bluish Purple and has 1EV. The three states’ political fluctuations are completely independent of one another. Then: (1) Almost always, Purple is the decisive / swingiest / tipping-point state. 538 would give Red and Blue only a tiny chance of playing that role. But (2) conditional on Blue being tied, Blue will almost certainly be decisive.
So maybe the probabilities of being tied are 0.1% each for R and B, and 0.2% for Purple (yes, these are terribly small states), and Pr(Blue decisive) is also 0.1%, but Pr(Blue decisive | Blue tied) might be 90%. Then Gelman et al would say that Pr(your vote matters) is negligible in R, 0.09% in B, and 0.2% in P, and summarize that by saying “in most states, your vote has on the order of 0.1% chance of mattering”. And then you’d come along and look at the FiveThirtyEight numbers—excuse me, I mean the Five numbers—and say: “Aha, so since I’m in Blue which has 2⁄5 of the population and a 0.1% chance of being decisive, clearly the chance that my vote matters is about 0.1% 5⁄2 0.1%, which is far far less than Gelman et al said. Things must have changed.” But things haven’t changed; these hypothetical numbers are all for a single election; it’s just that you simply can’t legitimately combine the Gelman et al and FiveThirtyEight numbers in the way you’re trying to. The numbers don’t work that way.
True, that number may have changed somewhat. It may have decreased somewhat due to the voting population being larger, or increased somewhat due to the election being projected to be somewhat closer than 1992 turned out to be. But I’d expect the probability to mainly just shift between states. So 10^-7 made a pretty good baseline.
Since you press the issue, I looked up how exactly Nate Silver defines the probabilities of being decisive that he uses on 538. He says:
So you’re right; the probability of a state being decisive is not quite the same as the probability conditional on it being tied. [Edit: actually they are not even close to the same. And they wouldn’t have been even if 538 defined tipping-point state differently.] But (probability of single vote in California being decisive) = (probability of CA being the decisive state) * (probability that CA is tied given CA is the decisive state) = (probability of CA being the decisive state) * (probability of a randomly selected vote being a vote that ties CA given CA is the decisive state) / (probability of a randomly selected vote being cast in CA).
The assumption that I made was that (probability of a random vote tying CA given that CA is the decisive state) is close to (probability of a random vote tying whatever the decisive state happens to be), which seems fairly reasonable. I did NOT assume that (probability that CA is tied given that CA is the decisive state) is close to (probability that CA is tied). ( [Edit: ignore this parenthetical comment] At least I think I didn’t, but I’m tired right now, so it is conceivable that I could have made an error on that front. If I did mess that up, then the actual probability of a vote in CA swinging the election should be greater than 1 in 1 billion, but still probably less than 1 in 100 million.)
That assumption is not even close to correct in US presidential elections. Not that that makes much of a difference (I think).
Almost certainly? I thought you said Red was solid and Purple was only slightly bluish, so there should be a significant chance that Red and Purple both vote red, and Blue’s surprise red vote is redundant.
Sounds like you are using the Gelman et al meaning of a state being decisive. Not what 538 calls being the tipping-point state, which is what I was using. That’s why you get garbage when you plug that into my formula.
So, first of all, there’s a factor of 2 error in there: your last equality says, in effect, Pr(CA tied | …) = Pr(a random vote ties CA | …, and that vote is in CA) but when CA is tied only half the votes there tie it.
I’m already late for work, so will look harder at the rest of what you’re saying later. (I find myself somewhat convinced both by my toy example and by the more-detailed argument you’re now making, but the two don’t seem consistent with one another. I expect I’m missing something.)
I know. That’s one reason why the example is a toy. But no part of your argument appeals to the correlations between states’ results, and the point of the toy example is to show that the calculation you’re doing produces completely wrong results in a toy example, so in the absence of anything in your argument that makes it apply to the real election and not to the toy example something’s got to be wrong with the argument.
Sorry, “slightly bluish” was meant to describe vote share rather than win probability. I’m assuming that P is a win for the Blue candidate about 90% of the time, which with simple-but-unrealistic models of voters will happen if it’s reasonably big and, say, 55% Blue.
I was intending to use the 538 meaning. Pr(Blue decisive) is small because in almost all elections the state that gets the winner that crucial third EV—the one whose EV is in the middle when you line them up in order—is Purple. What do you find wrong with this reasoning?
Nope. Half the votes prevent a Romney victory, and the other half prevent an Obama victory.
Your confusion is understandable, especially since I confused myself and started bullshitting you for a while before rederiving what I did in the first place. Sorry about that.
That’s right. Sorry, I shouldn’t have been stressing the high correlations between voting fluctuations in different states.
Ah, ok.
Numbers from your toy example: Pr(Blue tied) = 0.1% Pr(Blue decisive | Blue tied) = 90% Pr(Blue decisive) = 0.1% implications: Pr(Blue decisive and tied) = 0.09% Pr(Blue decisive and not tied) = 0.01% This is not plausible. Presumably Pr(Blue decisive and votes blue by 1 vote) is also roughly 0.09%, in which case Pr(Blue decisive and not tied) cannot possibly be less than that. Assuming Red never enters the picture, Blue is decisive whenever it ends up voting more reddish than Purple does. Given how often Blue ties, I would expect this to actually happen fairly frequently.
Apologies for the slow response; I’ve been unreasonably busy. Executive summary of what follows: Yup, you were right.
So I tried generating more realistic numbers with the general structure of my toy example, and my conclusion is: Oops, you’re right and my example is no good. Sorry. And I think I agree with your simple probability-pushing argument that 538′s probability for California being decisive isn’t consistent with the numbers from Gelman et al being applicable in the 2012 election.
So, it seems to me that there are (at least) the following possibilities. (1) Gelman et al had a good model, and it remains reasonably applicable now, and 538 had too low a probability of California being decisive. (2) Gelman et al had a good model, but the political landscape has changed, and now California is less likely to be decisive than their model said it was in 1992. (3) Gelman et al had a screwed-up model, and their probabilities weren’t right even in 1992.
I agree with you that #2 is the least likely of these, and I offer the following statistic which, if cited at the outset, might have saved us a good deal of argument :-). In 1998, California went Democratic by about 51:48. In 2012, California went Democratic by about 59:39.
I accordingly agree with you: Academian’s numbers for his own case, which used the Gelman et al figures for California, likely gave much too high an expected value for his vote in California.
I assume you meant #2 is most likely? And you’re right; I should have pointed that out initially (even though it was before the election, I could have used 2008 figures).
Yes, of course I meant most likely. Duh. I’ve edited my comment for the benefit of our thousands of future readers.
testing: blah
Forget 1 in 10 million. For my state (Texas), a simple binomial model suggests my chance of being the critical vote is about 1 in 10^51121. I did vote, but it wasn’t due to a instrumental pursuit of expected value. For me, it was an intrinsic value of civic participation and a feeling of connection with the political struggles of past generations. These things are part of my notion of the good life. If they’re not part of yours, that’s fine.
Are you sure? The simplest possible binomial model for Texas (which has 26 million people) gives a probability of 0.016% that exactly 13 million people will vote for each candidate, and therefore your vote will be critical. What exactly are you calculating?
Edit: I forgot to take into account the probability that Texas will matter to the election. But there are 2^49 < 10^15 equally likely outcomes for the other 49 states; if even one of them results in Texas being a pivotal state, then we only get a factor of 10^-15, which is still very far away from your estimate.
Edit: I guess you’re assuming that Texans have a roughly 55% chance of voting Republican, which does give roughly the probability in your comment (although at that point we can also take into account the number of people that voted in the last election, which brings the probability up to better than 10^-25000.) I guess that’s a reasonable thing to take into account; there are of course objections people could make, but I see where your math is coming from.
Edit: Here’s a fancier model. Let P be the probability that someone votes Republican in an election. We have a good estimate of what P was in previous elections; suppose the change in P is normally distributed. Then we find that with a 0.08% chance, P will be between 49.99% and 50.01%, at which point the correction factor from the 50% binomial distribution is negligible. Given that P is in this range, the chance your vote will be pivotal for Texas is better than 0.02%, so the overall probability is about 1 in 5 million. Of course, then there’s the probability that the Texas vote changes the election to take into account.
I expected Texas voter turnout for a Presidential election to be about 8,075,000. Assuming everyone votes either for Obama or Romney, averaging the polls gives a probability for each vote of about 0.415 for Obama and 0.595 for Romney. That story fits a binomial distribution, and my vote would be critical if the votes were split evenly.
binopdf(0.5*8075000,8075000,0.415) evaluated to approximately 10^-51120, and at that point I just upped the exponent one rather than trying to figure out the electoral college details.
A binomial distribution is far too narrow.
Now that the election season which inspired the writing of this article has passed, I feel less like dirty discussing it. Less like I’m doing politics and more like actually thinking.
First off I recommend reading these three articles by Eliezer and paying special attention to the last one:
The American System and Misleading Labels
The Two-Party Swindle
Stop Voting For Nincompoops
In response to the last article on the list (which I recommend) Robin Hanson responds:
Why indeed?
What if the person who I like best would make a terrible President?
I should surely rather vote for the person who I think will do the best job, even if I think he’s insensitive, often tactless, and smelly.
Did you read EY’s article or just RH’s comment?
My comment was addressed to RH’s abovequoted comment alone.
I’m not sure it would make that much difference whether Obama or Romney wins the election. See this. Where did you get the “$7 trillion” figure from?
Disregard opening post for at least a few days because of meta level concerns.
Could you clarify that a bit?
The timing of this posts and its counterpart makes suspect the processes that produced them. Motivated cognition.
I have posted on Gelman and similar reasoning in non-election periods.
That’s cool but you weren’t cited by the author of either articles so your work seems unlikely to have inspired the authors who published on November 5th (the day before the US presidential election).
Disregarding this post’s instructions because it told me to.
I actually understand the point you were making now (I think before the parent comment said “disregard this post” [as opposed to “parent” one] and I honestl thought you were just being silly. I think both this and your other curt thread would have better served to actually explain the gist of your concern.)
For those LW users who are well-informed on this topic: Which major candidate do you estimate will have a greater positive impact on humanity’s total utility if elected?
(Poll for the benefit of those US LWers who are less informed, to save them time if they want to freeload off thinking and research done by other users. I’m leaving out third party candidates because it seems likely that the optimal strategy for third-party supporters varies by state.)
[pollid:202]
To be completely honest, I don’t know enough about economics or life outside of the state I live in the United States to have any clue which candidate will affect the world for the better. I want to understand what it is I should do according to my values (not just regarding voting, but in general), but the world is such a big place that I can’t even begin to fathom how I would go about trying to figure this out. Does anyone have any advice about where to start, what resources to consult? I want to shut up and multiply, but I don’t even know what I’m multiplying!
For politics there is a lot going on, but one of the biggest of big picture items is macro-economic philosophy. If you get your macro right, you are most of the way there on issues like prosperity and job creation which are a big component of what matters to people’s daily lives.
-Look at what the big schools of macroeconomics have to say
-Pick some schools which have actual models (i.e. not just talk and rhetoric) that are capable of making at least directional predictions about changes in GPD /GPD growth, interest rates, inflation etc. in response to changes to various components of spending.
-Pull a representative model out of a text book or article that’s at least 8 years old to avoid something that’s just been fit to recent data
-Check the model with data from the St. Louis Fed and Euro Stat
-Do a Google search to see if other people have gotten similar or different results to you and to see if there are any known pitfalls in the data which might impact your results
-Repeat above 3 steps for each school of economics that seemed worth checking
More simply, you could just ask economists directly. But then they might tell you that the US President has very little impact on the economy.
The linked IGM poll is great though, it can also give you a good feel for which policies economists agree about, and their comments and links can give you some idea of their reasoning.
There are lots of LWers working on argument mapping software. I think that one day such software will actually be useful for answering questions like this.
Ah, I was hoping to see a pseudo-Pascal’s Mugging* argument constructed for voting. Now I can ask people who bring it up in response to any topic, ‘do you vote for consequentialist reasons?’
* I say pseudo because people go around claiming that any argument involving small probabilities of large benefits or harms is a “Pascal’s mugging” even though this is not what either Bostrom or Yudkowsky meant when they wrote on it; yet no one ever seems to realize this, which mystifies me a little—the LW post and PDF are both online, just a Google away!
Here’s a more germane objection: a single vote, in reality (as opposed to in “should universes”) never truly comes even close to deciding an election. When the votes are close to a tie, the courts step in, as in Bush v. Gore. There are recounts and challenges. The power of connections and influence by judicial politics completely overwhelms the effect of a single vote.
Don’t you think it perverse to derive the value of voting from the very high value of the outcome of an extraordinary event?
Take an electorate with 1,000,000,000 voters, deciding between A and B. If 550 million vote for A, and 450 million vote for B, then A is 90% likely to win. Conversely, if B leads 550 million to A’s 450 million, B is 90% likely to win. With very finely balanced vote totals both candidates have sizable chances at winning depending on the outcomes of recounts, etc (although the actual vote total in a recount certainly matters for the recount and challenge process!).
Say we make a graph, assigning a probability of victory for A for every A vote total between 450 million and 550 million. Over the whole range, there needs to be an 80% swing in win probability, on net. So, if we count every change in win probability as vote totals increase, the average change in win probability per vote for A has to be (80%)/(100 million) over this range.
So if the polls leave you with a roughly uniform distribution over vote totals between 450 and 550 million votes for A, then you should assign a probability of about 1 in 125 million to being decisive, despite recalls and court challenges and so on. This will reflect being the marginal vote that pushes a key vote total one way or the other, making a lead large enough that a judge or official doesn’t bother to do a recount, being the decisive vote in a recount, increasing the vote margin from 999 to 1000, a psychologically significant difference, and so forth.
In non-iterated PD, someone who cooperates is a cooperator.
No, the cooperators actually lose when playing each other, because they gain less than what they could, while the only reason they get anything at all is because they are playing against other cooperators. Likewise, the defectors win when playing other defectors, and they obviously win against cooperators. Cooperating could only win if it effected your opponent’s decision, which is not the case in PD.
It seems your definition of winning is flawed in that you want your agents to achieve results that are clearly outside their influence. Rationalists should win under the constraints of reality, not invent scenarios in which they have already won.
A couple of assumptions that you did not state. You assume that your favored candidate’s budget contains truly optimal uses of charitable dollars. You need a step down function unless your preferred charity is funding government programs.
You assume that the opposition candidate’s spending is valueless. Otherwise you need to consider the relative merits.
You assume that there is no portion of the opposition budget that is preferable. If you believe that each candidate has some portions right, you need to be subtracting this spending from the value of your contribution.
You assume that the proposed budget will be implemented. Given the track record of campaign promises, this is an iffy assumption. As this probability is necessarily less than 100% it should reduce the value of your contribution.
These assumptions are the mind killing biases of politics.
No, they don’t all have to be assumed. What needs to happen is something resembling their budget, on the order of plus or minus a few trillion dollars, is implemented.
ETA: However, even this is unlikely to be entirely affected by the outcome of the presidential election, as this depends mostly on Congress.
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The link is dead. Here’s the paper.
Note that the last name of the third author is Boscardin, not Boscodarin.
Thanks, fixed!
“You know, given human nature, if you lived in a country in which there was democracy, pretty soon someone would try to sound deep by inventing reasons that voting was a good thing. But if you lived in a universe in which democracy wasn’t the high-status mode of governance, and asked them if they wanted it, with all its attendant consequences, they would say no. It would never occur to them to invent all the clever rationalizations that someone resigned to democracy would devise.”
You know, it would be nice to say what specifically is wrong with the original post. Accusing someone of inappropriate rationalisation without a shred of supportive argument but using a fancy quote of the locally revered author, that’s what I call trying to sound deep without actually being deep.
“You know, given human nature, if you lived in a country in which there was Monarchy, pretty soon someone would try to sound deep by inventing reasons that hereditary rule was a good thing. But if you lived in a universe in which Kingship wasn’t the high-status mode of governance, and asked them if they wanted it, with all its attendant consequences, they would say no. It would never occur to them to invent all the clever rationalizations that someone resigned to monarchy would devise.”
Why wait until we live under a monarchy to start practicing for Ideological Turing Test tournaments? Let’s start now: According to the CIA World Factbook, the forms of government of the three countries with the greatest GDP per capita (PPP) are a hereditary constitutional monarchy, an emirate, and a constitutional monarchy. Wait a minute...that was a little too easy.
It would be a better argument if it didn’t rely on people not knowing what a constitutional monarchy is.
Good point. While the CIA is technically correct in referring to Luxembourg as a constitutional monarchy, it also has a large democratic component, making the description somewhat misleading.
patrissimo advises me that others have noticed Liechtenstein’s (relative) awesomeness.
Those who historically lived under monarchies relied more on the Divine Right of Kings, I believe.
Really? It was my understanding that the Divine Right of Kings was a recent (17th century) invention. Care to share you evidence?
Check out the relevant Wikipedia page, for starters. The Divine Right of Kings as a notion went back to medieval times, when rulers would only rule with the blessing of the Pope, though the theory so named was not spelled out until later.
Note that the Divine Right of Kings was refuted in 1689 by John Locke, and I’ve heard it said that he was kicking a dead horse.
I’m not very impressed with the Wikipedia article on the subject. It seems to conflate several different theories of civil authority that were historically used in opposition to each other. According to the Catholic Encyclopedia, The Divine Right of Kings asserts that:
If I’m not mistaken, The Mandate from Heaven and medieval divine right theories were generally thought to limit a kings power (by making it subject to revocation by religious authority), whereas The Divine Right of Kings (the Post-Reformation concept; note the capitalization) seeks to expand monarchical power. In any case, it would be wise not to update very strongly on my vague impressions from my university days (which are somewhat hazy and long before I started using spaced repetition software).
Well, Egyptian Pharaohs ruled by divine right, if nothing else. I was referring to the general idea that the monarch rules by divine permission.
However, as noted below, the theology and so on became more explicit around that time, according to Wikipedia.
This was my understanding as well; the Divine Right of Kings is a ‘recent’ thing and was for European kingdoms specifically.
The oldest example I can think of that is sort-of-related is the Mandate of Heaven, and it seems to me like various forms of divine ancestry were the most common things to rely on to assert monarchic authority.
The Mandate of Heaven was double-edged though, unlike the divine right of kings.. The peasantry was considered a force of nature, and a rebellion was thus a sign that heaven revoked the ruler’s mandate.
The on-topic point I attempted to make was that both were appropriate arguments of the form that would definitely pass an ideological turing test for “people who are rationalizing that their monarchy is the best thing ever”.
IIRC, the Mandate of Heaven did help quite a bit in getting imperial rulers to not be total assholes, though.
This seems both true and false. Plenty of apologia for monarchical governments exist, some of them quite famous). But there do seem to be some few latter-day monarchists glaring from beyond the edges of the Overton window. I’ve talked to a couple of them, and they’ve been quite clever in inventing rationalizations.
I imagine the same was true for republicanism when it was the low-status option.
Universal Counterargument Alert!
The point is that the modified quote can be modified to talk about almost anything, so it’s not actually a useful statement to make as to whether or not something is good or bad.
I think it’s better treated as a statement about human psychology than about any particular system. If most people support the system they’re embedded in for biased reasons, then their opinions about it are suspect and so’s the appeal to popularity that comes with their aggregate; however, none of that means they’re necessarily wrong.
Of course you’re technically correct. There are, and have been, terrible arguments for monarchy advanced in the past. But today, democracy is the high-status mode of governance, and so the terrible arguments generated by motivated cognition, such as this OP, are in favor of democracy, not monarchy.
Worrying about bad arguments for monarchy now is like someone worrying about bad arguments for evolution in a creationist school board meeting. Yes it could potentially be a problem, but this over-concern is hardly our biggest problem right now and is very likely itself generated by motivated cognition.
Um, historically that is precisely what happened in the 18th and 19th centuries.
Is this accurate? Isn’t it better to say they wanted representative governance while at first denouncing democracy as a horrid system (at least the US founding fathers did) but found themselves on a slippery slope.
Related to: Schelling fences on slippery slopes
Democracy (in the sense of electing your leaders) seems to be actually be a Schelling Point instead; it seems to occur independently across lots and lots of cultures. It doesn’t always last long as a democracy, sometimes devolving into tyranny/hereditary rule/whatever—but it nonetheless occurs frequently.
So I think you’re just wrong on this.
If you’re so concerned with helping other people, why not just abstain from voting, thereby increasing the effectiveness of the votes cast by those other people, and thus giving them more direct say about how they are governed?
I actually also think your estimate of 55% belief is overconfident, for any utility function that properly distinguishes between terminal and instrumental values (i.e. a utility function that takes into account aggregate health is proper, while one that specifically refers to people having health insurance would not be in my view).
A slight math error:
Here you left the 30% chance of being wrong from the previous example, but if you have a 90% chance of being right, you only have a 10% chance of being wrong. The actual expected dollar value is $1.6 million, which is actually a little better for your argument.
I rarely make decisions involving such low probabilities, so I don’t really know how to handle risk-aversion in these cases. If I’m making a choice based on a one-in-ten-million chance, I expect that even if I make many such choices in my life, I’ll never get the payoff. This is quite different than handling one-in-a-hundred chances, which are small but large enough that I can expect the law of large numbers to average things out in the long term. So even if I usually subscribe to a policy of maximizing expected utility, it could still make sense to depart from that policy on issues like voting.
BTW, in my state, Maryland, Obama has a 18-point margin in the polls. That could easily be six standard deviations away from the realm where I even have a chance of making a difference.
How small does the chance have to be before it isn’t a chance anymore?
Also, are you intending to research and vote only for the presidential election? Local offices have smaller budgets but also smaller margins...
“Less than one expected payoff per human lifetime” seems like a good threshold.
So… there is no chance that you will be married if/when you die. There is also no chance that you will be single if/when you die. (Assuming that you will only ‘die’ once). There are many things that happen one or fewer times per human lifetime; the expected chance of them happening is less than once per human lifetime.
Most people stop attempting to acquire additional spouses after they find a good one, so the actual rate of success isn’t reflective of the number of successes someone could statistically expect if they worked at it continuously for 100 years.
Many people marry more than once in their lifetime; I’m not sure what the average is offhand- but I didn’t reference marriages, I measured conditions at a specified point in lifespan.
Of course, this is LW; local notions of how long a human lifetime is differ by many orders of magnitude.
Zero?
Re: other stuff on ballot. Yes, that’s right. I was just replying to the content of the post.
Sorry, I don’t understand what was meant by your first sentence.
Is a .001% chance of making a difference still a chance of making a difference? Is a seven-sigma chance still a chance?
All of them are obviously still chances. I never said that a very small probability wasn’t a chance. I said that it might rationally be treated in a different manner than larger chances due to risk-aversion.
Not to mention that, if he lives in Maryland, he has at least seven ballot questions to answer on the poll.
Voting for electoral impact doesn’t make sense from a causal decision theory selfish point of view: you won’t consider a $1 trillion gain to the U.S. to be a billion times as great as $1,000 for you. This argument presumes that you have a “risk-neutral charity budget.”
If you’re loss averse, the expected value could easily be negative: cost(voting for wrong candidate) > benefit((voting for right candidate).
You reason, I think, that since most everyone has better knowledge of the identity of the better candidate than chance, Chance (to reconstruct the argument) is the relevant criterion because, for your vote to be decisive, the other voters would have shown themselves (as a whole) to be indifferent between the two outcomes—I find that a convenient way to put it. In the only circumstance where your vote “matters,” you can improve the group average if you can do better than 50%. And surely just about everybody thinks their political judgment superior to a coin flip!
But consider another thought experiment. Should a potential voter vote when he knows he is below average, simply because he can pick the better candidate better than chance? He should—only if the only point of voting is deciding a tie vote. But to the extent voting is for signaling the strength of factions rather than merely deciding binary outcomes, perhaps the below-average voter should abstain. There are a lot more compelling reasons not to vote than to worry about draws. Your analysis leaves them out.
As soon as you’re talking about communities, you’re talking about meta-PD, not PD, and as I’ve explained above, rationalist agents play meta-PD by making sure cooperation is desirable for the individuum as well, so they win. End of story.
Nitpick: Superrationality is not a decision theory.
Quick correction:
The beginning of this should be 90%-10%, which changes the projected value to $1.6 million, not $1.2 million.
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The FiveThirtyEight blog has a state-by-state return-on-investment index in the sidebar.
Extremely relevant.
The relevance is at best superficial as far as I can tell. Please don’t turn Holden’s point into a fully general counterargument against surprising expected utility calculations.
This is an expected utility calculation that involves a small probability of a large payoff with large margins of error. Here’s what I take as the essence of Holden’s post: “an estimate with little enough estimate error can almost be taken literally, while an estimate with large enough estimate error ends ought to be almost ignored.” I have very little confidence in both my and Academian’s estimate of which candidates winning will actually turn out to be better overall, and what the monetary value of each winning over their alternatives would actually be. Obama may seem to align with my values slightly more than Romney, but an office as powerful as the President of the US has many small, complex effects on many people’s quality of life, and we could all easily be wrong.
And let the other guy win? Madness!
Which, of course, should encourage all sane states to have compulsory voting for the same reason that paying taxes is compulsory rather than voluntary. (Or, rather, to make attendance at the polling booth compulsory such that a decision to abstain is permitted but not more convenient.)
That would reduce the average level of education, political knowledge, and intelligence in the electorate.Turnout rates by education in 2008:
Less than high school, 39.4%
High school, 54.9%
Some college to bachelor’s degree, 71.5%
Post-graduate education, 82.7%
http://elections.gmu.edu/CPS_2008.html
Is there data supporting the claim that these traits correlate with selecting “better” candidates?
Yes—see Caplan’s “Myth of the Rational Voter”, showing education predicted “votes like an economist”
“Has beliefs about economic policy like an economist” more.
What evidence is there that compulsory voting wouldn’t just add noise to the selection process? This seems like the obvious outcome to me.
There are about two dozen countries that use compulsory voting. Looking at the ten countries that actually enforce it we find that it in fact doesn’t just add noise to the selection process. We find that they in fact don’t have a selection process particularly dominated by noise.
If we look at actual compulsory votes, and find that practically nobody votes for some candidates while others get a lot of votes despite the addition of the reluctant voters then that which was added can’t have been just noise. In this example only 1.4% of all (primary) votes went to the “Family First” candidate. Even assuming zero of the voluntary voters voted for “Family First” somehow the additional “noise” still knew to favor the other three candidates and mostly avoid Family First. Additional votes made by constituents and which systematically favor one candidate far above another aren’t called “noise”, they are just called “votes”.
I happen to know Mortimer Q. Snodgrass, who lives at 128 Ordinary Ln. is well informed about politics and economics but chooses not to vote because he is personally better off staying at home to play catch with his son. Obliging him to vote introduces information into the process that is not noise.
By the above I mean to reject the framing whereby “it would just add noise” is set up as priveliged hypothesis that significant ‘evidence’ must be expended just to escape from.
If the new voters actually “just add noise” it would mean every single one of them had no preference or information about what they are voting on and all choose to vote using a noise source. Even if we weaken the hypothesis to “the amount of noisy votes added relative to signal votes would do more harm than good to the preference extraction process” it is still an overwhelmingly unlikely proposition.
The basic voting systems just aren’t especially vulnerable to noise, they are vulnerable to corrupted or biased input (some of which they cause themselves). If even 1 out of 20 of the new votes represents information about population preferences while the other 19 are ‘noise’ the system still ends up better informed. Noise just isn’t the potential downside here, the respective biases held by the people who would have voted vs those that wouldn’t and how much you endorse the groups and biases in question. It is at least plausible for someone to declare that the preferences of the demographic that would vote voluntarily are more important for some intrinsic or instrumental reason than the preferences of the demographic that must be compelled.
Thank you for the detailed response. Lots of interesting ideas that I’ll definitely read through in detail later on when I have more time.
I do think I meant something different by the term ‘noise’ than the way you read it but I’m not convinced it will matter in the end. You seem to be using noise to cover the case where voters make their decisions arbitrarily because they lack preferences. I was trying to make the point that the average forced voter might be little better than random at actually identifying the candidate that would lead to the greatest fulfillment of his preferences.
You are right that the difference doesn’t matter in the end and I would certainly extend my reply to cases where “little better than random” voters are classed as ‘noise’. Adding “little better than random” voters is (practically) no problem, adding worse than random voters would be a problem. The latter is actually a possibility worth considering as at least arguable for some demographics. As dbaupp said, there are considerations along those lines that go either way.
I note that even assuming the “average” additional voter is noise (and that the mean, median, mode and the ones denoting each border of the interquartile range are too) doesn’t result in a plausible “just add noise” picture. I go as far as to say that if one in twenty of the new voters have a clue and the rest are “little better than random” the voting system wins. For the additional voters en masse to “just add noise” it would require none (or close to none) of the new voters to make meaningful better-than-random votes. This is unlikely and in fact isn’t compatible with the historical data we have on how compulsory voting actually occurs in practice.
(This just affirms your observation that the differences in our positions aren’t merely the result of different usages of the term ‘noise’.)
Even if a poll of all eligible voters is more noisy or just worse than a poll of typical voters, compulsory voting changes the game from the point of view of the politicians. In the US, convincing people on your side to vote seems to be a lot more effective than convincing people to switch sides. Compulsory voting changes the relative value of the two strategies, perhaps making voter turnout irrelevant. I don’t know if such a change would be good or bad, but it sounds big to me. I also don’t know what campaigns in actually existing compulsory voting regimes look like.
What evidence is there that voluntary voting doesn’t just add noise to the selection process?
That’s a serious question: voluntary voting means that a higher percentage of the voters are in a blue-vs-green mindset (since they are more likely to vote than someone who has weak preferences), while compulsory voting gives a more accurate picture of the feelings of the entire population, even if that involves people who donkey-vote etc.
(That’s not to say your point isn’t valid, just that the sword cuts both ways.)
A protest that you aren’t using approval voting? This not only implies that your country using something worse than approval voting (for which you have my sympathy) but that you believe that if you managed to change your voting system to something better you would choose approval voting. If something is worth changing it is changing to something good.
http://www.panix.com/~tehom/essays/hay-extended.html
Thankyou, that’s well worth a read.
Wikipedia is not a determinative source.
Which answer is the “superrational” one in Newcomb’s problem? In a game of chicken? In an ultimatum game?
Decision theories like Causal Decision Theory and Evidential Decision theory have answers, and can explain why they reached those answers. As far as I am aware, there’s no equivalent formalization of “superrationality.” Until such a formalization exists, it is misleading in this type of discussion to call “superrationality” a decision theory.