I agree that this definition of “matters” is odd; not the one most people use in everyday speech. I think that there are ways to make other definitions rigorous (in ways that aren’t addressed in the wikipedia article I linked). But this is the narrowly consequentialist definition, so it does deserve analysis.
Jameson Quinn
Karma: 1,213
Nicely done.
In my experience, “Farmer’s Dilemma” (aka Chicken/Snowdrift) is both more common than PD, and harder for human players to coordinate away from pathological outcomes. I think it should be the prototypical “nasty” game instead of PD. We’ve all been assigned a group project at school; we have not all been interrogated by the police in a situation where the payoffs are truly PD.
I very much do not include superrationality in my assumptions. I’m not assuming that all other voters, or even any specific individual other voter, is explicitly using a meta-rational decision theory; I’m simply allowing the possibility that the “expected acausal impact” of my decision is greater than 0 other voters. There are, I believe, a number of ways this could be “true”.
In simpler terms: I think that my beliefs (and definitions) about whether (how many) other voters are “like” me are orders of magnitude different from yours, in a way that is probably not empirically resolvable. I understand that taking your point of view as a given would make my original question relatively trivial, but I hope you understand that it is still an interesting question from my point of view, and that exploring it in that sense might even lead to productive insights that generalize over to your point of view (even though we’d probably still disagree about voting).
If you like, I guess, we could discuss this in a hypothetical world with a substantial number of superrational voters. For you this would merely be a hypothetical, which I think would be interesting for its own sake. For me, this would be a hypothetical special case of acausal links between voters, links which I believe do exist though not in that specific form.
I think that the ideal community size (the regime at which positive network effects clearly dominate negative effects) is much larger for a wiki than for a forum like here. Thus, though I don’t have experience with RationalWiki, my prior would be to be skeptical of its value.
But there is an obvious acausal path in this case. If other voters are using the same algorithm you are to decide whether or not to vote, or a “sufficiently similar” one (in some sense that would have to be fleshed out), then that inflates the probability that “your” decision of whether or not to vote is pivotal, because “you” are effectively multiple voters.
Is that sufficient, or do you need actual numbers? (I’d guess it is and you don’t.)
[Question] (answered: yes) Has anyone written up a consideration of Downs’s “Paradox of Voting” from the perspective of MIRI-ish decision theories (UDT, FDT, or even just EDT)?
Thanks, fixed. (A numerator of 1 gives an answer in dimensionless units of “fraction of voters”; using V gives units of voters. I tend to prefer the former but I agree that at first read the latter is more intuitive.)
Fleshing out “allocating responsibility” and beginning “Pascal’s other wager”.
What about trolls? What about pile-ons?
Trolls: some people are not upset by negative feedback or even actively seek it. I think this could be structured such that this negative feedback would not be rewarding to such people, but it merits consideration, because backfire is at least in principle possible.
Pile-ons: There are documented cases of organized downvote brigades on various platforms, who effectively suppress speech simply because they disagree with it. Now, I wouldn’t object to a brigade of mathematicians on a proof wiki downvoting and pages they disagreed with and thereby censoring the pages or driving away their authors; but in most other cases, I think such brigades would be a problem. Again, you might be able to design a version that successfully discouraged such brigades (for instance: have “number of downvotes”, “correlation with average downvoter”, and “correlation with most-similar downvoter” all visible in someone’s profile?), but it merits thought.
Began the “allocating responsibility” section.
I’ve switched over to responding to your comments/suggestions one-by-one.
On your point 1, regarding loss functions: I agree that a strictly utilitarian/consequentialist PoV would care about which side won, not about vote totals. I think there are three reasons to nevertheless build a loss function around vote totals.
1. Mathematically more well-behaved. For instance, the whole “MSE decomposition” idea I bring in later would be much much messier with a binary-outcome-based loss function.
2. I believe that in practice, if there’s a question where the target support would be, say, 70%, but the legislature supports it at 90%, you can probably use it to construct some other at-least-somewhat-reasonable question where the target support would be 40% but the legislature supports it at 60%. That is, in practice, errors in vote totals go hand-in-hand with errors in outcomes, even if this is not a logical necessity (at least, not without additional assumptions about convex lotteries and stuff).
3. Some of the votes/decisions of the legislature may be made in a non-majority-rules fashion. For instance, you could have some situations where each legislator gets to allocate a share of some resource. In such cases, the vote-total-based loss function is clearly correct even from a consequentialist standpoint. (This might be seen as a special case of 2, but it’s different enough to list separately.)
I think that saying 1 and 2 in the main article would be too much of a digression, but I will think further about whether there’s a way to include point 3.
When you train on old data, you get a lag of about 10-12 days between changes in cases and corresponding changes in deaths. There are several reasons that could be not true on new data:
1. Cases are getting caught earlier by more/faster testing.
2. Cases are leading to fewer or slower deaths (due to either treatment or population effects)
3. The lag on old data is using the reported date of death, but that’s not the same as the date of the reporting of the death, which has an additional lag.
Are you saying it’s (at least partly) #3?
This may not be the right place for this. But gotta say it somewhere.
Overall, I like this font. But I hate hate HATE that it makes it impossible to distinguish “1” (one) from “I” (capital-i), except in the amount of horizontal space they take up. The numeral one should have a hook at the top, even in a sans-serif font. This is really important if you’re going to be having mathematical discussions. (Of course, “l” (lower-case L) is also indistinguishable here. But letters are either clear from context or, if used as variable names, a choice. So two indistinguishable letters is no big deal; a numeral and a letter is a PROBLEM.)
I meant “𝓮” to be the number whose natural logarithm is 1 — “𝓮” is the closest to the math version of the character that I can type on my keyboard as-is. I don’t have any argument for why it should be precisely that value, it’s just the most famous number in between 2.5 and 3, which is roughly where I think the correct value will lie. I am aware of the larger literature on people’s political preferences, but that’s all from a world that’s already conditioned by more-or-less non-ideal voting methods, so I don’t think this is a question with an easy-to-find empirical answer like that. I may expand the section you reference to talk about these issues a bit more, and to discuss the available data/literature, but when I first wrote it, I was hurrying through to get somewhere else.
Thanks for the close read and the thoughtful comments!
Open:
1. Loss function, future-oriented: interesting questions; I have thoughts on them; I left them out the first time through but may add them later.
2. gerrymandering; “infinite”; proposal I don’t fully grasp: Also interesting but I think beside the points I want to make here.
3. Dimensions.
“The choice of dimensions seems like a bigger deal than the number.” I’m implicitly assuming that they’re chosen by principal component analysis or something similar. Of course that’s not robust to scaling or other monotone transforms, but I think it’s close enough to being well-defined to handwave away for my purposes.
But if I’m wrong, and the variation in political opinions/interests that are politically salient in an ideal world is much higher, then the very “republican idea” of representative democracy is problematic.
“whether things interact with each other to greatly affect outcomes”: good point. I’ll see if I can incorporate it without being too wordy.
4. Weighted legislatures: yes, that’s a whole topic I could write an entire section on. For now, can’t afford to get that sidetracked, sorry.
“Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.”
Um. It’s possible I’m not being clear what I mean by “variance”. I don’t mean variance of ideologies of legislators; I mean variance (meta-variance?) of distributions. That is to say, a 1-dimensional procedure for picking 2 legislators would have higher variance if it sometimes picked {5,5} and sometimes picked {4,6}, than if it reliably picked {0,10}.
I think there may something to your critique here aside from that possible misunderstanding, though. I have some thoughts but I’m not sure how I should or will deal with this issue. Probably, I should respond to that in a separate comment.
5.
“Weird methods:” Maybe I should explain how my existing proposal for rating voting methods would handle that? Because I have thought about it, and it is a tricky case. But I think I’ll save that for later; for now, I want to stick with simpler cases.
...
to be continued; probably in a separate comment or comments, for better notification.
A bit of polishing of existing parts; skeleton headings for remainder
How can we add alt-text, so that our articles with images are accessible to visually-impaired readers?
What about captions?
That link is broken, and I’m very interested to read this. Is there a newer link?
ETA: I think I found it: https://arxiv.org/abs/1810.10862
I’m having difficulty with this in a way that “smells” like either “too much jargon” or “not enough effort expended explaining terms at start”. That is, I (recent PhD in statistics) can more-or-less parse individual statements, but unable to chunk things into parts that are large enough to seem non-trivial. Note that I’m coming here from the “deep double-descent” article which does seem intuitive for me at first read (that is, definitely interesting, but closer to being too trivial than too complex).
I’ll come back and read this again later, but for now: if you’re editing this, I’d suggest starting slower and/or working to de-jargonify.
Wait, what?
“You play the game with many other CDT agents” — this seems demonstrably false, at least, if we accept the Paradox of Voting as being a thing, in which case, CDT agents have by assumption removed themselves from the game. (I understand your response that voting may be altruistically-CDT-rational; as you know, it’s been discussed before, and very rightly so. But I also think it’s still worth considering the boundedly-altruistic/diagonally-dominant case.)
It seems to me that the only way you can claim there’s “many other CDT agents” is if “CDT” is being used as a catch-all for “not explicitly FDT/UDT”, and I’d strongly dispute that usage. I think that memetically/genetically evolved heuristics are likely to differ systematically from CDT. It may be best to create an entirely separate model for people operating under such heuristics, but if you want to force them into a pure CDT-vs-UDT-vs-random-noise (ie, mixture distribution) paradigm, I’d say they would be substantially more than 0% UDT.
ETA: I guess I can parse “other voters are CDT” as a sensible assumption if you’re explicitly doing repeated-game analysis, but such an analysis would pretty much dissolve both the Paradox of Voting and the CDT vs. acausal-DTs distinction.