Consider .
Optimization Process
Karma: 574
The Anthropic Principle: Five Short Examples
Speculative Evopsych, Ep. 1
(Strong approval for this post. Figuring out how to deal with filtered evidence is close to my heart.)
Suppose that the facts relevant to making optimal decisions about an Issue are represented by nine rolls of the Reality die, and that the quality (utility) of Society’s decision is proportional to the (base-two logarithm) entropy of the distribution of what facts get heard and discussed.
Sorry—what distribution are we measuring the entropy of? When I hear “entropy of a distribution,” I think -- but it’s not clear to me how to get from there to , , and .
Ahhh! Yes, that helps a great deal. Thank you!
Some wagers have the problem that their outcome correlates with the value of what’s promised. For example, “I bet $90 against your $10 that the dollar will not undergo >1000% inflation in the next ten years”: the apparent odds of 9:1 don’t equal the probability of hyperinflation at which you’d be indifferent to this bet.
For some (all?) of these problematic bets, you can mitigate the problem by making the money change hands in only one arm of the bet, reframing it as e.g. “For $90, I will sell you an IOU that pays out $100 in ten years if the dollar hasn’t seen >1000% inflation.” (Okay, you’ll still need to tweak the numbers for time-discounting purposes, but it seems simpler now that we’re conditioning on lack-of-hyperinflation.)
Does this seem correct in the weak case? (“some”)
Does this seem correct in the strong case? (“all”)
Clearly not all—the extreme version of this is betting on human extinction. It’s hard to imagine the payout that has any value after that comes to pass.
Agreed that post-extinction payouts are essentially worthless—but doesn’t the contract “For $90, I will sell you an IOU that pays out $100 in one year if humans aren’t extinct” avoid that problem?
How can I reconcile these COVID test false-negative numbers?
Further point of confusion: the Emergency Use Authorization summary mentions n=31 positive samples and n=11 negative samples in the “Analytical Specificity” section—how do you get “98%” or “99%” out of those sample sizes? Shouldn’t you need at least n=50 to get 98%? Heck, why do they have any
positive(edit: negative) samples in a “Specificity” section?
[Question] Does there exist a detailed Bayesian COVID tracker?
If no such thing exists, I might take a stab at creating one—so I’d even love to hear if you know of some causal-graph-inference-toolkit-thing that isn’t specifically for COVID but seems like a promising foundation to build atop!
But, if no such thing exists, that also seems like evidence that it… wouldn’t be useful? Maybe because very few social graphs have the communication and methodicalness to compose a detailed list of all the interactions they take part in? Conceivably because it’s a computationally intractable problem? (I dunno, I hear that large Bayes nets are extremely hard to compute with.)
Is this some kind of attempt at code injection? :P
Only the benign kind! I’ve got some ideas burbling in my brain re: embedding dynamic content in my writing, so I’m just exploring the limits of what Less Wrong permits in its HTML. (Conclusion: images hosted on arbitrary other domains are okay, but svgs are not. Seems sane.)
[Question] Any layperson-accessible reference posts on how to operationalize beliefs ?
I would love to live in this world.
This seems like a really hard problem: if a market like this “wins,” so that having a lot of points makes you high-status, people will try to game it, and if gaming it is easy, this will kill respect for the market.
Specific gaming strategies I can think of:
Sybil attacks: I create one “real” account and 100 sock puppets; my sock puppets make dumb bets against my real account; my real account gains points, and I discard my sock puppets. Defenses I’ve heard of against Sybil attacks: make it costly to participate (e.g. proof-of-work); make the cost of losing at least as great as the benefit of winning (e.g. make “points” equal money); or do Distributed Trust Stuff (e.g. Rangzen, TrustDavis).
Calibration-fluffing: if the market grades me on calibration, then I can make dumb predictions but still look perfectly calibrated by counterbalancing those with more dumb predictions (e.g. predict “We’ll have AGI by Tuesday, 90%”, then balance that out with nine “The sun will rise tomorrow, 90%” predictions). To protect against this… seems like you’d need some sort of way to distinguish “predictions that matter” from “calibration fluff.”
Buying status: pay people to make dumb bets against you. The Metaculus equivalent of buying Likes or Amazon reviews. On priors, if Amazon can’t squash this problem, it probably can’t be squashed.
[Question] “New EA cause area: voting”; or, “what’s wrong with this calculation?”
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Possible answer: “No election is decided by a single vote; if it’s that close, it’ll be decided by lawyers.”
Rebuttal: yeah, it’s a little fuzzy, but, without having cranked through the math, I don’t think it matters: my null hypothesis is that my vote shifts the probability distribution for who wins the legal battle in my desired direction, with an effect size around the same as in the naive lawyer-free model.
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Possible answer: “You’re doing a causal-decision-theory calculation here (assuming that your vote might swing the election while everything else stays constant); but in reality, we need to break out [functional decision theory or whatever the new hotness is], on account of politicians predicting and “pricing in” your vote as they design their platforms.”
Hmm, yeah, maybe. In which case, the model shouldn’t be “my vote might swing the election,” but instead “my vote will acausally incrementally change candidates’ platforms,” which I don’t have very good models for.
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Possible answer: “Sure, it’s individually rational for you to devote your energy to Getting Out The Vote instead of donating to charity, but the group-level rational thing for people to do is to donate to charity, rather than playing tug-o’-war against each other.”
Ugh, yeah, maybe. I see the point of this sort of… double-think… but I’ve never been fully comfortable with it. It sounds like this argument is saying “Hey, you put yourself at a 60% probability of being right, but actually, Outside View, it should be much smaller, like 51%.” But, buddy, the 60% is already me trying to take the outside view! My inside view is that it’s more like 95%!
It sounds like down this path lies a discussion around how overconfident I should expect my brain to be (and therefore how hard I should correct for that). Which is important, sure, but also, ugh.
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Sure! I’m modeling the election as being coin flips: if there are more Heads than Tails, then candidate H wins, else candidate T wins.
If you flip coins, each coin coming up Heads with probability , then the number of Heads is binomially distributed with standard deviation , which I lazily rounded to .
The probability of being at a particular value near the peak of that distribution is approximately 1 / [that standard deviation]. (“Proof”: numerical simulation of flipping 500k coins 1M times, getting 250k Heads about 1⁄800 of the time.)
Very interesting! I like this formalization/categorization.
Hm… I’d have filed “Why the tails come apart” under “Extremal Goodhart”: this image from that post is almost exactly what I was picturing while reading your abstract example for Extremal Goodhart. Is Extremal “just” a special case of Regressional, where that ellipse is a circle? Or am I missing something?