The understanding I came away with: there are (at least) three stages of understanding a problem:
"Shuffle-sort" achieves the second level of knowledge re: sorting lists. Yeah, it's cartoonishly wasteful, and it doesn't even resemble any computationally feasible sorting algorithm (that I'm aware of) -- but, y'know, viewed through this lens, it's still a huge step up from not even understanding "so... (read more)
Yeah, a fair point!
Ah! You're saying: if my "500k coin flips" model were accurate, then most elections would be very tight (with the winner winning by a margin of around 1/800, i.e. 0.125%), which empirically isn't what happens. So, in reality, if you don't know how an election is going to turn out, it's not that there are 500k fair coins, it's that there are either 500k 51% coins or 500k 49% coins, and the uncertainty in the election outcome comes from not knowing which of those worlds you're in. But, in either case, your chance of swinging the election is vanishingly small... (read more)
Also, note that your probability of swinging the election is only 1/√n if the population is split exactly 50/50; it drops off superexponentially as the distribution shifts to one side or the other by √n voters or more.
Yesss, this seems related to shadonra's answer. If my "500k coin flips" model were accurate, then most elections would be very tight (with the winner winning by a margin of 1/800, i.e. 0.125%), which empirically isn't what happens. So, in reality, if you don't know how an election is going to turn out, it's not that there are 500k fair co... (read more)
Wait... your county has a GDP of over half a million dollars per capita? That is insanely high!
I agree! (Well, actually more like $1-200k/capita, because there are more people than voters, but still.) Sources: population, GDP, turnout.
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 1/80... (read more)
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, th
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.
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.
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:
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.)
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.)
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?
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?
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
... (read more)Ahhh! Yes, that helps a great deal. Thank you!
(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
... (read more)Consider .
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?
Hmm. If we're trying to argmax some function f over the real numbers, then the simplest algorithm would be something like "iterate over all mathematical expressions e; for each one, check whether the program 'iterate over all provable theorems, halting when you find one that says e=argmaxf' halts; if it does, return e."
...but I guess that's not guaranteed to ever halt, since there could conceivably be an infinite procession of ever-more-complex expressions, eking out ever-smaller gains on f. It seems possible that no matter what (reasonably powerful) mathe... (read more)