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PaperclipPerfector  9mo ago (text post)   30165 thread views

Culture War Roundup for the week of August 14, 2023

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I tried plotting the difference in EV of these (based on very handwavy assumptions: suppose your prior probability of C% of the other pill takers choosing red is a Gaussian with mean x and standard deviation y, ignore everything that's discrete rather than continuous here so the factors of n cancel out and we can express the problem as a simple integration, ignore the fact that this can give us C less than 0 or greater than 100 so we can use erf to evaluate the integrals...).

The expected value of you not dying because you picked red, 1/2*(1+erf((x-1/2)/(y*sqrt(2)))), is here. It's one if you're certain most people are picking red, zero if you're certain most people are picking blue, and the less certain you are the more smoothly the result depends on your mean estimate.

The expected value of people not dying because you picked blue, 1/(2*y*sqrt(2*pi))*exp(-1/2*((1/2-x)/y)^2), is plotted (in the negative, to keep red/blue consistent with red/blue) here. Except in the situation where your expectation has a mean near 50% and a standard deviation as small as that nearness, your choice doesn't matter, since either all the blue-pickers are doomed or they aren't unless you specifically cast the tie-breaking vote ... but the "I'm certain I'll be the tie-breaker" case is a hell of an off-to-infinity singularity. I had to truncate the y axis above zero to keep this random web app I picked from yelling at me.

The difference between the two is here, but because the color scale on that doesn't match up nicely, let's just look at the "which one is bigger" comparison here.

And boy, that's a hell of a scissor statement graph, isn't it?

If you're sure that most people are going to pick blue, or if you think a small majority are going to pick red but your uncertainty is just wide enough to make you think you might be the tie-breaking vote, you picking blue has the higher EV! And since everybody thinks like you, you're right to expect that blue is the default, so those red jackasses are just free riders!

If you're sure that most people are going to pick red, or if your uncertainty is so wide you really don't know what's going to be picked, you picking red has the higher EV! And since everybody thinks like you, you're right to expect that red is the default, so those blue idiots are just suicidal!

since either all the blue-pickers are doomed or they aren't unless you specifically cast the tie-breaking vote

Y'know, this interests me strangely, because I'm nearly certain a lot of the "you should pick blue becuse your choice is going to save people" are also the ones going "it's stupid to vote because one single vote in an election is meaningless and can't affect the outcome".

So my vote in millions of votes is worthless and won't tip any balances, but my picking blue in millions of selections is the vital saving decisions? Make up your minds!

Nate Silver once made a cute little calculation about the probability that your vote will matter in a presidential election.[1] Basically, take the probability you'll be the swing voter in your state times the probability your state's electoral college votes will be the swing which decides the presidency.

If you were in Colorado or Virginia for the 2012 election, there was a whopping 1-in-10 million chance that your vote would matter. It's not inconceivable that you might consider the difference between the candidates to be large enough for it to be rationally altruistic to spend your time voting. If voting gives you the equivalent of 10 dollars of disutility, then the better candidate need only provide the equivalent of 100 million dollars of relative value to the world. EG: Maybe you believe the better candidate would remove a 1% chance of war. More local elections have lower stakes, but also a higher chance your vote matters.

[1]: What is the Probability Your Vote Will Make a Difference (Gelman, Silver, Edmin, 2012)

PS: I'm not on the blue-pill side, here. I believe in rule utilitarianism, and "oppose suicide cults" is a very good heuristic, no matter how strongly people argue I'm evil for following it. The pro-social move in this scenario isn't to take the blue-pill; it's to contact all your friends and loved ones, make sure they aren't taking the blue pill, and if need be, shove an emetic down their throats. Similarly I vote because I think it's usually good to do so, and don't bother to calculate whether the expected value shakes out in each case before heading to the polls.

If the vote is mandatory, why would I vote against blue provided I think blue is winning anyway? Some sense of contrarianism? To show FarNearEverywhere on the internet that I'm not a sheep nanny virtue signaler but instead an enlightened rational lifemaxxer?

If you're sure that most people are going to pick blue, or if you think a small majority are going to pick red but your uncertainty is just wide enough to make you think you might be the tie-breaking vote, you picking blue has the higher EV!

One caveat here, this is EV of lives saved which counts your life as equal in value to a random persons life. By revealed preference of how people actually live their lives almost everyone values their own life at least an order of magnitude higher than a random persons life. Taking that into account I think red should be prefered in the majority but not all situations. Heres the graph for when red is prefered using a 10x multiplier on your own life (link isn't working but I just added a zero to your expression it goes to a small blue region in the corner and red ahead everywhere else) https://academo.org/demos/3d-surface-plotter/?expression=if(10%2F2*(1%2Berf((x-1%2F2)%2F(ysqrt(2))))-1%2F(2ysqrt(2pi))exp(-1%2F2((1%2F2-x)%2Fy)%5E2)%3E0%2C1%2C0)&xRange=0%2C1&yRange=0.01%2C1&resolution=100

Ha! I was just pulling up my own comment to reply with basically what you just said, except that I added a 20x multiplier to make it seem more selfish. The higher you make the multiplier, naturally, the lower the uncertainty you can tolerate before red becomes the preferred option.

Is this how some blue pickers are modeling red pickers? "Just like me he knows we're probably going to pick blue, so the only way his red pick makes sense if he would prefer the deaths of twenty strangers over his own one; that selfish jerk!"

All that said, I think the "trembling hand" model makes for a good reason to try to coordinate around blue. It doesn't take too high a percentage of irrational choices before you start to be tempted by the hope of saving all of them.

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