tag:blogger.com,1999:blog-235663687017051886.post4900538463026976784..comments2017-10-04T23:57:08.035-07:00Comments on Sperling Grove: Rational Voting Models – The Problem SpaceMatt Sperlinghttp://www.blogger.com/profile/09068116459532701291noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-235663687017051886.post-57771444852412492572017-06-09T04:40:23.373-07:002017-06-09T04:40:23.373-07:00Really nice article..i respect your words..
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great effort!!!<br />Latest News Updateshttp://newsklic.comnoreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-34737955327344681652017-04-20T02:38:27.906-07:002017-04-20T02:38:27.906-07:00i really enjoyed your blog but i had no idea what ...i really enjoyed your blog but i had no idea what you said!!!Latest Technology newshttp://newsklic.com/category/technology/noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-35970665357870927102017-04-19T05:35:16.997-07:002017-04-19T05:35:16.997-07:00great share..
AFL Sports newsgreat share..<br /><a href="http://newsklic.com/category/sports/" rel="nofollow">AFL Sports news </a>zainab sheikhhttps://www.blogger.com/profile/15813380386551174680noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-14146984938290728632016-10-18T14:22:35.385-07:002016-10-18T14:22:35.385-07:00>Because you can’t distinguish between the “cor...>Because you can’t distinguish between the “core” backers and those on the margin, you have to allocate to each participant both the gains and the losses.<br /><br />Just because the first option (finding the core contributors) is impossible doesn't mean the second option is automatically coherent. They can both be nonsense. What exactly does "allocate" mean? That they "get" the Total_Value/Total_Participants? It has no meaning whatsoever except as sort of an infographic way of patting yourself on the back.<br /><br />SA's point, and the point of most voting skeptics, is that as far as any individual brick-donator can tell, they should have stayed home. The only necessary assumption is that their actions don't impact too many others' actions, which is quite a safe assumption in private elections. <br /><br />The brick thought experiment also seems to lead to some strange recommendations. Do you encourage 2500, 3000, 5000, 100000, people to get out and participate? Because that is a lot of wasted bricks. At some point, rational people would look at forecasts, do some fast math, and stay home. Hopefully you agree this is correct. But this is exactly what many people do in national elections.<br /><br />>This is the challenge of collective action in a nutshell. I’m not saying I have a solution for the short term (unless you count this blog post as my best attempt at a first step). But it’s instructive to notice that we have overcome other collective action problems with negative initial conditions, through shifting the definition of rational behavior – through changing the model.<br /><br />>Do you feel duty-bound to recycle even if the expected value is opaque and the returns are tiny at the individual level? Do you think your great-grandparents felt that way? <br /><br />>Do you feel duty-bound to vaccinate your kids even if you don’t live in an area with other unvaccinated kids (meaning your kids are extremely, extremely unlikely to be exposed to the diseases you’re vaccinating against)? <br /><br />No one calculates the EV of recycling or vaccinating. It's just something you do to belong to the middle class. It has nothing to do with "changing the model" of rationality. If you don't vax everyone talks behind your back about how stupid and what a bad parent you are. So you should probably vax even if it does nothing. <br /><br />And if your only point is that "irrational people would do better in this one instance", the obvious counterpoint is that they'll do TERRIBLY in all sorts of other instances. The world is a better place with an extra Scott Alexander not voting than with moron #17825912859 who thinks voting is his civic duty.<br />Joseph Tanseyhttps://www.blogger.com/profile/03922469315531646613noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-84005642155996055912016-10-18T08:12:24.767-07:002016-10-18T08:12:24.767-07:00K should be willing to pay 0.9 utilons *conditiona...K should be willing to pay 0.9 utilons *conditional on L not paying anything*, and similarly for L conditional on K. But if K knows that L is going to pay 0.9 utilons, then K should only be willing to pay up to 0.1 utilons to get there. And if K and L can't communicate, coordinating the right utilon-payments isn't easy. You've described a coordination game, not a paradox.<br /><br />I get that "decide as if you're the last voter" sounds counter-intuitive. I'll think about it and see if I can better explain why it's reasonable. But fundamentally, I'm just trying to describe the math. If I'm wrong, there should be a problem in the math I've been using in order to actually determine K & L's decisions. Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-62684383514447911522016-10-17T17:19:02.856-07:002016-10-17T17:19:02.856-07:00First, thank you for the nice writeup in the paste...First, thank you for the nice writeup in the pastebin. That was helpful. I still feel like "In short, you decide as if you were the last voter, but you assign credit as if you were the average voter." is an "I expect to be surprised in exactly this direction" situation that rational agents shouldn't be subject to. <br /><br />If K really believes his expectation is 1, he should pay 0.9 to get there. So should L. Then they wake up the next morning down 0.8 utilons because assigning credit obeys the total but their subjective decisions did not. They used math we thought was sound, paid an amount of utility consistent with what their subjective estimate of future utility was, and lost.Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-36342722808778404282016-10-17T13:58:38.472-07:002016-10-17T13:58:38.472-07:00pastebinning again because I broke the character l...pastebinning again because I broke the character limit for comments: http://pastebin.com/MHswKBSr<br /><br />"Next step: do you agree that if everyone has the same shared information, the expected utilities of rational agents must sum to total utility? (No rush, I'm also multitasking)." <br /><br />Yes, marginal utilities must sum to the total utility, but you have to be careful about *which* marginal utilities you sum. See the link for details.<br /><br />"If so, isn't working from the same distribution that produces 1/60M chance of 1-vote-tie a shared-info setting?"<br /><br />Sort of. Strictly speaking, when Ken consider's his vote, he assumes a probability distribution over Leslie's vote, and when Leslie considers her vote, she assumes a probability distribution over Ken's vote. They do not have the same information sets - each voter has a probability distribution over a different subset of voters, to wit, each other voter. Now, their information *is* assumed symmetric, that is, what Ken believes about Leslie, Leslie believes about Ken (conditional on what stat they're in, etc). Or at least, this is the strictly speaking correct way to model it. But when N>300 million, one person's vote doesn't change the aggregate probability distribution a noticeable amount, so we round it off to "everyone has a 1/60M chance of casting the deciding vote (conditional on their state)."Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-42202309094679757312016-10-17T11:53:25.968-07:002016-10-17T11:53:25.968-07:00Next step: do you agree that if everyone has the s...Next step: do you agree that if everyone has the same shared information, the expected utilities of rational agents must sum to total utility? (No rush, I'm also multitasking). <br /><br />If so, isn't working from the same distribution that produces 1/60M chance of 1-vote-tie a shared-info setting?Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-30704033930473464062016-10-17T11:30:43.375-07:002016-10-17T11:30:43.375-07:00(Running away for now so I can actually be product...(Running away for now so I can actually be productive; I'll return later)Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-16811424668053466742016-10-17T11:28:16.247-07:002016-10-17T11:28:16.247-07:00"Even if Ken knows things Leslie can't kn..."Even if Ken knows things Leslie can't know..." I take that back. If I know the coin has landed heads and you don't know, my ev on a bet of heads is 1 and yours on tails is .5 and that doesn't sum. I'm starting to see your point, I have to think harder now about how it applies to the voting scenarios. Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-90492026181034820812016-10-17T11:21:50.560-07:002016-10-17T11:21:50.560-07:00Okay but that's superficial, you're examin...Okay but that's superficial, you're examining the steps before they solve for their utility. Now have them each solve for the expected utility! That *output* has to sum to total utility even if their prior steps are relative not objective. Even if Ken knows things Leslie can't know, if they are both to be VNM rational, their expected utilities can't exceed the total utility. <br /><br />Say they are the only voters, and it takes 2 votes to win and the prize is $300B to american primary schools. If Ken looks down and says "looks like I create $300B of wealth every time I vote here (since Leslie's vote is Yes and my vote is thus the deciding vote)" and Leslie looks down and draws the same conclusion, then on November 8th they both generated half the utility they expected since they can't actually tell who cast the "key vote" or however you want to describe them dividing the win by N in order to allocate the gains. Notice how easy it was to accurately model the others' behavior. Of course the other will vote yes. But when they go to calculate expected utility, they better divide by the N of the collective they are acting as.Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-87346683077857300492016-10-17T11:11:07.484-07:002016-10-17T11:11:07.484-07:00Put another way, suppose Ken and Leslie are the on...Put another way, suppose Ken and Leslie are the only voters. Ken fixes Leslie's vote and asks "what's the counterfactual difference between voting for A and B?" while Leslie fixes Ken's vote and asks "what's the counterfactual difference between voting for A and B?" So suppose that in a deterministic world they both vote for A. Ken is comparing U(A,A) and U(B,A), while Leslie is comparing U(A,A) and U(A,B) - two different sets of counterfactual comparisons.Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-37444161377387617502016-10-17T11:08:14.686-07:002016-10-17T11:08:14.686-07:00My position is 100% independent of determinism. I&...My position is 100% independent of determinism. I'm just describing the math. (Though I agree with you about determinism here).Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-48681492474655312032016-10-17T11:04:33.596-07:002016-10-17T11:04:33.596-07:00Well, looks like this is devolving into a determin...Well, looks like this is devolving into a determinism debate. My philosophy allows for Leslie's consciousness to be "deciding" and also for her decision to be ~100% predictable by Ken. Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-36580684288063125572016-10-17T11:01:46.622-07:002016-10-17T11:01:46.622-07:00No, they are different counterfactuals. You have t...No, they are different counterfactuals. You have to look at the vote arrangements. When Ken is choosing to vote in the certainty scenario, he knows Leslie's vote. But when Leslie is choosing to vote, her vote isn't fixed because that's precisely the variable she is choosing!Matthttps://www.blogger.com/profile/04870838636994186277noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-16448575785898830262016-10-17T10:56:53.758-07:002016-10-17T10:56:53.758-07:00These aren't different counterfactuals, they a...These aren't different counterfactuals, they are the same scenario. Ken and Leslie both have 100% certainty the election will come down to 0-1 vote depending on whether they vote (this is not practical, but they live in a simulation the Creator has told each of them that every other person WILL vote, Creator knows this will make each of them vote, so he ends up correct in the future - these are the parameters that allow for 100% certainty... ok moving on...). They each must decide what to do in that single election, under those conditions. One scenario, one world. If they don't divide their expected value by N, then a million Kens and Leslie will each add their "I cast the winning vote!" expected prize to the sum predicted and they will be off by a factor of N.Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.comtag:blogger.com,1999:blog-235663687017051886.post-69021093219477196822016-10-17T10:51:50.376-07:002016-10-17T10:51:50.376-07:00Comment I received via Twitter, posting here so I ...Comment I received via Twitter, posting here so I can reply here:<br />Let's start by supposing a hypothetical voter Ken has 100% certainty about the outcomes and everyone else's vote. He knows that U(A wins) = 1 and U(B=wins) = 0. If more people are voting for A than B, or if more than 1 more are voting for B than A, then it's clear that it doesn't matter who Ken votes for or if he votes at all. In this case the marginal utility of him voting for A over B is 0. But if there is a tie, or if B is leading A by exactly 1 vote, then the marginal utility of voting for A over B is 0.5 (assume ties are broken by coin flips - exact procedure is not really relevant to this discussion). This, I think, is uncontroversial. Ken looks at what everyone else is going to do and figures out if his vote will have an impact. If it will, he has a positive marginal utility of voting for A over B. Otherwise, the difference is 0.<br /> <br />But what about another hypothetical voter, Leslie. If we put Leslie in the exact same situation as Ken, we get the exact same results. And against for a 3rd hypothetical voter, Jordan, and a 4th, etc. When any given voter believes there will be a tie, the utility of voting for A over B is 0.5. Then if we sum this utility over the population, suddenly the total utility is N/2 where N = number of voters. But total utility is supposed to be 1! This isn't double counting, it's N-counting!<br /> <br />That's your complaint, I think. Do correct me if I'm wrong. But there's a subtle mistake there. That summation is taking the marginal value of a single person's vote from N *different* counterfactuals, and adding them up. You don't add up marginal values across counterfactuals. You add them up from the same counterfactual.<br /> <br />There's nothing special about the 100% certainty assumption here either. In the standard voting model that Scott talks about, each voter assumes a probability distribution over the votes of the other voters. So while the assumptions are different, Ken's problem and Leslie's problem still are considering different counterfactuals. It's worth going into it in a bit more detail. When Ken computes the expected utility of voting for A vs. B in the uncertainty case, he does so by dropping down to each counterfactual, computing the utility of each counterfactual, computing the probability of that counterfactual occurring, then takes the average utility over counterfactuals weighted by probabilities. I.e.<br /> <br />E[U(vote for A)] = sum_{possible arrangements of votes} U(vote for A | arrangement) * P(arrangement)<br /> <br />Each arrangement of votes is a counterfactual with each other voter's vote specified, e.g. one arrangement Ken considers might be: Leslie votes for A, Jordan votes for B, etc. The point being here that *Each voter considers a different set of counterfactuals than each other voter.* Now, we simplify this by assuming that each voter faces the same probability distribution over possible aggregate arrangements, i.e. that each voter has the same chance of casting the deciding vote (assuming they're in the same state), even if one is vastly more likely to vote for A than another. This is an approximation, but as long as N is very large the impact of one voter on the aggregate probability distribution is tiny.<br /> <br />The upshot to all of that is, again, that *each voter averages over a different set of counterfactuals in order to compute the marginal value of their vote*. So summing the marginal values is not and should not be meaningful. Marginal values don't sum to total value because they're computed under different counterfactual assumptions. Adding uncertainty to the mix doesn't change anything. If you want to get from marginal values to total values, you have to compute the marginal value of each vote *under the same set of counterfactual assumptions*, then add those up.Matt Sperlinghttps://www.blogger.com/profile/09068116459532701291noreply@blogger.com