Obviously you are willing to extend this sort of cost benefit analysis to all kinds of influencing government?
If me grabbing a nanoslice of power in the form of casting a vote is like donating a thousand dollars to charity, me grabbing more than a nanoslice even by illegal means shouldn't be dismissed out of hand and deserves even handed analysis. The value of such information seems to be pretty high.
Yes, this. I'd like to see the author of the article give a similar analysis on whether or not we should quit our jobs and become lobbyists.
It's worth pointing out that the $100 you "donate" probably goes much, much less far than a $100 donation to an effective charity. So it might be better to think in terms of shifting $100 in federal funds. That makes it seem like a lot less of a slam dunk to me. Would I take half an hour out of my day to move $100 from an ineffective government agency to an effective one? Meh. Feels like my other attempts at altruism probably have a much higher expected impact.
I'm also worried about getting called up for jury duty if I re-register to vote now that I'm living in a different county.
On the whole though, fairly persuasive.
You might want to specify that when you talk about "donations" you are referring to charitable donations rather than campaign donations. It might just be me, but the political priming made this distinction less obvious than it probably should have been.
Being in California, Gelman et al. put my probability of a decisive vote around 1/(5 million).
As the paper says:
[W]e consider how the results would change as better information is added so as to increase the accuracy of the forecasts. In most states this will have the effect of reducing the chance of an exact tie; that is, adding information will bring the probability that one vote will be decisive even closer to 0.
And as it turns out, conditional on polls and other information from right before the election, one would have to assign a very low probability that California will (almost) vote Republican. Also, conditional on California (almost) voting Republican, one would have to assign a very high probability that enough other states will vote Republican to make California's outcome not matter.
It seems to me that a reasonable probability estimate here would be multiple orders of magnitude lower than the cited estimate; and it seems to me that together with the optimal philanthropy point made by user:theduffman and user:dankane and user:JohnMaxwellIV elsewhere in the thread, this makes voting in states like California not worthwhile based on the calculation presented in the original post.
On the other hand, if you want to strictly adhere to utilitarian principles, you would probably have to note that the "altruistic dollars" obtained through selection of the better candidate probably produce much less utility per dollar than a dollar donated to one of givewell.org's top rated charities. Standards of living in the US are already so high that a marginal dollar is worth much less than a marginal dollar in a less developed country. Then again, if you really followed this philosophy and lived in the US, you should probably actually devoting essentially all of your time to earning money to donate to such charities, which is not something that many people are actually willing to do.
US policy and wars have a large effect on people in poor countries. They are presumably considered in the $100 billion "better for the world" sum.
Unless they would be earning fabulous sums in that hour, an altruist would probably be justified in considering the expected value of their vote higher than the expected value of whatever else they would do with that one hour per year.
Gelman, Silver, and Edlin have a more recent paper looking at the 2008 election, which estimated that California voters had a 1 in 1 billion chance of being decisive and that 1 in 10 million was the maximum probability of being decisive (for voters in the four swingiest states).
The problem is that the thousands of dollars are being stolen anyway and you need to vote to have any say in which charity, or to reduce the amount of money being stolen.
That makes (70%-30%)1/(5 million)($700 billion) = $56,000.
These figures seem implausibly high if we are comparing to the best donations you can pick out. Trivially, the campaigns spend only a few billion dollars, with $700 billion you could use the interest alone to spend ludicrously on voter turnout and advertising in every election, state, local, and national going forward, for an expected impact greater than winning one election.
That is to say, voting yourself can't be be worth more than $n if you can generate more than one vote with political spending of $n. And randomized trials find voter-turnout costs per voter in the hundreds of dollars. Even adjusting those estimates upward for various complications, there's just no way that you wouldn't be able to turn out or persuade one more vote for $56,000.
This seems to actually underestimate the value of voting, in that it assumes that a vote is only significant if it flips the winner of the election. But as Eliezer wrote:
But a vote for a losing candidate is not "thrown away"; it sends a message to mainstream candidates that you vote, but they have to work harder to appeal to your interest group to get your vote. Readers in non-swing states especially should consider what message they're sending with their vote before voting for any candidate, in any election, that they don't actually like.
Also, rationalists are supposed to win. If we end up doing a fancy expected utility calculation and then neglect voting, all the while supposedly irrational voters ignore all of that and vote for their favored candidates and get them elected while ours lose... then that's, well, losing.
Amount of money spent is a radically different thing from amount of good done. Even among charities effectiveness can differ by about 1000x. Government spending is likely to fall more in line with the least effective charities because it is biased by political motives. Most spending is not even in areas that are likely to be effective like global health, or rationality outreach. The money that is spent on global health is politically directed, going largely to local neighbours and sites of war and terrorism, not to those most in need.
As the most effective charities are likely 100-10000x more effective than government spending, the calculation should be adjusted down by 3-5 orders of magnitude. We're looking at more like $0.01 - $15,000 as the equivalent impact.
Hmm... The calculations work, but somehow it seems against our intuitions. Thinking about it, it seems that the problem is one of scope insensitivity. $100 billion, $700 billion, $7 trillion. They all feel more or less the same, which of course, is absolutely insane. When I look at the numbers, it just feels like "a lot". Ultimately, what this post is saying is to simply shut up and multiply, which is a very good and and very relevant point.
This was a post well worth making, particularly because of how much rhetorical support the superficial arguments against voting get
So I found this paper by Gelman, King, and Boscodarin (1998), where they simulate the electoral college using models fit to previous US elections, and find that the probability of a decisive vote came out between 1/(3 million) and 1/(100 million) for voters in most states in most elections, with most states lying very close to 1/(10 million).
So... what you're telling me here is that, in America, different people's votes count for different amounts. If I have Tom, whose vote has a one-in-a-hundred-million chance of affecting the election; and John, who l...
Scott Aaronson and Peter Norvig make similar arguments.
Contrast with my analysis of the "voting" phenomenon.
Let X = the amount of money such that you are indifferent between being given X and getting to choose who wins the election.
Let P = the probability your vote would decide the election.
XP = the rough expected value of voting.
Say we need XP>$10 to make it worth voting. If P = 1/20M then you need X>$200M, which seems way too big.
Of course risk aversion would complicate this.
If one Virginia voter does an expected 1/(3.5 million)*($7 trillion) = $2 million good by voting for candidate X, then there is another Virginia voter that does an expected $2 million of damage by voting for candidate Y. It seems that either
Roughly half of the population is misinformed about which alternative is objectively better. In that case, how do I justify a belief that I have a greater than 50% chance of being right, when everyone else has access to the same information?
There are real differences in values, and by my vote I direct the outcome towards my preference instead of the other Virginia voter's. In that case, sure I want to vote, but should we really call it altruism?
"In any case, 55% is pretty conservative; it means I consider myself to have almost no information." I'm wondering what evidence there is for a probability above 50. That's what I would consider "conservative". It's not literally "no information", it's "no more information than the median voter". That's what it would mean for your vote to affect the outcome in a positive manner. Conditional on your vote affecting the outcome, there must be as many people (in your area) for one candidate as the other. The more lopside...
The probabilities of deciding the election by state given in that paper are for 1992. If we assume that on average, a vote has a 1 in 10 million chance of deciding the election, and that 538 accurately forecasts the probabilities of each state being decisive, then a vote in California has a (1/10^7)*9*(<1/10^3) = less than 1 in 1 billion chance of deciding the election (since about 1/9 of voters live in California, and California has a less than 0.1% chance of casting the decisive electoral votes).
Now that the election season which inspired the writing of this article has passed, I feel less like dirty discussing it. Less like I'm doing politics and more like actually thinking.
First off I recommend reading these three articles by Eliezer and paying special attention to the last one:
In response to the last article on the list (which I recommend) Robin Hanson responds:
...You say don't try to use game theory to figure out how to best "make a difference
For those LW users who are well-informed on this topic: Which major candidate do you estimate will have a greater positive impact on humanity's total utility if elected?
(Poll for the benefit of those US LWers who are less informed, to save them time if they want to freeload off thinking and research done by other users. I'm leaving out third party candidates because it seems likely that the optimal strategy for third-party supporters varies by state.)
[pollid:202]
To be completely honest, I don't know enough about economics or life outside of the state I live in the United States to have any clue which candidate will affect the world for the better. I want to understand what it is I should do according to my values (not just regarding voting, but in general), but the world is such a big place that I can't even begin to fathom how I would go about trying to figure this out. Does anyone have any advice about where to start, what resources to consult? I want to shut up and multiply, but I don't even know what I'm multiplying!
Ah, I was hoping to see a pseudo-Pascal's Mugging* argument constructed for voting. Now I can ask people who bring it up in response to any topic, 'do you vote for consequentialist reasons?'
* I say pseudo because people go around claiming that any argument involving small probabilities of large benefits or harms is a "Pascal's mugging" even though this is not what either Bostrom or Yudkowsky meant when they wrote on it; yet no one ever seems to realize this, which mystifies me a little - the LW post and PDF are both online, just a Google away!
Here's a more germane objection: a single vote, in reality (as opposed to in "should universes") never truly comes even close to deciding an election. When the votes are close to a tie, the courts step in, as in Bush v. Gore. There are recounts and challenges. The power of connections and influence by judicial politics completely overwhelms the effect of a single vote.
Don't you think it perverse to derive the value of voting from the very high value of the outcome of an extraordinary event?
Take an electorate with 1,000,000,000 voters, deciding between A and B. If 550 million vote for A, and 450 million vote for B, then A is 90% likely to win. Conversely, if B leads 550 million to A's 450 million, B is 90% likely to win. With very finely balanced vote totals both candidates have sizable chances at winning depending on the outcomes of recounts, etc (although the actual vote total in a recount certainly matters for the recount and challenge process!).
Say we make a graph, assigning a probability of victory for A for every A vote total between 450 million and 550 million. Over the whole range, there needs to be an 80% swing in win probability, on net. So, if we count every change in win probability as vote totals increase, the average change in win probability per vote for A has to be (80%)/(100 million) over this range.
So if the polls leave you with a roughly uniform distribution over vote totals between 450 and 550 million votes for A, then you should assign a probability of about 1 in 125 million to being decisive, despite recalls and court challenges and so on. This will reflect being the marginal vote that pushes a key vote total one way or the other, making a lead large enough that a judge or official doesn't bother to do a recount, being the decisive vote in a recount, increasing the vote margin from 999 to 1000, a psychologically significant difference, and so forth.
In non-iterated PD, someone who cooperates is a cooperator.
Nevertheless the CooperateBots win when playing between each other, while the rational agents lose when they have no mean to credibly commit.
No, the cooperators actually lose when playing each other, because they gain less than what they could, while the only reason they get anything at all is because they are playing against other cooperators. Likewise, the defectors win when playing other defectors, and they obviously win against cooperators. Cooperating could only win if it effected your opp...
A couple of assumptions that you did not state. You assume that your favored candidate's budget contains truly optimal uses of charitable dollars. You need a step down function unless your preferred charity is funding government programs.
You assume that the opposition candidate's spending is valueless. Otherwise you need to consider the relative merits.
You assume that there is no portion of the opposition budget that is preferable. If you believe that each candidate has some portions right, you need to be subtracting this spending from the value of your...
So I found this paper by Gelman, King, and Boscodarin (1998)
The link is dead. Here's the paper.
Note that the last name of the third author is Boscardin, not Boscodarin.
"You know, given human nature, if you lived in a country in which there was democracy, pretty soon someone would try to sound deep by inventing reasons that voting was a good thing. But if you lived in a universe in which democracy wasn't the high-status mode of governance, and asked them if they wanted it, with all its attendant consequences, they would say no. It would never occur to them to invent all the clever rationalizations that someone resigned to democracy would devise."
That expected $100 - $1,500,000 is going to get spread around to 300 million people...
If you're so concerned with helping other people, why not just abstain from voting, thereby increasing the effectiveness of the votes cast by those other people, and thus giving them more direct say about how they are governed?
I actually also think your estimate of 55% belief is overconfident, for any utility function that properly distinguishes between terminal and instrumental values (i.e. a utility function that takes into account aggregate health is proper, while one that specifically refers to people having health insurance would not be in my view).
A slight math error:
(90%-30%)*1/(3.5 million)*($7 trillion) = $1.2 million
Here you left the 30% chance of being wrong from the previous example, but if you have a 90% chance of being right, you only have a 10% chance of being wrong. The actual expected dollar value is $1.6 million, which is actually a little better for your argument.
I rarely make decisions involving such low probabilities, so I don't really know how to handle risk-aversion in these cases. If I'm making a choice based on a one-in-ten-million chance, I expect that even if I make many such choices in my life, I'll never get the payoff. This is quite different than handling one-in-a-hundred chances, which are small but large enough that I can expect the law of large numbers to average things out in the long term. So even if I usually subscribe to a policy of maximizing expected utility, it could still make sense to depart...
If you're loss averse, the expected value could easily be negative: cost(voting for wrong candidate) > benefit((voting for right candidate).
I estimate that for most people, voting is worth a charitable donation of somewhere between $100 and $1.5 million. For me, the value came out to around $56,000.
You reason, I think, that since most everyone has better knowledge of the identity of the better candidate than chance, Chance (to reconstruct the argument) is the relevant criterion because, for your vote to be decisive, the other voters would have shown themselves (as a whole) to be indifferent between the two outcomes--I find that a convenient way to put it. In the only circumstance where your...
Clearly in a community of unconditional cooperators every agent obtains a better payoff than any agent in a community of defectors.
As soon as you're talking about communities, you're talking about meta-PD, not PD, and as I've explained above, rationalist agents play meta-PD by making sure cooperation is desirable for the individuum as well, so they win. End of story.
Quick correction:
(90%-30%)1/(3.5 million)($7 trillion) = $1.2 million
The beginning of this should be 90%-10%, which changes the projected value to $1.6 million, not $1.2 million.
The relevance is at best superficial as far as I can tell. Please don't turn Holden's point into a fully general counterargument against surprising expected utility calculations.
This is an expected utility calculation that involves a small probability of a large payoff with large margins of error. Here's what I take as the essence of Holden's post: "an estimate with little enough estimate error can almost be taken literally, while an estimate with large enough estimate error ends ought to be almost ignored." I have very little confidence in both my and Academian's estimate of which candidates winning will actually turn out to be better overall, and what the monetary value of each winning over their alternatives would actually be. Obama may seem to align with my values slightly more than Romney, but an office as powerful as the President of the US has many small, complex effects on many people's quality of life, and we could all easily be wrong.
People often say that voting is irrational, because the probability of affecting the outcome is so small. But the outcome itself is extremely large when you consider its impact on other people.
Which, of course, should encourage all sane states to have compulsory voting for the same reason that paying taxes is compulsory rather than voluntary. (Or, rather, to make attendance at the polling booth compulsory such that a decision to abstain is permitted but not more convenient.)
That would reduce the average level of education, political knowledge, and intelligence in the electorate.Turnout rates by education in 2008:
Yes - see Caplan's "Myth of the Rational Voter", showing education predicted "votes like an economist"
What evidence is there that compulsory voting wouldn't just add noise to the selection process? This seems like the obvious outcome to me.
What evidence is there that compulsory voting wouldn't just add noise to the selection process?
There are about two dozen countries that use compulsory voting. Looking at the ten countries that actually enforce it we find that it in fact doesn't just add noise to the selection process. We find that they in fact don't have a selection process particularly dominated by noise.
If we look at actual compulsory votes, and find that practically nobody votes for some candidates while others get a lot of votes despite the addition of the reluctant voters then that which was added can't have been just noise. In this example only 1.4% of all (primary) votes went to the "Family First" candidate. Even assuming zero of the voluntary voters voted for "Family First" somehow the additional "noise" still knew to favor the other three candidates and mostly avoid Family First. Additional votes made by constituents and which systematically favor one candidate far above another aren't called "noise", they are just called "votes".
What evidence is there that compulsory voting wouldn't just add noise to the selection process?
I happen to know Mortimer...
Summary: People often say that voting is irrational, because the probability of affecting the outcome is so small. But the outcome itself is extremely large when you consider its impact on other people. I estimate that for most people, voting is worth a charitable donation of somewhere between $100 and $1.5 million. For me, the value came out to around $56,000. So I figure something on the order of $1000 is a reasonable evaluation (after all, I'm writing this post because the number turned out to be large according to this method, so regression to the mean suggests I err on the conservative side), and that's be enough to make me do it.
Moreover, in swing states the value is much higher, so taking a 10% chance at convincing a friend in a swing state to vote similarly to you is probably worth thousands of expected donation dollars, too.
I find this much more compelling than the typical attempts to justify voting purely in terms of signal value or the resulting sense of pride in fulfilling a civic duty. And voting for selfish reasons is still almost completely worthless, in terms of direct effect. If you're on the way to the polls only to vote for the party that will benefit you the most, you're better off using that time to earn $5 mowing someone's lawn. But if you're even a little altruistic... vote away!
Below is an example Fermi calculation for the value of voting in the USA. Of course, the estimates are all rough and fuzzy, so I'll be conservative, and we can adjust upward based on your opinion.
I'll be estimating the value of voting in marginal expected altruistic dollars, the expected number of dollars being spent in a way that is in line with your altruistic preferences.1 If you don't like measuring the altruistic value of the outcome in dollars, please consider making up your own measure, and keep reading. Perhaps use the number of smiles per year, or number of lives saved. Your measure doesn't have to be total or average utilitarian, either; as long as it's roughly commensurate with the size of the country, it will lead you to a similar conclusion in terms of orders of magnitude.
At least 1/(100 million) = probability estimate that my vote would affect the outcome. This is the most interesting thing to estimate. There are approximately 100 million voters in the USA, and if you assume a naive fair coin-flip model of other voters, and a naive majority-rule voting system (i.e. not the electoral college), with a fair coin deciding ties, then the probability of a vote being decisive is around √(2/(pi*100 million)) = 8/10,000.
But this is too big, considering the way voters cluster: we are not independent coin flips. As well, the USA uses the electoral college system, not majority rule. So I found this paper by Gelman, King, and Boscardin (1998), where they simulate the electoral college using models fit to previous US elections, and find that the probability of a decisive vote came out between 1/(3 million) and 1/(100 million) for voters in most states in most elections, with most states lying very close to 1/(10 million).
At least 55% = my subjective credence that I know which candidate is "better", where I'm using the word "better" subjectively to mean which candidate would turn out to do the most good for others, in my view, if elected. If you don't like this, please make up your own definition of better and keep reading :) In any case, 55% is pretty conservative; it means I consider myself to have almost no information.
At least $100 billion = the approximate marginal altruistic value of the "better" candidate. I think this is also very conservative. The annual federal budget is around $3 trillion right now, making $12 trillion over a 4-year term, and Barack Obama and Mitt Romney differ on trillions of dollars in their proposed budgets. It would be pretty strange to me if, given a perfect understanding of what they'd both do, I would only care altruistically about 100 billion of those dollars, marginally speaking.
I don't know which candidate would turn out "better for the world" in my estimation, but I'd consider myself as having at least a 55%*1/(100 million) chance of affecting the outcome in the better-for-the-world direction, and a 45%*1/(100 million) chance of affecting it in the worse-for-the-world direction, so in expectation I'm donating at least around
(55%-45%)*1/(100 million)*($100 billion) = $100
Again, this was pretty conservative:
That makes (70%-30%)*1/(5 million)*($700 billion) = $56,000. Going further, if you're
you get (90%-30%)*1/(3.5 million)*($7 trillion) = $1.2 million. This is so large, it becomes a valuable use of my time to take 1% chances at convincing other people to vote... which I'm hopefully doing by writing this post.
Now, I'm sure all these values are quite wrong in the sense that taking account everything we know about the current election would give very different answers. If anyone has a more nuanced model of the electoral college than Gelman et al, or a way of helping me better estimate how much the outcome matters to me, please post it! My $700 billion outcome value still feels a bit out-of-a-hat-ish.
But the intuition to take away here is that a country is a very large operation, much larger than the number of people in it, and that's what makes voting worth it... if you care about other people. If you don't care about others, voting is probably not worth it to you. That expected $100 - $1,500,000 is going to get spread around to 300 million people... you're not expecting much of it yourself! That's a nice conclusion, isn't it? Nice people should vote, and selfish people shouldn't?
Of course, politics is the mind killer, and there are debates to be had about whether voting in the current system is immoral because the right thing to do is abstain in silent protest that we aren't using approval voting, which has better properties than the current system... but I don't think that's how to get a new voting system. I think while we're making whatever efforts we can to build a better global community, it's no sacrifice to vote in the current system if it's really worth that much in expected donations.
So if you weren't going to vote already, give some thought to this expected donation angle, and maybe you'll start. Maybe you'll start telling your swing state friends to vote, too. And if you do vote to experience a sense of pride in doing your civic duty, I say go ahead and keep feeling it!
I've found a couple of papers by authors with similar thoughts to these:
Also, just today I found this this interesting Overcoming Bias post, by Andrew Gelman as well.
1 A nitpick, for people like me who are very particular about what they mean by utility: in this post, I'm calculating expected altruistic dollars, not expected utility. However, while our personal utility functions are (or would be, if we managed to have them!) certainly non-linear in the amount of money we spend on ourselves, there is a compelling argument for having the altruistic part of your utility function be approximately linear in altruistic dollars: there are just so many dollars in the world, and it's reasonable to assume utility is approximately differentiable in commodities. So on the scale of the world, your affect on how altruistic dollars are spent is small enough that you should value them approximately linearly.