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Should the Rational Public-Spirited Person Vote?

Ilya says yes, drawing on this very interesting article of his. Here is his explanation (inspired by Derek Parfit):

Assume that Uv = the expected utility of voting; Cv = the cost of voting; and D = the expected difference in welfare per person if the voter's preferred candidate defeats her opponent. Let us further assume that this is a presidential election in a nation with 300 million people; that the voter's ballot has only a 1 in 100 million chance of being decisive (Riker and Ordeshook 1968); and that the voter values the welfare of his fellow citizens an average of 1000 times less than his own. Thus, we get the following equation:

D*(300 million/1000)/(100 million) -- Cv = Uv.

If we assume that Cv is \$10 (a reasonable proxy for the cost of voting) and that D is \$5000 (this can incorporate monetary equivalents of noneconomic benefits as well as actual income increases), then Uv equals \$5, a small but real positive expected utility.

If you care about the well-being of others, even a little bit, you should vote, despite the cost of voting. The reason is that the cost of voting is very low, while the benefit is not as low as you might think. Although your chance of breaking a tie is very low, the benefit from breaking a tie is very high—it's felt by 300 million people. This multiplier effect offsets, to some extent, the very small chance that your vote will make a difference.

However, breaking a tie is beneficial only if your vote is more likely correct than not—that is, you actually vote for the better candidate. Surely your vote is more likely to be correct than not? After all, you have some information, and that means you are doing better than flipping a coin. However, you need to reflect on your own ignorance with some humility. If, by hypothesis, your vote breaks a tie, then it means that (putting aside the vagaries of the electoral system) half the country prefers one candidate and the other half prefers the other. If all of these people have enough information that their votes are not random, the existence of a tie (aside from your vote) indicates that the two candidates are almost exactly equal in quality. The probability that your own puny knowledge (elsewhere in the same article Ilya discusses the problem of rational ignorance—people have weak incentives to inform themselves about the candidates and policy in general) will distinguish the infinitesimally better candidate is itself infinitesimal.

In other words, D, the expected difference in welfare per person if the voter's preferred candidate defeats her opponent, is not realistically \$5,000; more realistically it is in the range of \$0.000000005. Using the equation above, your expected utility from voting is a shade higher than negative ten dollars. Ilya, stay home!

Related Posts (on one page):

dm:
Posts like this make me wonder why I am bothering to get my Masters in Political Science. I realize the post was done in a joking manner, but I don't get the value of this type of quantitative "analysis". What does it tell us really? Everyone votes or doesn't vote for their own reasons and to measure the utility you would need to get inside the head of each person. As for making a difference, it seems that every person who votes for one of the two major candidates has the same chance of making that difference.
10.31.2008 11:08am
TJIC (www):
Interesting analysis.

Because of the electoral college, the likelihood of a vote changing the election depends on what state you vote in.

In Massachusetts, the P of my vote changing the electoral vote is 0.00000000000000000000000.

However, I do care about a lot of other issues (e.g. state income tax repeal), so I will go to vote ... even if I will abstain from voting for either of the major party presidential candidates.
10.31.2008 11:08am
anomdebus (mail):
My view is this: elections are about taking the temperature of the country's politics. The only way you can get an accurate view is if you sample as many as possible. Imagine if you were literally trying to take the temperature of a substance and only the most active atoms bothered to strike the thermometer. You would get an inaccurate reading of the substance's temperature..

I also wish people would vote for what they want, also for the same reason. I have thought at one time that if given a political wish, I would have everyone who is eligible vote for the candidate that best supports their views, even if just once. There is a fair chance the winner would not be my view, but it would shake things up enough that it is unlikely to go back to the current equilibrium.

(nb my political procedural wish would be to get rid of singel vote winner takes all elections, though work should be done to figure out the best alternative)
10.31.2008 11:13am
cboldt (mail):
My point of view is that when the government has such a big impact on one's personal life that the vote is that important, "Houston, we have a problem here." Government should be of trivial importance (as to individual personal impact/benefit), in the land of the free.
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Fed up with government? Don't feed it. Don't legitimize it with a ballot, and don't contribute to it financially. Join a monastery, take a vow of poverty, and do something spiritually rewarding.
10.31.2008 11:13am
anon.:
"After all, you have some information, and that means you are doing better than flipping a coin."

Given the harmful biases people have when making political decisions (See The Myth of the Rational Voter), it would probably be better if people flipped a coin. Or just stayed at home.
10.31.2008 11:27am
Ken Arromdee:
If all of these people have enough information that their votes are not random, the existence of a tie (aside from your vote) indicates that the two candidates are almost exactly equal in quality.

Now imagine that a few million people happen to all prefer one candidate, but they all also use this line of reasoning. (Obviously people willing to use reasoning must be unevenly distributed among the candidates.)

They will each conclude that their vote isn't important because they could only make a difference if the candidates are tied, and therefore equal in quality. Yet the few million votes as a group could make a difference even if the candidates are not tied.

The key is that it's not always good to think "what would happen if I did something different and everyone else acted exactly the same". If you are acting logically, the fact that you did something different means that other people would also do something different, because their reasoning would lead to the same conclusion as yours.

This is http://en.wikipedia.com/wiki/Superrationality without the emphasis on cooperation.
10.31.2008 11:30am
Aultimer:
By the author's own reasoning, the final line suggests that Ilya does not "care about the well-being of others, even a little bit". Since the communication is between two law professors, I consider this confirmation of everything I suspected about that profession.
10.31.2008 11:34am
cboldt (mail):
-- They will each conclude that their vote isn't important because they could only make a difference if the candidates are tied, and therefore equal in quality. Yet the few million votes as a group could make a difference even if the candidates are not tied. --
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The public isn't engaged in making rational and reasoned decisions. It's being led around by polls that purport to predict the results, and by sound bites.
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As a thought exercise, imagine the scene from announcement of candidacy until counting of the ballots, if the interim was conducted without poll results being reported. IOW, force people to decide on just the sound bites, or whatever else they decide to dig up. No more ability "vote/not vote" based on a predicted poll result.
10.31.2008 11:36am
cboldt (mail):
-- the final line suggests that Ilya does not "care about the well-being of others, even a little bit". Since the communication is between two law professors, I consider this confirmation of everything I suspected about that profession. --
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Bugs you that they don't subscribe to "to each according to his needs," eh?
10.31.2008 11:38am
PLR:
Since we have two opposing theories, each of which is plausible, I suggest that Ilya vote, and Zywicki stay home.
10.31.2008 11:43am
fortyninerdweet (mail):
My own voting motivation has become "how may I best neutralize the voters in another area who are [selfishly, imo] voting for the worst candidate?" ie: The multi-term pol that most works the earmark system?
There is 0.00000000000% chance I would take a moment to consider my political knowledge to be "puny", so that equation must fail, even though one accepts adaequatio intellectûs nostri cum re
10.31.2008 11:46am
Sasha Volokh (mail) (www):
Humility about one's correctness in light of the assumed 50-50 split is relevant if you think other people's views are relevant to the truth. This may be false in a couple of ways relevant to Ilya:

(1) If everyone is badly informed or votes for reasons unrelated to the truth, then Ilya, who's better informed than most, can still rely on his own views.

(2) If one's own views are moral/ideological, like a view that only libertarianism is just, then everyone else's views -- even if they're all Ph.D.s -- are likewise irrelevant. Unless they're really trying to answer the same question, for instance if I disagreed with lots of Ph.D. libertarians, in which case humility would again be in order.
10.31.2008 11:46am
Pragmatist:

If we assume that Cv is \$10 (a reasonable proxy for the cost of voting)

This is a laughable approximation. First, it takes at least an hour of the average voter's time to vote and most people value their time at more than \$10 an hour (if not, you can mow my lawn for \$10/hour whenever you want).

Second, transportation costs need to be factored in as well, which by itself is likely \$5-10 on average.
10.31.2008 11:51am
Anderson (mail):
Ilya, stay home!

Anderson, J., concurs in the judgment.
10.31.2008 11:52am
Pyrrhus (mail) (www):
This model is all well and good. But I'd bet most people don't experience a utility function that has a multiplier for the number of people affected past a certain point. IE few people will experience more utility from swinging a 200 million person election than a 300 million person election.

Meanwhile as population goes up, odds of swinging the election still go down.
10.31.2008 11:57am
TerrencePhilip:
Eric,

I think you are overlooking something: voters' desire to reap the benefits of turnout. Politicians know which neighborhoods people always turn out to vote in, and the neighborhoods they don't. It may not matter for a president or governor. But if your city council or state rep hears from you one day, and they know that you are from a high-turnout part of town, your needs may get more attention. The presidential election is not close in my state, for example, but even if there were not other races on the ballot I care about, I would still go vote because it does a little bit to keep turnout high in my neighborhood. This, it seems to me, is a very rational choice.
10.31.2008 11:57am
Pyrrhus (mail) (www):
I guess my comment is more relevant to Ilya's model btw...
10.31.2008 11:58am
cboldt (mail):
-- First, it takes at least an hour of the average voter's time to vote and most people value their time at more than \$10 an hour (if not, you can mow my lawn for \$10/hour whenever you want). --
.
How do figure the cost when the activity is leisure? What about when done at leisure, or in lieu of alternative leisure?
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How do you figure the cost of becoming informed? Of forming an opinion? Is that to be "wasted" if undertaken, or not undertaken at all?
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And as for direct cost, vote absentee. A few stamps. Probably in the 2 buck area. A substantial number of people have access to free transportation by either of the major parties, who field GOTV operatives.
10.31.2008 12:01pm
frankcross (mail):
Sasha, I think your point is answered by Bill Buckley's preferences about being governed by random folks rather than Harvard professors. Being better informed is marginally relevant to choosing a better president, but even the very well informed are often wrong. Having an ideology, though, seems irrelevant. The ideology may be a wrong one. Why no humility about ideology?
10.31.2008 12:07pm
Eli Rabett (www):
the utility of a vote extends beyond winning. Having a large(r) majority allows the winner to govern more effectively, and having allies elected (legislative and executive) who appear on the same ballot also allows one to carry out a mandate that could easily be frustrated with a narrow individual win.

Whoever did this calculation did not think very deeply. As an example of the power of a large win think Reagan in 1980, who was able to overcome a Democratic Congress because of the size of his vote. As to the advantage of bringing allies along with you think FDR. For the problems of a narrow win which leaves your opponents standing think Truman in 1948.
10.31.2008 12:10pm
EdwardF (mail) (www):
The fact that most elections aren't perfectly 50/50, and that even a 51/49 drastically cuts your chance of affecting the outcome, sets the probability unimaginably lower than just one in 100 million.

http://www.slate.com/id/2107240/
10.31.2008 12:14pm
BABH:
OK, but now say that Prof. Somin values other people as much as 1/100th as he values himself. This is not unreasonable - most folks would like to think that they would lay down their lives to save 100 others. Say also that the cost of voting is closer to \$100.

Now the calculation gives us a positive utility of \$50.

I think TerrencePhilip is on to something, though. The benefits of voting in local races are much higher (perhaps distributed over fewer people, but they are people you care about more). And once you are in the voting booth, the marginal cost of voting in national races is \$0.
10.31.2008 12:14pm
donaldk:
Categorical Imperative. An important principle of ethics. You must vote AS IF it made a difference. If not, how would it be if everyone acted that way?

Goodbye, self-government.
10.31.2008 12:26pm
BABH:
donaldk:

The categorical imperative is a seriously deficient principle of ethics, and utterly useless as a practical guide to behavior.

If everyone acted acted according to its precept when choosing a line of work, we would have no division of labor. Everyone would *have* to be a farmer (or a hunter-gatherer). The choice of any other profession would result in famine.
10.31.2008 12:47pm
BABH:
Come to think of it, I think I just offered a proof that being a lawyer is inherently immoral.
10.31.2008 12:48pm
Eli (mail) (www):
I have a different critique. Suppose that by unanimous acclamation, the voting public decided that it would solicit a bid from Ilya to decide the election. That is, if Ilya's bid were high enough, the public would go along with McCain or Obama, whichever Ilya preferred. What is the maximum that Ilya would bid to have this privilege. According to the numbers in his example, Ilya seems to think that it is plausible to bid \$1.5 billion. Even if Ilya had such a sum of money, I really doubt he would blow it all on picking the next president (out of a crappy field).
10.31.2008 12:49pm
Oren:
Voting in Oregon (everyone votes by mail) was even less of a burden. If you only want to vote the big-ticket races, it's no more than 2 minutes to fill out the ballot and drop it in the mailslot (+\$.50 for a first class stamp).

What is the maximum that Ilya would bid to have this privilege. According to the numbers in his example, Ilya seems to think that it is plausible to bid \$1.5 billion.

This is contingent on his assumption that he values others welfare at 1/1000th of his own on a per capita basis. That's all well and good for a single person (give the bum on the street \$1) but for 300 million other people, it's not realistic.

The amount of weight you put on other's welfare is a lump-sum, not a per-capita value.
10.31.2008 12:55pm
BABH:
America seems to think that the Presidential race is worth spending \$5.3 billion.

\$1.5 billion would be a steal!
10.31.2008 12:57pm
arbitraryaardvark (mail) (www):
Ilya understates both the costs and benefits of voting.
Let's say \$50 is a better approximation of the opportunity costs of informed voting.
I live in a district where a recent council election was decided by 5 votes, and the next state rep over won by 8 votes. I have 8 friends, I think. In my state there's usually one or two races decided by a flip of the coin after a tie.
My precinct leader knows whether or not I vote. That might be relevant to whether my trash gets picked up on time.
Voting is a vestigal social norm. Not voting was deviant, and there's still a bit of that attitude floating around.
Voting is entertaining. I get more entertainment from the election than from the world series. Might as well get a good seat.
My social networks include people that I work on campaigns with. I've gotten a job once based on a campaign contact; I've gotten jobs for people who've helped me campaign, and one time I didn't get a job I'd been offered because they found out who I campaign for.
Voting is a nice way to meet some of the little old ladies who live in my neighborhood.
In my case I have a bit of extra incentive - I have a hobby of litigating election issues,and I should get back to work...
10.31.2008 1:06pm
anomdebus (mail):
Another thing I don't like about this sort of theory is that it falls into the "it is true as long as not too many people believe in it" type of fact. In other words, it becomes less reliable in truth the more persuasive it is.
10.31.2008 1:26pm
q:

My view is this: elections are about taking the temperature of the country's politics. The only way you can get an accurate view is if you sample as many as possible.

Only half of all eligible voters actually vote, yet the outcomes have been very good representations of the population. You could probably get very accurate views with 10% voting, even with the self-selection problem.
10.31.2008 1:43pm
Ubu Walker (mail):
Whether people vote is a straight forward question of utility, IMHO. In Australia, there is 95% turnout. Unless you are excused by a court, there is a penalty of \$20 AUS to \$50 AUS for failing to vote. This suggests that the marginal utility for whether to show up to vote is between \$20 to \$50, roughly, I imagine, what losing 2 to 4 hours of work would mean to an average person. Of course, this suggests strong social and legal significance to voting in Australia that might not apply to the US, but it is illustrative of the marginal utility of not voting.

So, the question is, would you pay \$20 instead of voting? If the answer is yes, you don't vote.

This explains lots of voters behavior. For example, someone who is 65+ is likely to vote for someone who will increase medicare benefits, since that translates to a benefit of hundreds of dollars a year. Someone who is 18 years old might not feel any incentive to vote because there is no draft and they aren't receiving any direct benefit from the government that they can quantify for themselves. However, there will be more young people voting in this election because they are unable to get health insurance through their employers...and the possibility of getting that benefit is greater than ever...which translates into a greater likelihood of voting.
10.31.2008 1:57pm
cboldt (mail):
-- Unless you are excused by a court, there is a penalty of \$20 AUS to \$50 AUS for failing to vote. --
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Freedom of choice, Aussie style.
10.31.2008 2:23pm
Calculated Risk:

This is a really excellent question. I would be interested in Sasha's answer as well.
10.31.2008 2:49pm
cboldt (mail):
-- Why no humility about ideology? --
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See James Burnham's "Suicide of the West" for one man's take on that question.
10.31.2008 3:01pm
einhverfr (mail) (www):
Yes you should vote. Why? Because politicians want your vote.

However, you shouldn't assume your vote matters by itself. It is far more important to talk to the politicians who represent you frequently. Otherwise all they hear is from lobbyists.....
10.31.2008 3:04pm
Tomm:
I completely disagree
that the voter values the welfare of his fellow citizens an average of 1000 times less than his own

I may value the welfare of a single random citizen 1000 times less then my own, by I do not value the welfare of 300,000,000 citizens at 1/1000 of my own on average. That would imply that the value of welfare of others scales linearly with the number of citizens. It also implies that I value the welfare of all citizens at 300,000 times my own. Both are ridiculous assumptions.
10.31.2008 3:06pm
anomdebus (mail):
Only half of all eligible voters actually vote, yet the outcomes have been very good representations of the population[1]. You could probably get very accurate views with 10% voting, even with the self-selection problem[2].

How do you know your first claim is accurate and how certain can you be of the second claim?

I believe there is a significant percentage (5-10% of all voters) of non-voters who do not vote just based on the lack of viable choices. If they had reason to vote, I believe together they could make a difference.

Unfortunately, I don't think we will have the chance to see whose intuition is more correct.
10.31.2008 3:18pm
KevinM:
If your vote isn't "more likely correct than not," then you should weigh the options carefully, decide whom to vote for, and then vote for the other candidate. Problem solved! After all, it worked for George Costanza:

http://en.wikipedia.org/wiki/The_Opposite

George: Excuse me, I couldn't help but notice that you were looking in my direction.
Victoria: Oh, yes I was, you just ordered the same exact lunch as me.
George: My name is George. I'm unemployed and I live with my parents.
Victoria (with a huge smile): I'm Victoria, hi!
10.31.2008 3:26pm
BABH:

That would imply that the value of welfare of others scales linearly with the number of citizens. It also implies that I value the welfare of all citizens at 300,000 times my own. Both are ridiculous assumptions.

Is it a fair assumption that Tomm never served in the military?
10.31.2008 4:08pm
Rodger Lodger (mail):
Something about the problem of whether it's rational to vote causes people to make the same errors over an over. Above, somebody says turnout can be important. How does that make it rational to add your one puny vote? (I assume you don't live in a town of, say, 78 voters). Another person says he lives in a state where it doesn't matter, presumably because it is heavily leaning toward a party. But even if you live in a closely divided state, what are the chances of your vote being decisive to swing the state's electoral votes? Then there's the argument I've been hearing all my life: "what if everybody thought like you, nobody would vote!" I patiently explain there is no evidence to believe people will be influenced or controlled by my decision not to vote. Actually, in fact I do vote, because other than taxes and the Post Office it's my only contact with the federal government, and I like to keep in touch.
10.31.2008 4:43pm
Tomm:
Is it a fair assumption that Tomm never served in the military?

There is a wide range of values greater than 1 and less than 300,000.
10.31.2008 4:49pm
anomdebus (mail):
Ah, that is another analogy, immunization. If you were the only one not getting the immunization, then that inaction is unlikely to have any effect. However, if this belief becomes widespread, then infectious disease can get a foot-hold.

I am not suggesting this as a strict analogy, suggesting only a supermajority voting will keep us all from dying. However, it is the same sort of argument against: how can my one act affect others?
10.31.2008 4:59pm
Duffy Pratt (mail):
How does the same analysis apply to voting for all-star games?

Rationality, especially when it has to be "economic" rationality, is way over-rated. By the way, I think its fairly safe to say that following this blog, at least for the vast majority of the followers, is fundamentally irrational.
10.31.2008 5:20pm
Greg Q (mail) (www):
Well, if you're voting for Obama, I encourage you to follow the advice you gave.

OTOH, you greatly overestimate the cost of voting. I don't gather information about the candidates because I'm going to vote, I gather information because I'm interested in politics. I don't have to take time off from work to vote, so that's not a cost. The cost to travel to my polling space is about \$0.10, using IRS travel costs (of course, I could walk, and get some exercise while I'm at it).

GIGO.
10.31.2008 6:36pm
Duffy Pratt (mail):
Greg Q:

You do understand that gathering information because you are interested in something is irrational don't you? Surely you could be doing something else with your time to make more money. Since you've already admitted you behave irrationally, then why does it matter to you whether voting is rational or irrational.
10.31.2008 6:42pm
Pragmatist:

How do figure the cost when the activity is leisure? What about when done at leisure, or in lieu of alternative leisure?

It's very difficult to determine the utility of leisure, but I don't think it matters since hardly anyone would characterize the hassle of voting as leisurely.

How do you figure the cost of becoming informed? Of forming an opinion? Is that to be "wasted" if undertaken, or not undertaken at all?

Again, very hard to determine and again I doubt it matters since the average amount of voter initiated information gather is pretty low.

And as for direct cost, vote absentee. A few stamps. Probably in the 2 buck area. A substantial number of people have access to free transportation by either of the major parties, who field GOTV operatives.

A little more than half (28) of the states allow no excuse absentee voting, but since few people take advantage of it there will be little effect on the average cost. Far fewer people than that will use any form of free transportation, so again it changes the average cost of voting very little.

OK, but now say that Prof. Somin values other people as much as 1/100th as he values himself. This is not unreasonable - most folks would like to think that they would lay down their lives to save 100 others.

Not a reasonable comparison, many people will give up their life to save one other life, and at the same time wouldn't give up \$100 they earned so that 1,000 other people could have \$100 they didn't earn.
10.31.2008 7:01pm
Tinhorn (mail):
In most Presidential elections, my personal Uv has been negative. That is, the guy who won ended up disappointing me so much that I wished I hadn't voted for him (or, was glad I hadn't voted for him). If a particular person thinks his personal Uv of voting for either main candidate will be negative (that is, thinks it more likely than not that he will end up regretting his vote), isn't it perfectly rational for that person not to vote?
10.31.2008 7:51pm
TerrencePhilip:
Something about the problem of whether it's rational to vote causes people to make the same errors over an over. Above, somebody says turnout can be important. How does that make it rational to add your one puny vote? (I assume you don't live in a town of, say, 78 voters).

Rodger Lodger,

My "town" consists of more than 78 voters, but city council and state rep districts, along with some other local and sub-local districts, are small compared to statewide elections- even if quite large compared to "78." But politicians know by area of town, block by block, where turnout is very high. A state rep might not know you but if your letter to him comes from an address in a neighborhood where there's a high level of civic involvement he's likely to pay close attention. So I don't need to think my one vote will turn the election for a city councilmember or state rep to know that votes from my precinct matter.

Sure, as you suggest, my one vote does very little to boost "turnout." I could comfortably free-ride on the turnout of my neighbors if I wished. On the other hand voting is practically costless, and I draw some amount of utility from knowing I'm contributing to turnout, as well as from voting for specific candidates and issues. Eric's post did not seem to count these as a benefit to voters, instead focusing only on whether the individual voter could make a difference in an individual election.
10.31.2008 8:26pm
juris_imprudent (mail):
Eric-

Since you want to assert the utility of voting, I would like you to explain what is the measure of utility you are using. If you can't define that, the rest of the argument is really rather pointless.
11.1.2008 3:35pm
juris_imprudent (mail):
This suggests that the marginal utility for whether to show up to vote is between \$20 to \$50

Absolutely wrong. You cannot impute utility based on the disincentive. Utility is not expressed in monetary terms.

What you are talking about is the cost of conformity.
11.1.2008 3:38pm