Wednesday, October 11, 2006

Voting (Sean)

I'd like to hear responses to the following simple argument that voting for Nader in 2000 was at least as rationally defensible as was voting for Gore.

Either (a) a choice of vote should be based only on the expected value of its impact on the outcome of the election, or (b) it should be based on other considerations, such as, to name a couple of possibilities, the value of expressing one’s political opinions, the value of avoiding pangs of guilt, a civic duty to vote, etc. If (a), then the choice of whether one should vote should also be based only on the expected value of the impact on the outcome of the election and, therefore, leftists (nor anyone else for that matter) should not have voted, and everyone who did vote was equally irrational in doing so, given the vanishingly small probability of casting a vote that would have changed the outcome of the election and the small but genuine costs of voting. If (b), then it was rational for leftists to vote for Nader if they had the appropriate expressive preferences or if a civic duty required sincere voting of them, etc. These conditions were met for most Nader voters if they were met for most Gore voters. Hence, (most) Nader voters' vote for Nader was just as rationally defensible as the choices of (most) Gore voters.

Thoughts?

5 comments:

Sean said...

I take it this argument doesn't merit comment because it's so obviously sound!

Jesse said...

With regards to (a), I finally did some calculations to see what the probabilities actually were, and I was somewhat surprised. Perhaps concrete numbers will help the discussion:

Suppose that there are 10 million voters (the average swing state, maybe), and each voter has a 50% chance of voting for Gore and 50% chance for Bush. Suppose that Gore gains G votes and Bush gains B votes. The probability that G = B is .025%, which is small. Also noteworthy is that the probability that G and B are within 100 is 2.4%, and within 1000 is 24.3%.

Now compare these numbers to the following scenario. Suppose that now each voter has a 5% chance of voting for Nader, and he earns N votes. The probability that N is at least 4 million (i.e. 40% of the votes) is about
.0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
0000000000000000000000000
00000000000000000000000001

I put the zeros in there for effect. There are 500 of them.

The point is that there is may be an argument to make about voting for Gore based on probabilities (the numbers are small, but not horribly so); but voting for Nader based on probabilities is simply unjustified.

Sean said...

Thanks for the information on probabilities. A probability of .00025 is small, but I can entertain the thought that it was rational for Gore voters to get to the polls, given a sufficiently large difference between the values one attaches to Gore's versus Bush's presidency--and it would certainly be large, although from the vantage point of 2000 one might have expected a less disastrous, albeit still awful, presidency from Bush. Just to give one a sense for the ballpark in which these values would have to fall, for someone who valued an hour of leisure time at $10--which is not very high, relatively speaking--they would have to be willing to pay at least $40,000 to change the outcome from a Bush to a Gore victory. In evaluating the rationality of Gore voters by this standard, we should keep in mind that the probability of casting a decisive vote in 2000--estimated before it was known how close it would turn out in Florida--had to have been smaller than .0025, and most Gore voters could earn more (although perhaps not much more) than $10 an hour.

But (as Jesse proposed in a phone conversation) even if one's decision to go to the polls and one's decision to vote for a candidate can be rational and not be based solely on the expected value of one's impact on the election outcome, the expected value of one's impact might still be relevant. It might be rational for California voters to go to the polls and vote for reasons independent of the expected value of their impact on the outcome, but perhaps these other considerations, whatever they may be, get outweighed or trumped when the expected value of one's impact is sufficiently high. And, one might further argue, even if Nader voters in Florida would not have been willing to shell out $40,000 for a certain Gore victory, they should have been willing to do so. Perhaps they should have known that Bush was considerably more likely to engage in imperialistic wars that would result in the deaths of hundreds of thousands of people, and the avoidance of these deaths (even when discounted by the less than certain probability that Bush would engage in said wars) and the avoidance of all the other horrors of Bush's presidency that Gore probably would not have wrought are surely more important than keeping $40,000, and in such a case, one might argue, some Nader voters (e.g., those in Florida or other swing states) should have voted for Gore, even if it's true that voters elsewhere could justify their decision to vote and choice of candidate independently of their expected impact on the outcome of the election.

There are two questions raised by that line of reasoning. (1) Does it make sense to say that the expected value of one's impact on the outcome is a consideration that can outweigh or trump the otherwise valid reasons one has to vote sincerely? (2) Should Nader voters have estimated the expected value of Gore's victory so much more highly than Bush's, given the beliefs that it was reasonable for one to have in 2000? In response to (2), I am inclined to say yes, because of the war in Iraq and global warming. On the other hand, most Democrats were happy to give Bush the green light for Iraq (I forget what Gore's opinion was in 2003), and Gore's record in the White House in the '90s makes one less optimistic than his recent film does about what he would have actually gotten accomplished had he been elected.

As for (1), it's an easy case if the other considerations are things like the value of expressing one's preferences or avoiding pangs of guilt. Clearly, such considerations can be outweighed by the expected value of one's impact on the outcome. All of these considerations are consequentialist considerations, and there are surely ways of valuing all of the different consequences in question so that the answer to (1) comes out affirmative. But what if the alternative type of reason that rescues the rationality of, say, California voters is not even consequentialist? What if, to give just one example of what I have in mind, it is rational for them to vote because it is rational (and perhaps morally obligatory) to act on those principles such that, if everyone regulated their behavior according to those principles, things would go best? If everyone accepted the principle of voting for candidates whose platform had certain desirable features (say, those had by Nader's platform), then things would go much better than if everyone accepted the principle of voting for candidates who basically accept the status quo in this country (as did Gore). If these sorts of non-consequentialist considerations can be relevant, then it is not obvious how the expected value of one's impact on the outcome could trump or outweigh these considerations.

Sean said...

As any attentive reader noticed, it was silly to cite the war in Iraq as a reason why Nader voters should have greatly valued the difference between a Gore and Bush victory, as I did in my comment above. Not sure how that happened. But in any case it's clearly wrong; Bush was even contrasting himself with Gore/Clinton by his unwillingness to engage in "nation-building" wars, for what little that promise was worth to a rational, Bayesian Nader voter forming expectations about Bush. So I guess the $40-$80K difference in valuations would have to rest on issues like global warming and tax policy.

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