your vote doesn’t count
One of the first things you learn when you study social choice theory is that your vote will almost never make a difference. That is, if you calculate all the possible votes that a group of N people can cast, there is a very, very, very, very tiny chance that the margin of victory will be one vote. And it makes sense – most elections with moderate or large size electorates are decided by thousands, or millions, of votes.
But what about all those stories you hear from your civics teacher about how one vote could’ve avoided disaster? Like how Hitler rose to power from one vote in his party? Or that one vote saved America from becoming a German speaking nation? The Urban Legends reference page lists how most of these stories are either outright falsehoods or distortions. For example, the truth about Hitler and the Nationalist Socialists is that his party members voted almost unanimously, with one nay vote. The opposite of the “one vote” fallacy. To be generous, the story about Andrew Johnson escaping an impeachment conviction is true, but not in the way your civics teacher taught it. His opponents were one vote shy of the 66% needed for a presidential removal. One vote short, but not a 50%-50% split and it was a small electorate of 54 senators.
But you ask, surely, are there elections that actually were decided by one vote? The answer is yes, of course, but it is extremely rare. Probably the best source on the frequency of such pivotal votes is a 2003 paper in Public Choice by Casey Mulligan and Charles Hunter called “The Empirical Frequency of a Pivotal Vote.” They do a simple exercise: examine the vote tallies in 16,000 Congressional contests and 40,000 state legislative elections. The answer: there might have been 1 pivotal vote in the Cognressional races, possibly 9 in the state elections.
Aha! 1 vote does count – at least 1 in 40,000 times! Not so fast. Mulligan and Hunter have some more bad news for the “every vote counts crowd.” They consulted newspaper accounts to verify the close elections. Turns out that recounts often changed the final official vote tally. Most electoral systems have a bunch of rules that reduce the chance that a one vote margin will actually become the last word.
So what’s a civics teacher to do? They should just admit one vote almost never makes a difference and that we have some good rules to reduce these one vote outcomes. And maybe it’s a good thing – do you want a system that frequently puts a lot of power into small groups of voters?
Gerry Mackie. Democracy Defended (Cambridge, 2005).
Kieran
August 31, 2007 at 2:52 am
I remark though, that amongst the many stories proven to be embellishments of the truth or outright fabrications, one is not seriously challenged: that the French Republic was instituted on a one vote margin. There is some basis to that. After the crushing defeat against prussian armies in 1870-71, french institutions were quite unstable, oscillating uncomfortably between leftist republicanism, centrist constitutional monarchy and rightist semi-absolutist monarchy. The parliament had a comfortable royalist majority but the split between contitutional and semi-absolutist was getting wider. Enventually, an innocuously-looking legislative amendement instituted the Republic. “En première lecture”, as we say, it was adopted by 353 in favour and 352 against. Of course, subsequent votes on it passed with increasing margins. It was one of many small steps towards the Republic, but it was the very first time that enough defenders of the constitutional monarchy sided with the republican left to gain a majority. Never again would monarchy be a serious constitutional proposition in France.
Z
August 31, 2007 at 7:32 am
Oh, and just in case you are wary this a myth, you can have look, say, at http://www.asmp.fr/travaux/exceptionnelles/drago_wallon.pdf
The paper linked does a good job of putting the anecdotal one vote margin in context while still showing that it indeed was a significant symbolic turning point (it is in French though).
Z
August 31, 2007 at 7:36 am
I think of the fixation on single decisive votes rather uneconomical, which may be fine if you’re a political scientist, but not so much for the economics branch of this line of reasoning. Even if single-vote margins are rare (though 1 in 5600 — in races partly engineered to avoid close votes — isn’t exactly Powerball odds), very close elections are not (presidential vote in Florida, 2000, anyone?).
Seeing as economists might tend to think of a smooth schedule of net costs and benefits at the margin of participation, or preferences over candidates, it makes more sense to my mind to think in terms of replications. Replay an election, and various groups of voters near the margin will shift in and out of the electorate with smallish variations in the conditions that determine whether they decide to vote (or may come up tails instead of heads in near-random choices over candidates), and some close outcomes will change as a result.
Tom Bozzo
August 31, 2007 at 7:02 pm
Dr. Rojas,
(I may be a little off topic here; but I hope you get my point).
I have to disagree here. The 8th grade civics teacher should continue as such. By civics teachers speciously putting forward the power of one vote, they are, probably unwittingly, getting behind the quantitative obscurity of the political process. And thus making known what matters in politics: PUBLIC OPINION.
Additionally, the “civics lesson” is essentially a “thick description” of how democracy exists; that is, how it impels politicians to vote for whatever is popular.
Brian Pitt
August 31, 2007 at 10:36 pm
[...] No! not every single vote counts; and, Fabio also explains why that is a good thing; [...]
Friday late night links « Entertaining Research
September 1, 2007 at 4:17 am
Few elections are close, therefore “your vote will almost never make a difference.” There may be something wrong with this logic. If Candidate A beats B by 20,000 to 10,000, you are saying to 20,000 people that their votes didn’t make a difference. It makes sense only if you think of “making a difference” as something only individuals can do, or if you think that the only vote that made the difference was the 10,001st. And if the latter, then I can think that I did in fact make the difference because mine was the 10,001st vote. The 10,000 that came before and the 9,999 that came after — those were the votes that didn’t make a difference.
It sounds silly, but it’s the same logic that lets us to talk about a “game-winning basket” — the last shot of a close game — as though nobody else’s baskets contributed to the win. Or to blame the guy who, with his team down by one point at the end, misses two free throws. We blame him for the loss; we rarely look at all the fifteen free throws missed by his teammates in the previous 47.9 minutes of play and think that they made the difference.
Jay Livingston
September 3, 2007 at 12:06 pm
Each and every vote counts for without votes there would not be an election. If each voter thought their vote did not matter and stayed home there would be a tie of 0 to 0. If the outcome would have been 5% difference between candidate A and candidate B with A winning, and 10% of the voters did not vote but would have voted for candidate A, the abstentions would have allowed B to be elected. To every action there is a consequence. I’d rather have my consequence be an added vote for my candidate whether he win or lose.
I have probably the most comprehensive list of “One Vote Occurances” on the web at http://www.TimeLinesOfLiberty.us
I had recently posted one entry in the “by State” occurances where the incumbent won by one vote then, after a judge disallowed 27 votes and allowed one uncounted challenged vote, lost by one vote.
Roger W Hancock
October 1, 2007 at 2:02 am