Jan 24, 2011

The fallacy of the deciding vote

There is an obvious fallacy that is repeated by people who should really know better, including political philosophers:  the fallacy of the deciding vote.

For example, Thomas Christiano writes in Rule of the Many (25-26): "In the democratic case I am free to choose between two outcomes when my vote is the deciding one. The trouble with this argument is that this condition is virtually never satisfied. In large democratic societies, the winning option almost never wins by less than a thousand votes or so. In those cases, my vote does not decide the issue. Since I rarely, if ever, cast the deciding vote I will virtually never be free to choose the outcome."

Do you see the fallacy? The fallacious reasoning looks like this:
(1) There is an election in which the margin of victory is, say, one vote.
(2) There is one particular vote (e.g. "my" vote) that decided the election.

But (2) doesn't follow from (1) at all! (1) only implies that for any vote given to the winning side, subtracting that vote would change the outcome. But there is no one vote such that it is true of it and only it that removing it would change the outcome. (The only exceptions are votes of 1-1 or 1-0.)

No matter how large or small the election, with the two exceptions just noted, no one casts the deciding vote. You see the fallacy of the deciding vote from academic works on political philosophy to Hollywood films like Swing Vote, in which Kevin Costner's character "decides" the election. It's a popular fallacy, but not less the fallacious for being so.

As for why people are tempted by the fallacy, I think media coverage of elections in recent years plays a part. Turn on CNN during an election and you find exit polling data-- e.g., with 95% of districts reporting, Obama is favored 52% to 48%-- suggesting that the earlier votes somehow matter less than the later votes, with the later votes "deciding" the election. I imagine it'd be less tempting to perpetrate this fallacy in an age where elections were simply reported in the newspaper.


  1. It may be misleadingly worded, but it doesn't look like Christiano is committed to (2). He's saying that circumstances are hardly ever such that anyone gets to cast a deciding vote (i.e. a vote upon which the outcome is counterfactually dependent). That's compatible with holding that, in those rare occasions where one gets to cast a deciding vote, every other voter also cast a deciding vote.

  2. Richard, that's perhaps a more charitable reading. At best, I think the passage is deeply misleading.

  3. I think this misinterprets Christiano, since he's not out to show that any voter is decisive, but rather that no voter is (in practice). So his inference is from:

    1) No election (in practice) is decided by one vote.


    2) My vote is never (in practice) decisive.

    This doesn't commit him to saying that his vote would be the decisive one, had the election been won by a single vote. The point is that a winning margin of greater than one is sufficient (but need not be necessary) to show that his vote isn't decisive.