Does My Vote Matter?

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I must confess that I'm a bit intimidated debating such a venerable institution as the League of Women Voters, so I acknowledge that this is an uphill battle.  Here are a couple of thoughts on votes making the difference.  I have no quarrel with the claim that "one vote can make the difference," and there are indeed numerous examples of situations in which one vote has mattered.  There is a big difference between the possibility that a single vote can make a difference (which certainly exists) and the probability that a single vote will make a difference (which is practically zero in cases where there are millions of voters).  Let's look at the cases discussed by the League point-by-point:

1.  "In 2005, 1 Vote killed legislation banning discrimination against gays and lesbians in the State of Washington."  The League cites the measure's 25-24 defeat in the State Senate.  True enough.  But this was a vote among a relatively small deliberative body, not a national election.

2.  "In 2000, 1 Vote decided the presidential election."  Indeed, the Supreme Court voted 5-4 in favor of George W. Bush.  Again, though, this was a nine-person deliberative body and not a national election.  It is probable that such small polities will feature outcomes in which one vote matters, but again this does not suggest that a single vote will matter in a national election.  I'm sure we could all think of cases where in groups of three, four, five, or however many a single vote was decisive when the question was about where the group should go to dinner, but again, this is incredibly unlikely in a national election.

3.  "In 1994, 1 Vote would have decided a Wyoming state representative election."  Now we're getting somewhere.  Again, though, scale is what matters.  Wyoming has the lowest population in the US, so this shouldn't be too surprising.  The question, though, is what would have been the marginal difference in policy attributable to one legislator or another, and how does that compare to the costs of voting?  My guess is that the former is small relative to the latter.

4.  "In 1986, 1 Vote raised Iowa's drinking age from 19 to 21."  There's no context for this.  Was this a popular referendum?

5.  "In 1978, 1 Vote decided an Alaska state senate election."  Alaska is also a very sparsely populated state, much like Wyoming.  This isn't terribly surprising.

And so on.  I'm not convinced by examples of Supreme Court decisions in which a single vote matters; this says little about the probability that a single vote will matter in a national (or statewide, or usually even local) election.  And while there are some examples of a single vote mattering, these are buried under an avalanche of counterexamples in which a single vote failed to make a difference.  To use my own experience as an example, I've voted regularly in state, local, and national elections in four different states since I turned 18.  Not once have I voted in an election that would have had a different outcome had I voted differently or just stayed home.