Electoral Metaphysics

As General Election time rolls round again, it's time to address the age-old question, is it really worthwhile to vote?

The case against is made most eloquently by Steven Landsburg in the context of last year's US presidential election. The probability of one vote making a difference to the outcome is negligible -- comparable to winning the lottery 1000 times in a row.

There are some objections that can be made to this, most obviously that the result of the election isn't just who wins. The margin of victory has an effect on the actions of the government throughout their term. Indeed, in the US we have seen endless pontificating on what lessons parties should draw from the answers voters gave to pollsters on their way home.

There's another objection, however, which attacks Landsburg's reasoning directly:

Let's get mathematical:

Let a be the result of the election ( candidate X votes - candidate Y votes, to be simple) if I don't vote

Let b be the result of the election if I do vote (say for candidate X).
Now, b = a + 1, so the actual outcome of the election will only be different if a=0 or a=-1 (whatever the rules are for tied elections). This is Landsburg's calculation.

But what is the real justification for saying b = a + 1?

We can assume that my vote doesn't affect anyone else's vote. After all, they're not supposed to know.

But that's not sufficent. For b to equal a + 1, the votes of other people have to be statistically independent from mine. Can I assume that?

Now we get philosophical. The common view of me as a mind with "free will" seems to imply the independence assumption. But it isn't backed up by sociology or neurobiology. On the basis of either observation or a reductionist, mechanistic view of the human brain, my vote is likely to be significantly correlated with other peoples' votes. That, after all, is the assumption behind opinion polling.

And based on that correlation, b - a cannot be assumed to be 1. It might be 5, or 100, or 10000.

Imagine, as a thought experiment, that we are all identical robots. We process our various inputs, and reach our conclusions. In the simplest possible model, either we will all vote for the same candidate, or none of us will vote.

As one of those robots, my vote will not affect anyone else's, but if I vote for X, X will win.

We are not identical, and we will not all vote the same. But the correlation, though less than one, is surely greater than zero.

The tricky question: If I use this argument, and therefore vote, will there really be more votes for my candidate? Again, the opinion pollsters believe so. I think they're right.

Psychologically, we do not reach decisions entirely via explicit logic. In fact, we invent reasons to excuse the decisions we would have made anyway. If I am determined to vote, more other people will vote than if I am indifferent. If my candidate wins by 10 votes, I will say, "If I hadn't voted, he wouldn't have won."

Of course, if you live in a safe constituency, your vote won't alter the result. That makes the case for a better electoral system all the stronger, since it shows that many people are denied political influence in a way that other people are not.

In any case, I will vote for a fringe party, so my candidate won't win. But the same effect will amplify the secondary effects of my vote. A good percentage will have a real impact on UK politics.