I had a great set of responses to my recent post about electoral reform. I got emails, Tweets, blog comments, and comments on Google+. Many interesting thoughts and articles, which I thought I'd respond to in this follow-up.
Some folks argued with the decision not to vote. How could that be a good idea? What if everybody did that? This one's easy. Firstly, that'd be great. Secondly, it's irrelevant. Consider: I might do my bit about overpopulation by deciding not to have kids. Sure, if everybody did that then the consequences would be catastrophic but that doesn't disqualify it from being a rational individual choice. Indeed, many people do make that choice with net positive effect.
Nick provided an interesting post on the "fallacy of the deciding vote". It's a well reasoned piece, but premise (2) renders it inapplicable: the argument at hand isn't whether my individual vote unilaterally decides the result (which obviously it doesn't, as the article points out, in all but the most degenerate cases). It's about the probability that adding or subtracting my individual vote has an effect on the outcome. I don't need my vote to be the single deciding vote by any means.
So that we're clear, before we move on let's call a given individual voter democratically impotent in an election if the election has an identical outcome with or without their vote. Conversely the voter is democratically potent if removing their vote changes the outcome.
Premise: Your vote is the same as everyone else'sand he's right. My hyperbolic "I literally count for nothing" should really have been "in the span of my lifetime, with overwhelming probability, I'm democratically impotent in every election in which I'm eligible to vote". There's a mathematical distinction but barely a practical one.
Premise: Your vote literally counts for nothing
Conclusion: Everybody's vote counts for nothing
...and yet, we have a result. I suggest that premise 2 is faulty
Interestingly, as you remove more and more voters from the electorate the chances of a voter which remains being democratically potent increase significantly. Thomas Pogge, Yale's Professor of Philosophy and International Affairs, showed in a post last year that in a small population of 63 voters, with each voter choosing independently and with equal probability between two electoral candidates, a given voter has a full 10% chance of casting a deciding vote.
I like those odds, but in large populations things look much bleaker.
In the simple equiprobabilistic model which Pogge presents, in an electorate of 100,001 people the probability of a given voter casting a deciding vote is about 1 in 400. Not bad at all! Assume instead, though, a slight general preference in the populace for one candidate over the other, let's say 49% to 51%, and suddenly your 1 in 400 chance of affecting the outcome in Pogge's model sinks to 1 in 193 billion.
Scale up from there to a population of just a million, and you as an individual voter are democratically impotent with a novemvigintillion to 1 probability¹. If you voted in an election of this kind every second for as long as you lived (or even, hey, every nanosecond for the entire lifetime of the universe), chances are—by an inconceivable margin—that you'd not affect the outcome of even a single one.
I am being sadly sincere when I describe [democracy] as a system which is much better at giving the feeling of participation than actual participation. To me, this is one of the terrible things about democracy (and part of why it is so successful) - because voting lets people feel like they can influence things. Even if they don't vote, they feel like they could have voted.…as indeed is demonstrated above.
But any one vote never matters...
So we come back to that idea again of selecting the election winner by picking a single ballot at random and going with that. Now one's chances of democratic potency in an electorate of a million people voting between two candidates with a 49%/51% baseline preference is simply a million to one. Still sounds like long odds but it's a trillion trillion trillion trillion trillion trillion trillion times better than before. In this system people are thus vastly more individually empowered, the tyranny of the majority is ameliorated, and the end result remains proportionally representative, albeit with added statistical noise. It's a win-win-win!
At the end of the day, though, as James noted, whoever wins an election it's always a politician. A solution to that problem is left as an exercise for the reader.
Next in this series: Electoral reform, epilogue
¹ a novemvigintillion is a billion billion billion billion billion billion billion billion billion billion; about ten billion times the number of atoms in the universe.