Saturday, 7 September 2013

Election Game Theory, Or Why You Probably Voted for the Sex Party

By now most of you will have voted. 

Because I am one of those infuriating people who treat election day as if it was boring man's equivalent of Christmas, I thought I’d go through one of the examples that came up in Game Theory last year, dealing with voting preferences. 

Consider the situation where you have two parties (Douches and Assholes), and an odd-number N voters (we’re not going to allow ties). Voters 1 to k strictly prefer the D to A, and voters k+1 to N strictly prefer A to D. 

Each voter has two possible options - they can either vote for D or A. 

We will take every other voter’s action as given. 

Each voter feels happy if their preferred party wins the election, and sad otherwise. 

We will examine one voter’s decision. For argument, say he prefers D over A.

There are three possible scenarios:

1. More than half of the other voters vote for D. 
Voting for D or A does not affect the result. D wins regardless of his action.

2. Less than half of the other voters vote for D. 
Voting for D or A does not affect the result. D loses regardless of his action.

3. Exactly half of the other voters vote for D. 
Voting for D or A does affect the result. The voter’s decision wins the election.

What does this actually mean? It means that the voter’s decision only decides the election in the case that votes are split equally between the other voters. Even though he strictly prefers D to A it would make no difference to the election if he voted A instead. In Game Theory, we would call the decision to vote A over D a weakly dominated strategy (it is no worse than voting for D in the situation that a clear majority is found without the voter, and strictly worse than voting D when the votes are split).

How does this relate to the current election? In many seats a clear majority exists before the day of the election (call this a safe seat - one which always votes a particular way). In these seats, the individual’s vote doesn’t actually hold that much weight. You’re just as well off voting for a major party, or something like the Sex Party. It’s in marginal seats where a swing can be expected that the election is truly decided. This is reason why the Greens often described as holding the balance of power in the Senate, and why this balance is so important. It’s all about being that  voter. 

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