Commenter “tipper” supplies the numbers on an issue I’ve discussed previously, observing
Centrebet has the Coalition at $1.55 and Labor at $2.30. For the non-punters, that means you have to bet $7 to win $4 on the Coalition and $10 to win $13 on Labor. I think I read somewhere recently, that the bookies have picked the elections better than the polls for the last couple of years. So go all you “true believers”, make an honest quid for yourselves, for the first time in your lives, by proving the bookies wrong. Or as John would put it, prove the “efficient market hypothesis” wrong.
If I’ve done my arithmetic properly, and allowing for the bookies’ margin, I get the implied probabilities as 0.60 for the Coalition and 0.40 for Labor. The polls have Labor ahead, but looking at all the discussion, I’d say that the consensus view is that the election is a 50-50 proposition, and that’s also my subjective probability.
How good a test of the efficient markets hypothesis will this be? Bayesian decision theory provides an answer. If our initial belief is that the EMH is equally likely to be true or false, and the Coalition wins, we should revise our probability for the EMH up to 0.55. If Labor wins, we should revise it down to 0.45.
As regards the betting option, there’s a collective decision problem here. Given my subjective probabilities, a bet of $100 on Labor would have an expected net payoff of $15, but $15 isn’t enough to cover my transactions costs for placing the bet, etc. A bet of $1000 would have an expected net payoff of $150, which would be worthwhile in these terms. Unfortunately, the 50 per cent chance of losing the $1000 comes with the additional cost of having to explain to my (non-Bayesian) wife what a good choice I had made ex ante . The net expected benefit comes out as a big negative here.