## The markets and the election

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[1]. 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.

fn1. The workings are easy for those who know Bayes’ theorem and accept the modern subjectivist interpretation , but they won’t make much sense to those who don’t.

I think I read somewhere recently, that the bookies have picked the elections better than the polls for the last couple of years.I think this is right (although I’m not sure how they went with the hard ones, such as ’93). More to the point, I understand that they have picked it better than the polls

on the eve of the vote, not 6 weeks away. An index to watch.I’ve been thinking about this, in a shallow way, for some time. I’m tempted to put a hundred on the coalition, the reasoning being that if Labor gets up I’ll be too happy to even remember the loss; if the coalition is returned, the meagre winnings will at least cover the cost of a decent shiraz to drown my sorrows.

Does economic theory take this kind of deliberate perversity into account? Or does it just file it in the large basket marked ‘stupid’?

Warbo, this is exactly the (risk-averse)

Homo economicuschoice. Economists discuss this a lot, and point out that, with plausible preferences, expected utility is improved by betting against your preferred side. But that’s not what most people do.I know a number of people that do this for sports teams for just this reason.

Maybe I know too many economists.

I want Kerry to win in the US this November, and for this reason I’ve considered betting on Bush. The downside of risk-averse betting, however, is that if done right it makes one apathetic to a situation’s outcome. Which, in the case of an election, would discourage me from voting, advocating, donating, or volunteering for Kerry.

So perhaps, in situations where the bettor has some power to sway the outcome, a bet on one’s own side is optimal.

The betting markets are generally a poor guide to the Melbourne Cup 6 weeks before the event. My research indicates that about half of the winners over the past couple of decades didn’t even figure in the markets published in the sporting pages of the papers 6 weeks prior to the race. On the other hand, most of the winners in this period were pretty well in the markets on Cup eve. Now if we apply this to the Federal election. . .

BTW, get your $61 to win on Seul Amour for the Cup while it lasts.

I think this is a little clearer as the $7 example is slightly inaccruate.

Coalition: 1.55

ALP: 2.30

If I place a $1 bet on the Coalition and they win, I will receive $1.55 back from my $1 investment. So my return on $7 is $3.85.

Conversely, if I place a $1 bet on the ALP and they win, I will receive $2.30 back from my $1 investment.

An interesting aside, a few weeks ago the ALP was at 2.6. Since then they have gone to 2.4, and now 2.3 so it’s an interesting trend.

The odds on an ALP victory are shortening.

When the L/NP are at 1.55 it means that for every $5 wagered on them one will get a $2.75 return ie the Coalition are heavyish favourites at less than 3:5 on.

When the ALP are at 2.30 it means that for every $5 wagered on them one will get a $6.50 return. ie Labor are (a little less than even money) at more than 6:5 odds.

This means that the punters fancy the Coalition to win the election a bit more than twice as much as they do Labor.

But this market could be quite thinly traded, and its early days yet.

Take a look at TradeSports.com for all sorts of interesting markets, including politics.

The Iowa Electronics Markets was the first I believe.

Paul Norton

You can get $80 on Seul Amour at Betfair.

Just had 10 bucks on it at your urging.

Libs @1.62 and Lab @2.54 at present.

Click on the party names to see price/volume over time.

$290,215 already traded.

Don’t know why, but I felt compelled to check the latest Coalition vs. ALP odds on Centrebet.

The Coalition’s now paying $1.30, versus ALP on $3.20. That’s a spike from the $2.50-$2.60 level of just a few days ago, and implies an estimated probability of the Coalition winning of over 70% (71% by my calculation).

Did anyone say Jakarta bombing? Cue moral outrage…

Centrebet’s now offering $1.20 on the Coalition and $3.20 on the ALP. The ALP number blew out from the $2.50 to $2.60 range just a few days ago.

By my calculation that implies a 71% probability of a Coalition victory. Did anyone say Jakarta bombing? Cue moral outrage…

Sorry about the double post. It seemed to get stuck on something.

The claim that betting markets are more efficient than polls was made by Justin Wolfers and myself in an Australian Journal of Political Science paper after the last election. If you’re interested in reading the paper, it’s on my website – http://www.andrewleigh.com. You can also see the probabilities that the betting odds imply (updated each morning), and download a full history of what the betting odds have said about the two parties since mid-2003.

The biggest movement in the odds has been since the Jakarta bombing. On Thursday, Labor was 36%. Now, it’s down to 29%. I suspect we’ll see that reflected in the polls next week.