07 July 2010

Political Polls—The Odds

An Ekos poll gives the Conservatives 31% of the vote and the Liberals 27.7%, +/-2.4%, 19 times out of 20--what the media calls a "virtual draw". It's an interesting estimate, but not really useful for making decisions; a Liberal win is within the range of error.

Looking more closely, what these numbers say (but Ekos doesn't) is that the Conservatives are favored to win a plurality with at least 9:1 odds. Probabilities can be more useful than estimates, and they can have a dramatic impact on our understanding of the situation.

The 9:1 odds calculation assumes a Liberal/Conservative zero-sum game. Every vote gained by one party is a loss to the other. If this is relaxed and votes can be taken from or lost to the other parties, the odds favouring a Conservative win max out at about 40:1 (not a typo--that's forty).

These numbers come from a Monte Carlo simulation of 10,000 elections assuming the Ekos numbers represent Gaussian distributions. In the first case, the Conservatives win when they get more than 29.35% of the votes--a majority of the votes in play. In the second case, the Conservatives win when they get more votes than the Liberals.

Ekos hasn't told us enough to gauge the mobility of votes from the other parties, so we can't resolve the difference. On the other hand, they have the data so we're left wondering why they don't report the proper odds.

There's an Excel spreadsheet for this calculation that you can use to see the odds for other polls. It includes a 1000-election simulation. With only two uncertain variables, it's about as simple an example of Monte Carlo simulation as you can get. See http://smpro.ca/crunch/PollOdds.xls