Kamis, 01 November 2012

Why predict percentages?


"I'll bet you $20 that there's a 70% chance that Obama will win the election."

That's a bet nobody will ever collect on, because it's impossible to verify a percentage chance of something. So why do forecasters like Nate Silver - and any bookie or oddsmaker - say that there's a 70% chance of Obama winning? Why don't they just make an up-or-down prediction?

The answer is: Those percentages give you information to the extent that you believe in the forecaster. If you believe that Nate Silver's model is the best available forecast of the election results, then you believe that the odds he gives are the "fair" odds. Knowing the fair odds will help you hedge properly against the chance that Obama or Romney will be elected president, say for example if you have a business whose livelihood depends on policy. It might also help you make a buck on InTrade, especially if you believe that things like market manipulation can make those prediction markets temporarily inefficient.

But will those odds tell you whether to believe in a forecaster? Surprisingly, the answer is "maybe". The main way to ascertain how good a forecaster is is to observe a repeated sample - just watch the forecaster make 100 forecasts (of who will win, not of what the odds are!), and observe how often (s)he is wrong. This is the main way that you tell how good a forecaster is. But it isn't the only way. If you look at the forecaster's odds and find that they move in predictable ways, then you know that the forecaster could have done a better job. After all, why predict a 70% chance today when you have good information telling you that it will change to a 78% chance tomorrow? Just predict a 78% chance today!

So the odds can be useful in evaluating forecasters, as well as in making use of forecasts.

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