2008/05/11

Predictions, elections, polls, fractals, reflixivity & the kitchen sink

People argue about whether prediction markets do a better job of forecasting elections than polls, or it's an illusion due to timing.

Initially, I am inclined to believe this is one area where the market works better. This follows from their most basic properties. Let's assume both are mostly mediocre. That is many polls and prediction markets available, but just no good in general.

Now consider polls. If there was fewer of them, and they were well communicated, we could count on the fact that expert from all sides would scrutinize them and that they would thus be held to the highest standards. Or of course if you average a lot of polls, you should get a more accurate poll of polls, as errors cancel out. In both cases, centralization increases accuracy of polls. Conversely, when looking at any one poll alone chances are, the one you're looking at is a bad/biased one.

For markets on the other hand, even if you are looking at one market alone, if it was biased, all it would take is one person who has seen the other markets to arbitrage the bias away, in effect linking the two markets and making them two views of one more accurate underlying market. Two polls cannot get organically linked and become more accurate than each by itself. You have to add them up yourself. But two markets can! Thus any one market you stumble upon is more likely to be accurate than a poll you stumble across.

This argument seems particularly apt for the US presidential elections, since there's so much slicing and dicing... The polls are all complicated what-if scenarios. So anyway, according to Intrade, which I've written about before, here are the current probabilities for the next US President (taking bid prices, to get lower bounds):
And the Iowa Electronic Markets seem to agree. Thus, the above, in my humble opinion, is as close as you're gonna get to a prediction out there today.

But is it any good?

Getting back to the philosophical argument again... polls are trying to measure current feelings, i.e. they assume there's an underlying "true" preference of the public, and that they are an objective mechanism to reveal it, within a certain Gaussian error. But it could of course be that the error is much larger than we think possible, because the models are completely wrong. As Nassim Nicholas Taleb, the author of Black Swan, that I mentioned here a couple of posts ago, has argued, a lot of mistakes are due to imposing Gaussian models on a reality that has fractal or power-law or heavy-tailed scaling. For polls, if you think there is a true current preference, then I guess the error should be Gaussian (in other words, using Taleb's lingo, the preference is "in mediocristan"). But looking at it over time, as you must for a prediction, maybe a single poll of a few thousand people, even if it's not representing a wider reality, can have a fractal effect, replicating it's belief patterns at larger scales, through media. If that' s the case, most polls will be meaningless, some will be virally important. And prediction markets won't work well either. True the participants size can scale so maybe they can make fractal bets, but no matter how many expert bets the market brings in, it won't improve the information about a black swan type event which is what a fractally scaling popularity would be.

Some people, like George Soros in his recent book (that I just picked up this weekend) argue that, when it comes to human/social phenomena, the underlying reality doesn't exist separately, it is entangled with human attempts to understand it, and manipulate it (he calls it reflexivity). So taking his ideas to polls, are they measuring something that fundamentally may not actually exist? Probably, there's no objective public opinion that exists independently, waiting to be measured. But it exists reflexively (this is my interpretation/application of Soros idea here so sorry if it's wrong). The polls, even if totally arbitrary to start with, by being communicated, may induce the reality they purport to measure. People listen to the news, and the polls, and their future actions are affected in some way, may then come to act in the way that is suggested to them by the polls for people like them. It may or may not be controlled in concentrated way, but if we apply this theory, then polls are as much instruments of action as measurements, in robotic terms, as much actuators as sensors.