Surprising Popularity

This week Nature published some empirical data on a surprising-popularity consensus mechanism (a previously published mechanism, e.g., Science in 2004, with variations going by the name “Bayesian Truth Serum”). The idea is to ask people to pick from several options, and also to have each person forecast the distribution of opinion among others. The options that are picked surprisingly often, compared to what participants on average expected, are suggested as more likely true, and those who pick such options as better informed.

Compared to prediction markets, this mechanism doesn’t require that those who run the mechanism actually know the truth later. Which is indeed a big advantage. This mechanism can thus be applied to most any topic, such as the morality of abortion, the existence of God, or the location of space aliens. Also, incentives can be tied to this method, as you can pay people based on how well they predict the distribution of opinion. The big problem with this method, however, is that it requires that learning the truth be the cheapest way to coordinate opinion. Let me explain.

When you pay people for better predicting the distribution of opinion, one way they can do this prediction task is to each look for and report their best estimate of the truth. If everyone does this, and if participant errors and mistakes are pretty random, then those who do this task better will in fact have a better estimate of the distribution of opinion.

For example, imagine you are asked which city is the the capital of a particular state. Imagine you are part of a low-incentive one-time survey, and you don’t have an easy way to find and communicate with other survey participants. In this case, your best strategy may well be to think about which city is actually the capital.

Of course even in this case your incentive is to report the city that most sources would say is the capital. If you (and a few others) in fact know that according to the detailed legal history another city is rightfully the capital, not the city that the usual records give, your incentive is still to go with usual records.

More generally, you want to join the largest coalition who can effectively coordinate to give the same answers. If you can directly talk with each other, then you can agree on a common answer and report that. If not, you can try to use prearranged Schelling points to figure out your common answer from the context.

If this mechanism were repeated, say daily, then a safe way to coordinate would be to report the same answer as yesterday. But since everyone can easily do this too, it doesn’t give your coalition much of a relative advantage. You only win against those who make mistakes in implementing this obvious strategy. So you might instead coordinate to change your group’s answer each day based on some commonly observed changing signal.

To encourage this mechanism to better track truth, you’d want to make it harder for participants to coordinate their answers. You might ask random people at random times to answer quickly, put them in isolated rooms where they can’t talk to others, and ask your questions in varying and unusual styles that make it hard to guess how others will frame those questions. Prefer participants with more direct personal reasons to care about telling related truth, and prefer those who used different ways to learn about a topic. Perhaps ask different people for different overlapping parts and then put the final answer together yourself from those parts. I’m not sure how far you could get with these tricks, but they seem worth a try.

Or course these tricks are nothing like the way most of us actually consult experts. We are usually eager to ask standard questions to standard experts who coordinate heavily with each other. This is plausibly because we usually care much more to get the answers that others will also get, so that we don’t look foolish when we parrot those answers to others. That is, we care more about getting a coordinated standard answer than a truthful answer.

Thus I actually see a pretty bright future for this surprisingly-popular mechanism. I can see variations on it being used much more widely to generate standard safe answers that people can adopt with less fear of seeming strange or ignorant. But those who actually want to find true answers even when such answers are contrarian, they will need something closer to prediction markets.