As I mentioned in my previous post, I recently presented my Hayekian-inspired “truth markets” idea (see here and here) at the annual Loyola ConLaw Colloquium. After my talk, my colleague and friend David Schraub made an insightful observation. According to Schraub, the price of a belief contract won’t reflect the truth value of the conspiracy theory or fake news story being bet on and thus won’t converge on the “right” answer; instead, the price will track underlying beliefs among bettors about the beliefs of others. For Schraub, if we are placing bets not on their own beliefs (first-order bets) but rather on their beliefs about what others think (second-order bets), then all our bets are effectively “arbitrary” (Schraub’s term, not mine).
To illustrate this point, Professor Schraub referred to a multi-player number game known as “guess 2/3 of the average“. In this game, each player secretly chooses a real number between 1 to 100. The winner is the player who chooses the number that is closest to 2/3 of the average of the sum of everyone’s choices. Given this set-up, Schraub posed the following question to me: How is a someone’s belief that a player in this game will pick the number ‘31’ or ‘57’ and different from my proposed market in belief contracts?
As an historical aside, Schraub’s critique also reminds me of John Maynard Keynes’ psychological critique of stock market investors in Chapter 12 of his classic work on The General Theory of Employment, Interest and Money:
… professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view.
For Keynes, the optimal strategy in this beauty contest game is not pick the six faces that you, the contestant, may personally find the most attractive. To win, you must pick the faces that you think other people will find most attractive:
It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practise the fourth, fifth and higher degrees.
In reply, I am tempted to cite Hayek and be done with it. After all, Keynes is wrong: in the real world stock market prices do, in fact, reflect the underlying financial value of the companies whose stocks are being traded. (See here for example.) Also, contra Schraub, his artificial number game example does indeed have a rational or game-theoretic solution; see here and here. But that said, one could argue in counter-reply that my truth market idea is qualitatively different from a traditional market, since people would be trading “belief contracts”, i.e. people would placing bets on whether a conspiracy is true or false. I will therefore give Schraub’s Keynesian-inspired critique further thought and report back soon.
prior probability 