Alternative title: Is the World Truth League a Keynesian Beauty Contest?

Two of my previous posts (see here and here) have presented a tentative sketch of my colleague and friend Steve Kuhn’s original idea for a World Truth League. To recap, (1) the league would contain a select number of teams competing over the accuracy of their predictions and retrodictions. (2) These truth teams would then compete against each other during a finite number of truth rounds, and each round would consist of a discrete question either about an uncertain future event or a past one–e.g., will X occur in the future, or did Y occur in the past? (3) During each round, each team would have a limited amount of time to submit its truth estimate or best guess about the likelihood of X (a forecast estimate) or Y (a hindcast bet). (4) The team whose truth estimate is closest to the average of all the estimates would win that round. (5) And last but not least, members of the public could place bets on their favorite questions and on their favorite teams during each truth round.

The main virtue of this five-part blueprint is that it responds to Nick Whitaker and J. Zachary Mazlish’s recent critique of information markets. (See their excellent essay “Why prediction markets aren’t popular”, which was first published on May 17, 2024, and which I reviewed here.) To borrow Whitaker and Mazlish’s useful terminology, gamblers will love the fast-paced action of the World Truth League because the truth rounds would be short and all bets would be resolved instantaneously at the end of each round. Savers may love specific teams (e.g., the Microsoft Research team, the Mercatus Center team, the NY Times team, etc.), depending on their individual preferences and values. And the sharps will join once the the gamblers and savers are onboard.

Today, however, I want to consider one remaining objection to the World Truth League, a possible fatal one: the Keynesian beauty contest problem. (See the video below, for example. Also, shout out to my colleague and friend David Schraub, who first brought a game-theory variant of this problem to my attention after I presented an early draft of my paper on “Retrodiction Markets” at the Loyola Chicago Law School in November of 2022; see here.) In brief, the so-called “beauty contest” problem is this: when each team is asked to provide its best “truth estimate” about the likelihood of X (a forecast about a future event) or Y (a hindcast about a past one), there is no guarantee that the average of the truth estimates of the teams will actually track or converge on the “right” answer–that is, on the true value of X or Y. Why not? Because the teams may not be reporting to us their first-order beliefs about the truth of X or Y (i.e. what each team really believes about the substance of the question presented during each truth round); the teams might instead be reporting their second-order beliefs about what they think the other teams believe about X or Y!

By way of comparison, consider the original beauty contest problem in Chapter 12 of John Maynard Keynes’ classic study, 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.” For Keynes, the optimal strategy in this particular newspaper game is not to 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.

Similarly, the simple and elegant resolution mechanism of the truth league would be open to this same criticism. (Recall that the winner of each round would be the team whose truth estimate is the closest to the average of all teams’ truth estimates for that round. See Item #4 above or Item #2 in my previous truth league post.) Point blank, to what extent would each team’s truth estimate track that team’s true beliefs about the world versus its beliefs about the beliefs of the other teams? If enough teams are engaged in this second-order style of reasoning, would the World Truth League really be a reliable arbiter of truth, or would it unravel after just one or two rounds?

Is the beauty contest problem soluble? For now, we will conclude with an observation, followed by a conjecture: Keynes’s beauty contest was originally meant as a psychological critique of stock markets, but despite Keynes’s critique, stock markets still attract a sufficient number of gamblers, savers, and sharps to work in practice. Why wouldn’t a well-designed World Truth League with an enticing roster of teams be any different? I will conclude my series on the World Truth League next week with a call to action …