Betting on others reveals yourself

It is long known that making people bet on future events reveal what they think about these events. Predictions markets have been exploiting this idea. Prof. Baillon proposes a new kind of markets, ‘Bayesian markets’, to reveal unverifiable personal information. Instead of betting on future events, people bet on what the others feel, think or did, and this is used to reveal what they themselves feel, think or did.

Influenced by own behaviour
“Since the 1970s, it is known in psychology that what we think of others is influenced by our own characteristics. For instance, sad people expect more sad people than those who are not sad expect. Or, as one of my students found among his peers, those who cheat in exams expect more cheaters than expected by those who don’t cheat,” explained Prof. Baillon. “ He added: “We don’t expect 100% of the others to be exactly like us, but our expectations are strongly influenced by our own behaviour. What I propose is to use this intuition and make people bet on others. The bet rewards people for telling the truth about their feelings, their thoughts, or their past actions.”

Surveys and online evaluations
Prof. Baillon foresees two main domains to use the ‘Bayesian markets’. The first one is for social scientists, survey companies, but also companies collecting expert opinions. The method he proposes can reward respondents (citizens or experts) if they make the effort to give an honest and carefully considered answer. The second application is in the domain of online evaluation. “For example, all these websites or apps asking us to evaluate hotels, restaurants, movies… After reporting that you liked a movie, you could be asked: ‘Do you bet that more than 70% of the spectators will also like it?’ If you win your bet, you could earn ‘points’, which could be converted into an ‘expert score’, or vouchers, or donations to a charity… Such a mechanism could make online reviews more trustworthy,” he says.
Prof. Drazen Prelec from MIT sees that this could be extremely useful in combining opinions from experts, as well as ordinary citizens. Prelec says: “Like many great ideas, Baillon's Bayesian market is simple, but only in retrospect. He shows how one can create markets for betting for or against propositions, even if the actual truth of these propositions cannot ever be publicly verified. I hope that we will see this invention implemented on our iPhones in the not so distant future.”

Prof. Aurélien Baillon
Prof. Baillon (1980) joined Erasmus School of Economics in 2007, after obtaining a research master at the University of Toulouse and a Ph.D. at Arts et Métiers ParisTech. In the past years he was awarded a Veni and a Vidi grants from the Netherlands Organization for Scientific Research (N.W.O.) and a Starting Grant from the European Research Council. His research has been published in leading journals, including the American Economic Review.

Title
Bayesian markets to elicit private information

Significance Statement
People’s private information can be revealed by the way in which they trade specifically designed assets in a new type of market. People trade an asset whose value is the proportion of affirmative answers to a question. Their trading position then reveals their own answer to the question. In Bayesian markets, people can be rewarded for telling the truth even when the truth is not verifiable. Bayesian markets are simpler and more transparent than alternative methods, avoiding the measurements of meta-beliefs about others and prior beliefs.

Abstract
Financial markets reveal what investors think about the future, and prediction markets are used to forecast election results. Could markets also encourage people to reveal private information, such as subjective judgments (e.g., “Are you satisfied with your life?”) or unverifiable facts? This paper shows how to design such markets, called Bayesian markets. People trade an asset whose value represents the proportion of affirmative answers to a question. Their trading position then reveals their own answer to the question. The results of this paper are based on a Bayesian setup in which people use their private information (their “type”) as a signal. Hence, beliefs about others’ types are correlated with one’s own type. Bayesian markets transform this correlation into a mechanism that rewards truth-telling. These markets avoid two complications of alternative methods: they need no knowledge of prior information and no elicitation of meta-beliefs regarding others’ signals.
Read more here.