Bets and Beliefs

I fear that Tyler’s latest post on bets and beliefs will obfuscate more than clarify. Let’s clarify. There are two questions, do portfolios reveal beliefs? Do bets reveal beliefs?

Tyler has argued that portfolios reveal beliefs. This is false. If transaction costs were zero and there were an asset for every possible future state of the world then this would be true. Since transaction costs are not zero and there are many more states of the world than there are assets–even when we combine assets–portfolios do not reveal beliefs. Portfolios might reveal a few coarse beliefs but otherwise no go. Since most people have lots of beliefs about the future but don’t even have a portfolio (beyond human capital) this should be obvious.

Do bets reveal beliefs? Usually but not necessarily. Two people made bets with Noah Smith. Each thought Noah was an idiot for making the bet. Noah, however, had arbitraged so that he couldn’t lose. Clever Noah! Noah’s bets, either alone or in conjunction, did not reveal his beliefs.  But is this the usual situation? No.

For the same reasons that portfolios don’t reveal beliefs, high transaction costs and few assets relative to states of the world, it’s going to be difficult to arbitrage all bets. Many bets in effect create a new and unique asset that can’t be easily duplicated and arbitraged away in other markets. I once bet Bryan as to what an expert would answer when asked a particular question. Hard to arbitrage that away.

I also agree with Bryan that the question is empirical and not simply theoretical. When I say that a bet is a tax on bullshit the implication is not just that bullshitters are more likely to lose their bets but also that a tax on bullshit reduces its supply. The betting tax causes people to think more carefully and to be more precise. When people are more careful and precise the quality of communication increases. As Adam Ozimek writes:

In a lot of writing in blogs it is unclear specifically what the writer is trying to say, and they seem to wish to convey an attitude about a certain position without actually having to make a particular criticism of it, or by making a much actual narrower criticism than rhetoric implies…It is useful to have betting because deciding clearly resolvable terms of a bet leads to specific claims…

Tyler argues that under some conditions betting won’t change what people say (under a wide range of portfolios…a matter of indifference… bets won’t be authentic) but Tyler doesn’t give us a specific, testable prediction. The empirical evidence, however, is that small bets do cause people to change what they say. This is one of the reasons why even small-bet, prediction markets work well.

Tyler has his reasons for not liking to bet but if you think one of those reasons is that he has already revealed his beliefs then you are surely not a loyal reader.


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