On Bets

Update: I just Tweeted: “Ok seriously “bets reveal beliefs” is a belief. And a pretty strong one too. I don’t believe you believe that. Reveal it. Now!” Sounds like the impossibility of proving you believe in bets is a pretty good argument against expecting people to bet to reveal their beliefs if in such a world you can’t prove your own metabelief that bets reveal beliefs. Or make an exception and it’s turtles all the way down.

Since there are about fifty recent posts on wagers – each some permutation of “bet”, “belief”, and “portfolio” – I have no creative title for this post! The debate is mostly an outgrowth of a conversation between GMU economists (Tyler Cowen seems to be outnumbered) on whether bets reveal an individuals beliefs and whether marking beliefs to market makes for higher quality debate. Cowen doesn’t want to be locked into any particular viewpoint and sees bets working against a Bayesian updating of one’s beliefs. Alex Tabarrok, quite simply, thinks “bets are a tax on bullshit”. I have a few points to add.

Tabarrok, a libertarian economist, should perhaps consider the deadweight loss from such a tax. If the academic environment only respected predictions and models on which the designer is willing to wage a not insignificant bet, we would naturally see a fall in the supply of predictions. (Note, I’m not in general against bets, and think they can play a huge theoretical role for economics: only requiring them for respect). This might be a good thing, but I wonder, are he and other academics so bad at weeding out the crappy predictions? And what if the tax weeds out something truly cool and fascinating?

For one, it would put poorer academics at an unfair competitive disadvantage. A rich economist like Paul Krugman can easily wage bets at rather high odds without any risk. As I commented earlier:

Here’s the problem with thinking that bets reveal one’s true beliefs. Let’s say that I’m a prominent economist, and my career and theory has been suggesting significant hyperinflation for years now. Let’s say I take a 3:1 bet that inflation will remain below 5%. (Being generous in allowing even such people to bet against hyperinflation, just at far lower odds than rational people like Noah Smith who take 75:1).

Is it 3 cents to 1? Or 3 thousand dollars to 1? I imagine the prestige and pride in making such a bet outweighs – for such top economists – the cost of loosing it. That is I think people like Niall Ferguson or Paul Krugman would be indifferent within an order of magnitude except at very high values. (For example, if PK looses a 50:1 bet on a thousand dollars what’s the worst that happens… he has to give another speech?)

Therefore, only at extreme levels of confidence *and* high bet values (a bit of leniency between the two) can a bet actually reveal true preferences. Otherwise, if I was NF for example, I might take a much bigger bet just to make a statement because what’s the difference anyway?

Therefore, to the extent there is a prestige in making the bet itself, we will experience “prediction market failure”. More importantly, the Krugmans and Cowens will find it a lot easier to advance their theory among fellow academics than a newcomer. Alex Tabarrok’s “tax” – in line with his own market-oriented beliefs! – now deters competition and supports monopoly of academic thought.

Of course, this is very unlikely to happen, because academics (Tabarrok included) will pay attention to new theories. But that would bring serious question to the claim that bets are a tax on bullshit. Tabarrok, Caplan, and all naturally want us to place higher respect on theories in which the theoretician has financial stake. Further, if academic respect derives from bets, that will further tangle market signals as the value of a bet not only includes its discounted future return, but the social and professional value of having made such a bet. If this were to be the case academics will consistently bet at irrational odds in favor of their theory and, the market, knowing this would just constantly short everything and earn a constant profit. (I really want to know if Paul Krugman bet $50,000 on a Keynesian model whether they would take him more seriously; especially knowing that costs all of one speech for the man!)

There is an important, undermentioned, value to a bet – however. There are two layers on top of belief. The pro-bet economists argue that a bet aligns what I say (the topmost layer) not with what I believe, necessarily, but with what I think I believe. That is, they think that hyperinflationistas may be overselling their own confidence in their models, and that a bet would decrease the wedge. (This requires that the only value from a bet be the wager itself, but that’s another story). But there’s another gap, between what I think I believe, and what I actually believe.

Here’s a bet I’m willing to make. If you ask me what I would bet on a various series of events and, at an independent time, asked me to actually bet with my own money, my answers would be different. It’s not that I’m lying the first time, it’s just that it is impossible to know one’s actions until they are revealed – as much to the market as to the self. For example, in theory I would buy a $20,000 watch on sale for $1,000 – it’s entirely rational. I am less sure that this would actually happen given the choice. (There’s an epistemological impossibility in explaining this on myself, because self-doubt invalidates the initial prior. It’s like saying “I’m not as smart as a I think I am” which, by definition, means I don’t think I’m that smart. But, just like this oxymoronic phrase, the example conveys my point).

A bet forces me to reveal my belief to myself. Therefore, within small groups of academic friends, there might be value to making bets, as it compels a greater degree of introspection. A final note: I also think it’s important to demarcate the current advocacy for betting as a way to reveal actual beliefs and support for prediction markets. Like Cowen, I’m skeptical of the former, but while prediction markets really are just “bets”, they serve the far more useful purpose of aggregating information and hence are not really comparable.

My point? I’m somewhat skeptical that Bryan Caplan and Alex Tabarrok know their own hidden priors on betting. Because if they really respected the gambler more than the prude, they would be placing a tax not just on bullshit; but one on intellectual discovery and thought itself. In other words, their position on betting seems at odds with their otherwise libertarian ideology.