Consider a conditional prediction market, e.g. "if my cool policy is implemented, then widget production will increase by at least 15%". To my understanding, markets like this are intended as a tool for finding  and the market just gets unwound or undone or refunded if  doesn't occur.

I can work through the math and see that refunding the market indeed makes the price reflect , but this exacerbates one of the biggest issues with prediction markets: no one wants to lock up  of capital to extract  of profit in a year, so no one will lock up  of capital to extract  of profit in a year and only if some extra event happens.

My question is: are there any interesting or viable alternative ways to run a counterfactual or conditional prediction market? Off the top of my head, I could imagine using markets for  and  to derive , which would still pay out something if  didn't occur.

New Answer
Ask Related Question
New Comment

4 Answers sorted by

You could have the prediction market invest the bet in a portfolio of the user's choice (maybe out of a few preset options) and then return the money plus investment returns (maybe minus a small fee).

Have prediction markets which pay $100 per share, but only pay out 1% of the time, chosen randomly. If the 1% case that happens, then also implement the policy under consideration.

I don't think the capital being locked up is such a big issue. You can just invest everyone's money in bonds, and then pay the winner their normal return multiplied by the return of the bonds.

A bigger issue is that you seem to only be describing conditional prediction markets, rather than ones that truly estimate causal quantities, like P(outcome|do(event)). To see this, note that the economy will go down IF Biden is elected, whereas it is not decreased much by causing Biden to be elected. The issue is that economic performance causes Biden to be unpopular to a much greater extent than Biden shapes the economy. To eliminate confounders, you need to randomiser the action (the choice of president), or deploy careful causal identification startegies (such as careful regression discontinuity analysis, or controlling for certain variables, given knowledge of the causal structure of the data generating process). I discuss this a little more here.

Not an alternative, but an add-on: subsidize the market. This does require someone who wants the info badly enough to pay the subsidy. Robin Hanson recently blogged about how one might focus subsidy on trades one is most interested in.

1 comments, sorted by Click to highlight new comments since: Today at 8:12 PM

P(A|B) is defined as P(A & B) / P(B), and both P(A & B) and P(B) are straightforward things to bet on in a prediction market.

The problem is that you get some estimates P*(A&B) and P*(B), and P*(A&B)/P*(B) is not necessarily a good estimate for P(A&B)/P(B) even when each of the component estimates were good. It gets much worse when the estimates aren't very good.

It gets worse still if what you really want is something more structured than a simple conditional probability, such as a credence for a causal relation. I suspect that there are many complications here that may be beyond the scope of any plausible prediction market structure.