I'm trying to work out exactly what instruments should be traded for the purposes of a futarchy.

Let the decision be whether to adopt some proposal C; our options are C or ~C. In particular, we wish to know which of EV|C or EV|~C is larger, where EV is expected-value utility according to a utility function agreed upon somewhere offscreen.

For convenience, let our utility U be bounded on [0,1].

We can create the following primitive instruments:

a. U|C, worth (EV|C) * p(C)

b. U|~C, worth (EV|~C) * p(~C)

c. (1-U)|C, worth (1-(EV|C)) * p(C)

d. (1-U)|~C, worth (1-(EV|~C)) * p(~C)

It's worth pointing out a few compounds we can make by combining these:

a+b is worth EV. c+d is worth 1-EV.

a+c is worth p(C). b+d is worth p(~C).

a+b+c+d is worth 1.

I know that I can achieve what I want by establishing two separate markets, one trading a versus a+c and the other trading b versus b+d, and comparing the spot prices of the two.

The question is: is it possible in a single market?

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Well what we want is to be able to find the market's prediction for EV|C and EV|~C. In the course of this we also need to find p(C) = 1-p(~C). In other words, there are 3 free parameters, so you could use 3 traded thingies in one market. A, B and A+C, for instance.

This effectively results in three exchange rates (A/B, A/A+C, B/A+C) that need to be compared; the two-market solution (A/A+C, B/B+D) is actually simpler.

Well, "simpler" depends on your definition. But yeah, it's probably better because its easier to comprehend.

Here's a potential problem: if you bet against a proposal that passes, or in favor of a proposal that fails, you then have a financial incentive to deliberately sabotage the collective utility function. The results might look something like a Green Emperor trying to undermine the efforts of a Blue Senate.

If the utility function is amended while a market is running, should you use the old utility function to keep the market stable? What if the utility function changes after the policy is adopted or rejected, but before the investments pay out?

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