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?