Hi Mike,
I didn't think of this -- yes maybe the voting process has some feature of the path integral. But in the "real" path integral nature decides how to weight each path (by the Action) and in a social context (those described in my essay or as you point out the rating system for the essay contest) the weighting is more subjective (some might say it is completely subjective). And in terms of my essay I mention this as a weak point of the whole process. My idea would be that for every different social question one should beforehand come up with some way of weighting each social path that was tried. In reality what might happen is that people/administrators/government officials in charge of implementing a given program or path might come up with criteria "on the fly" to either stick with a given path or abandon a given path. For example the administration of George W. Bush decides to get the US involved in fighting in Iraq and when they are questioned as to if this is a good approach/ a good path they invent data to support their position -- "Iraq has a nuclear weapons program. We must stop them." all of which was invented data (i.e. a lie).
Anyway back to your original comment/question about the rating system of the FQXi contest -- it is probably no better or worse than other systems. I can't think of any system that would be considered completely fair by all the contestants. Also note the rating system for the FQXi contests now is much different from the first contest, thus there has been an evolution or a path integral selection of evaluation methods.
Finally let me emphasis again that my "path integral for society" is just a metaphor that in society as in science it's good to try out different approaches to things since people in general are not good at guessing the correct answer to scientific questions and I think they are also not so good at selecting (at first try) the best societal solution. I could as well have called the essay something like "Try as many different possible approaches to social questions and then use some objective or semi objective criteria for selecting those approaches which are best." I put the path integral in there since I do quantum field theory and physicists generally will describe things in terms of the language they are familiar with.
Best,
Doug