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saturn comments on How much was creating Google worth? - Less Wrong
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Interesting! I hadn't heard of Shapley Value before.
Regarding voting, let me do a back of the envelope calculation: every voter (that voted the same way) would, by symmetry arguments have contributed equal value. And since Shapley averages over every possible voter subset, and voters would only get credited for those subsets where they are the determining vote (which is proportional to the factorial of the margin of victory I think) then the value each voter (for policy A given two alternatives) contributes is something like:
Where n is the number of voters for policy A, RB is relative benefit of policy A compared to B, and MV is the margin of victory. But I think I made a mistake of ome kind somewhere.
Since the Shapley value of all players also has to sum to the value of the end result, I think the value of each A voter has to be just RB/n. I'm way out of my depth with the combinatorics here, but here's a paper I found that gives a bit more information than the wikipedia page.
Good point, but I don't think the value of the end result is necessarily equal to RB, for much the same reason that (I suspect) Shapley value would correspond to (something like) "market value" rather than "market value plus consumer surplus". That is, no matter how badly you want you bathroom cleaned, the value of the labor to clean the bathroom is only equal to the market value of that labor, irrespective of how happy I am to have it done.
While voting doesn't directly map onto a market like that, there is a similar sense in which being one of the voters for something that "had no chance of passing" (thus getting the high margin of victory) is worth less -- even per voter -- than voting for something whose fate was less certain.