Simulating Finer-grained Score Voting Given A Coarse-grained System

Someone commented on Facebook:

So basically approval is saying that for example a Green would be just as happy with a Democrat and that is not true. Too many think that Greens are similar to Democrats when the motives behind Democratic actions are hotly contested.

My response:

For voters, there’s a way around the coarseness of Approval Voting. Suppose for example it’s Bush, Gore, and Nader, and my true preferences are Bush -50, Gore -40, Nader 50. In finer-grained Score Voting, I would exaggerate my support for Gore and vote strategically Bush -50, Gore 49, Nader 50. Can I use the same strategy with Approval Voting? Yes. I obtain a random number from a computer or some coin tosses or something, and I approve Gore with probability 99%. If lots of people do that, he will receive the amount of support toward his final score, relative to the min and max possible, as though they were voting in a finer-grained Score system.

(Location of original conversation on Facebook: link).

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