I just learned that in ancient Sparta elections were determined by how loud people shouted for candidates. There is a certain attraction to taking into account intensity of opinion rather than merely ordinal preference, and I would expect a standard utilitarian/neo-classical analysis of voting would endorse that “range” method over alternatives or claim that the market does properly take that into account (though wealth effects make it unequal). This was inspired by this video (which despite fairly professional production did not eliminate some minor flubs) discussing the problems with voting and Arrow’s Impossibility Theorem, in turn via Alex Tabarrok (who has a paper on whether the Borda count could have prevented the Civil War and one on what systems could have resulted in President Perot). Caledonian/melendwyr has a post on Arrow’s Theorem here.

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