A theorem invoked by the lazy and uncurious?

On the fairness of actual voting systems it always strikes me as lazy and uncurious when people invoke Arrow’s theorem (New Scientist, Last Word, 26 July 2014). There may be no voting system that cannot in theory produce paradoxical outcomes, but actually existing preferential voting systems (in which voters rank candidates) almost never generate such outcomes.  The first-past-the-post systems used in the USA and UK often, however, produce winners who the majority of voters did not favor.  Proportional representation in multi-representative regions also ensures that most voters have at least one representative of their preferred party and thus a voice in deliberations.   (Interestingly two of the Last Word contributors were from the UK, but one was from Australia, which has preferential voting in all elections and proportional representation in the national Senate.)  Of course, whether representatives truly represent the voters that elected them, let alone all the people they are elected to represent, is another matter.  As are the alliances and compromises parties make to govern. But these are not  problems of fairness of voting systems.

I would be curious about whether those who invoke Arrow’s theorem at other times point to the transitional problem, e.g., system X would be more fair, but there is almost no way of getting a government elected under system Y (and constitution Z) to implement the change.  And whether at other times they point to empirical reality to trump arguments from theory, e.g., In theory a resource managed in common by non-communicating agents will get overexploited (the “tragedy of the commons”), but this theory does not address the real-world management of actual resources by communicating agents with unequal access to the resource in question and external resources (e.g., political power).


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