Alternative voting methods are in the news after Maine narrowly passed a ballot initiative allowing instant-runoff ballots in state and federal races, starting in 2018. Knowledgeable folks mention Arrow’s Theorem, which proved that there’s no perfect voting system and won a Nobel Prize in the process.
But we don’t want the perfect to be the enemy of the good, as somebody said (I’ve seen the quote attributed to everybody from Voltaire to Soviet Admiral Sergei Georgievich) – and Arrow’s Theorem doesn’t mean some methods might be better than others, depending on what factors you favor.
That’s the argument is a blog post by Matthew Simonson, a network science doctoral student at Northeastern University. The post at a blog run by the American Mathematical Society (see it here) discusses some of the factors which go into judging fairness – plus a very clever proof showing that the only totally fair system is a dictatorship.
While in theory no system can meet all the fairness criteria we may desire, our challenge is to design a system that will minimize the likelihood of an unfair outcome. Thus, our “perfect design” problem becomes an optimization problem, and luckily there are many candidates: instant runoff voting, approval voting, and the Condorcet method to name a few. The plurality system (the most common one used in the US) is almost certainly not the optimal solution since its highly manipulable by strategic voters and violates a number of other fairness criteria, though its simplicity does have great appeal.
Check it out; it’s worth a read.