> Arrow’s theorem demonstrated with mathematical rigor that what many people seemed to want - a reliable “democratic” procedure for aggregating coherent individ

> Arrow’s theorem demonstrated with mathematical rigor that what many people seemed to want - a reliable “democratic” procedure for aggregating coherent individual preferences to arrive at a coherent collective choice - was simply, logically, unattainable. To understand how reasonable "what many people seemed to want" is, we need to be clear about what is meant by "a coherent collective choice". For example, in the case of a simple yes/no question in a referendum, where all voters are perfectly informed and the consequences of both outcomes are well known, Arrow's theorem has nothing to say. Similarly, if the goal of an election is to reduce the scale of a political problem down from millions of voters to dozens of politicians, Arrow's theorem doesn't preclude that. What is precluded is the idea of reducing the complexities of millions of people's competing and contradictory preferences down into a single set of answers to all questions, or, more conventionally, choosing (in the general case) a single winner of an election who has the support of a majority of voters. That is not an unreasonable thing for many people to seem to want, and the world might be better if there were a simple way of achieving it, but societies can still build systems that are very close to the ideal of democracy despite these mathematical limitations.