> 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.
The article astutely distinguished between “the will of the majority” and “the will of the people”, which I think is important because there will always be some subset of "the people" that disagree with any policy.
(I suppose one could imagine trivial theoretical policies like "The government pledges not to nuke all of its own cities" which should have universal support from citizens, but this still might not be confirmable through polling data because of Lizardman's Constant.)
So yes, we might be able to say that democracy (if implemented well) allows the will of the majority to be represented most of the time, but the article's point still stands that a winning party or coalition must deliberately commit itself to enacting policies that are unpopular, when intuitively we would think "Why doesn't the party just drop those unpopular policies?".
This is perhaps not surprising, though, as, even considering real world politics in a simplistic one-dimensional way, we know that a left wing party needs to support some unpopular far-left policies if it wants to win the support of such voters, while also trying to appeal to moderates in order to achieve a majority. (Similarly right wing parties need to support some far-right policies to motivate such voters too).
With that observation made, the main thing the article really tells us is that this is an inherent result of majority government, and not specific to any particularly voting system.
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.