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> What do you mean?

Proportionality of representation in the legislature strongly predicts both number of sustainable parties and public satisfaction with government in modern democracies.

> These systems tend to select for "best compromise" or centrist candidates, which should represent the population pretty well.

Not really; it's not like views on political issues are clearly unimodally distributed such that a single compromise candidate does anything but make everyone in the electorate feel like they have no effective representation of their views in government. That's what proportionality avoids.

Well whether people feel like they are represented, is a very different goal. The ideal "compromise candidate" has the majority opinion on every individual issue, and so accurately represents their population.

> The ideal "compromise candidate" has the majority opinion on every individual issue

Even if they did, representing the majority opinion in each district in the legislature and taking the majority for those majorities as the policy is not the same as directly representing the diversity of views in the electorate in the legislature and taking the majority of that diversity as the policy.

An ideal single-winner system aims to approximate the former, an ideal proportional representation seeks to approximate the latter. Even an deal single-winner system doesn't approximate what PR is doing.

Proportionality, particularly, mitigates the difference in representation between geographically diffuse and geographically concentrated viewpoints that occurs in any, even ideal, single-member district system.

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