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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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