A Difficulty in the Concept of Social Welfare

Condensed Matter journal club

A Difficulty in the Concept of Social Welfare

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You may have noticed some difficulties reaching an agreement in recent political debate.  In part, this is because it is impossible to have a fair, democratic vote when there are more than two options.  Unlike the normal usage (i.e. "In accordance with my personal prejudices") "Democratic Fairness" has to be defined rigorously for a voting system, as follows.

Democratic - no one individual is guaranteed to get their preference

Deterministic - if the process is run again with the same voter preferences, it gives the same answer

Universal - the process should provide a complete ranking of all options.

Independence of irrelevant alternatives - the fact that option A is preferred to option B, cannot be changed by including/excluding some other option C in the vote

Unianimity - if everyone prefers A to B, then the system must rank A above B

Unrestricted - for any possible outcome some set of voting preferences exists which will give it.

The impossibility to devise a fair voting system was elegantly proved by Arrow in 1950, and is one of the things "everyone should know, but nobody does". I'll go through the proof.

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Given the diversity of research in the CM group, chosen topics vary widely. We tend to stick to high-impact journals - Nature, Science, PNAS and PRL have been popular - but this is not prescriptive..

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