Arrow’s Theorem

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Arrow’s Theorem#

Arrow’s is often formulated as a theorem on voting methods. Technically, it is a theorem about logic, on the non-existence of a certain mathematical structure known as a “principal ultrafilter”.

There are many reasons that make this theorem so interesting and influential.

Mathematically, it is simple and beautiful. It also proved to be surprisingly robust under various changes of the basic assumptions.

Moreover, the theorem can be interpreted in many different ways. For example, Diane Coyle in her book “Cogs and Monsters” says

Arrow’s theorem is really a formal statement of the obvious truth that there are unavoidable conflicts of interest or dilemmas in society. [1]

More traditional is to say that Arrow’s theorem shows the impossibility of a fair voting procedure that aggregates the preferences of all voters.

… to be continued …

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