Posted by: maroonmaurader | November 11, 2009

Arrow’s Impossibility Theorem

It’s a theorem in the mathematical field of voting theory. The full mathematical proof is probably inaccessible, and unless you’re a voting theory mathematician probably not as interesting. The informal proof on wikipedia is not necessarily easy to follow for a non-mathematician, but with some careful thought should be accessible to anyone with a basic understanding of logical reasoning. And it has an amusingly disconcerting outcome, unless you read it with a very keen eye for hidden assumptions.

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Responses

  1. 1. The paper on which Wikipdia’s informal proof is based is easier to follow: http://cowles.econ.yale.edu/P/cd/d11a/d1123-r3.pdf.

    2. I guess you can get from the same body of facts from which Arrow deduced his impossibility theorem to the conclusion that (assuming preferences are configured as they often are), whoever sets the voting agenda in a majority-rules body is the “dictator.” There’s an article in the 1977 Virginia Law Review (“Agenda influence and its implications,” which I’ve been unable to find) that dramatically illustrates this.

    A description: “Levine and Plott (1977) describe a case of agenda manipulation that students will find interesting. The authors were members of a flying club and were selected to be on the committee that determined the agenda to be used in deciding which types of airplanes to purchase. They conducted a survey of members’ preferences and then designed the agenda to achieve the configuration of types of planes that they preferred. The votes in the actual meeting went as they had predicted, and the president of the club tried unsuccessfully to deviate from the agenda during the course of the meeting.”


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