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By Donald G. Saari

This hugely obtainable ebook deals undergraduates and pros a brand new, diverse interpretation and determination of Arrow's and Sen's theorems. utilizing uncomplicated arithmetic, it exhibits that those detrimental conclusions come up simply because, in every one case, a few of their assumptions negate different the most important assumptions. as soon as this is often understood, not just do the conclusions turn into anticipated, yet a large category of alternative phenomena is additionally expected. those contain inter alia legislative cycles, offer and insist economics, statistical paradoxes, and various voting/election paradoxes.

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Additional resources for Decisions and Elections: Explaining the Unexpected

Example text

The attraction of this example is that although the plurality outcome ranks Ann above Barb, the election outcomes for all subsets of candidates rank Barb higher. But, while informative, this example has nothing to do with binary independence. Instead, the argument casts doubt on the plurality vote by showing how its outcome is directly contradicted by the outcomes of a large class of unspecified procedures. Wait; what methods? No other procedures are mentioned in the example. Yet, the extreme conformity of the election outcomes for the triplets conveys the strong sense that any reasonable method using the rankings of triplets must rank Barb above Ann.

Remember, a wrong decision can be costly; it can create inefficiencies. " Here, the engineer identifies the top-ranked alternative for each criterion and then selects the alternative which is top-ranked most often. As this is equivalent to using the plurality vote where the ranking of each criterion is treated as the preferences of a voter, our engineer's choice is to use the Milwaukee company's what-ma-call-it. But, suppose our engineer, fully aware of the dangers and costs of using a faulty part in the design of his product, is risk-adverse.

Allowing voters to have all possible preferences is akin to complicating the needle search by dropping another load of hay on the pile. Rather than adding to the disarray, let's first understand what happens when voters have strict, transitive preferences. The next condition captures the sense that voters should be allowed to rank the candidates in any desired strict manner. Ann's supporters (from the introductory example on page 27), for instance, could correctly argue that freedom fails to exist if nobody is permitted to rank Ann as their favorite candidate.

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