Fair Division

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If we use taking turns to divvy up a collection of objects between two people (Bob and Carol), then there is an obvious advantage to going first. Assume that we have decided that Bob will, in fact, choose first (say, by the toss of a coin). Let’s think about how Carol might be compensated. First of all, if there are only three objects, then the “choice sequence” Bob-Carol-Carol seems to be the only reasonable one. Do you agree? For four objects, however, there are two choice sequences that suggest themselves: Bob-Carol-Carol-Carol and Bob-Carol-Carol-Bob. Do you think that one of these is obviously more fair than the other? What if there are four identical objects? What if both Bob and Carol value object A twice as much as B, and B twice as much as C, and C twice as much as D? What sequences suggest themselves for five objects? For eight objects? In one page or less, discuss these questions.

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