By Alan D Taylor; Mathematical Association of America

ISBN-10: 0521008832

ISBN-13: 9780521008839

ISBN-10: 0521810523

ISBN-13: 9780521810524

"Honesty in balloting, it seems, isn't really constantly the simplest coverage. certainly, within the early Nineteen Seventies, Allan Gibbard and Mark Satterthwaite, development at the seminal paintings of Nobel Laureate Kenneth Arrow, proved that with 3 or extra choices there is not any moderate vote casting method that's non-manipulable; citizens will continually have a chance to learn through filing a disingenuous poll. the consequent many years produced a few theorems of notable mathematical naturality that handled the manipulability of vote casting structures. This publication provides a lot of those effects from the final region of the 20 th century - specially the contributions of economists and philosophers - from a mathematical perspective, with many new proofs. The presentation is nearly thoroughly self-contained and calls for no must haves other than a willingness to keep on with rigorous mathematical arguments."--BOOK JACKET. Read more... 1. An creation to social selection concept -- 2. An creation to manipulability -- three. Resolute balloting principles -- four. Non-resolute vote casting ideas -- five. Social selection services -- 6. Ultrafilters and the limitless -- 7. extra on resolute tactics -- eight. extra on non-resolute methods -- nine. different election-theoretic contexts

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**Additional info for Social choice and the mathematics of manipulation**

**Sample text**

The ballots of the other voters are held fixed. This corresponds to the assumption that this particular voter has complete knowledge of how everyone else voted (or perhaps better: will vote) and can capitalize on this knowledge to secure a better outcome – better, that is, from his or her point of view – by submitting an insincere ballot. We are, by the way, considering only the kind of manipulation that involves a ballot change by a single voter. 4. More precisely, a voting rule V is manipulable if there are two profiles P and P and a voter i such that P|N − {i} = P |N − {i} and voter i, whose true preferences we take to be Pi , “prefers” V(P ) to V(P).

In general, a sufficiently optimistic voter will compare two election outcomes (that is, two sets of alternatives) by asking which has a larger max according to the voter’s true preference ranking of the alternatives – that is, by using (iii). On the other hand, if a voter is sufficiently pessimistic, and if he or she ranks a over b over c over d, then he or she will prefer an election outcome of {b, c} to an election outcome of {a, d}. This is because he or she will assume – pessimistically – that d (his or her worst choice overall) will result from an election outcome of {a, d}, while c (his or her third choice overall) will result from an election outcome of {b, c}.

15) The Borda Count: An alternative is a winner if no alternative has strictly more total points in one-on-one contests, where a point is gained for an alternative x each time we have xPi z for some i and some z. More precisely, the voting rule V is the Borda count if, for every x ∈ A, x ∈ V(P) iff ∀y ∈ A {W(x, z, P) : z ∈ A} ≥ {W(y, z, P) : z ∈ A}. (16) The Pareto Rule: An alternative is a winner unless there is some alternative that every voter prefers to it. More precisely, the voting rule V is the Pareto procedure if, for every x ∈ A, x ∈ V(P) iff ∀y ∈ A ∃i ∈ N xPi y.

### Social choice and the mathematics of manipulation by Alan D Taylor; Mathematical Association of America

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