Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life – Avinash K. Dixit, Barry J. Nalebuff

Chapter 10

The Strategy of Voting

The foundation of a democratic government is that it respects the will of the people as expressed through the ballot box. Unfortunately, these lofty ideals are not so easily implemented. Strategic issues arise in voting, just as in any other multiperson game. Voters will often have an incentive to misrepresent their true preferences. Neither majority rule nor any other voting scheme can solve this problem, for their does not exist any one perfect system for aggregrating up individuals’ preferences into a will of the people.*

* This deep result is due to Stanford University professor Kenneth Arrow. His famous “impossibility” theorem shows that any system for aggregating unrestricted preferences over three or more alternatives into a group decision cannot simultaneously satisfy the following minimally desirable properties: (i) transitivity, (ii) unanimity, (iii) independence of irrelevant alternatives, (iv) non-dicatatorship. Transitivity requires that if A is chosen over B and B is chosen over C, then A must be chosen over C. Unanimity requires A to be chosen over B when A is unanimously preferred to B. Independence of irrelevant alternatives requires that the choice between A and B does not depend on whether some alternative C is available. Non-dicatorship requires that there is no individual who always gets his way and thus has dicatorial powers.

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