The general relevance of the impossibility teorem in smooth social choice

✍ Scribed by Norman Schofield

• Publisher: Springer US
• Year: 1984
• Tongue: English
• Weight: 984 KB
• Volume: 16
• Category: Article
• ISSN: 0040-5833
• DOI: 10.1007/bf00141673

✦ Synopsis

A complete classification theorem for voting processes on a smooth choice space Ir of dimension w is presented. Any voting process a is classified by two integers v*(a) and w(a), in terms of the existence or otherwise of the optima set, IO(a), and the cycle set IC(a).

In dimension below v*(o) the cycle set is always empty, and in dimension above w(a) the optima set is nearly always empty while the cycle set is open dense and path connected. In the latter case agenda manipulation results in any outcome.

For admissible (compact, convex) choice spaces, the two sets are related by the general equilibrium result that IO(a) union IC(a) is non-empty. This in turn implies existence of optima in low dimensions. The equilibrium theorem is used to examine voting games with an infinite electorate, and the nature of structure induced equilibria, induced by jurisdictional restrictions.

"Disequilibrium, or the potential that the status quo be upset, is the characteristic feature of politics".