Combinatorics of social choice
Noga Alon gave a plenary lecture at the recently concluded EURO 2010 conference . He presented six results in social choice theory, which included classic theorems and also some new work by Alon and his coauthors. The results are stated in an informal manner and therefore should be taken with a grain of salt: Majority can be irrational (Condorcet's Paradox) Majority can be chaotic (McGarvey's Theorem) Only reasonable voting scheme is a dictatorship (Arrow's impossibility theorem) Any reasonable leader election scheme can be manipulated (Gibbard–Satterthwaite theorem) Bigger committees require bigger budgets. Cheating is inherent in 'reality show survivor games' .