- Arrow’s Impossibility Theorem
- Condorcet Paradox
- Duverger’s law, Micromega rule
- Electoral/Voting paradoxes: Downs’ paradox, Discursive dilemma
Arrow’s like paradoxes:
Arrow’s Theorem and Measure Theory:
“The problem of finding good voting systems has been studied at great length. For example, a quick browse reveals a bunch of impossibility theorems related to Arrow’s: the Gibbard–Satterthwaite Theorem, the Duggan–Schwartz Theorem, the Holmström Theorem, … . I know nothing about all this. But perhaps there’s something to be gained by thinking about means of structures.” + a few links there, e.g.:
- Tao: https://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-management/
- Taylor, A. Mathematics and Politics: Strategy, Voting, Power, and Proof. New York: Springer-Verlag, 1995.
Not politcs but economics, and fun: Phillips Machine
Also:
“The society is wise precisely when even the most influential individual’s influence vanishes in the large society limit”