Voting systems

Mathematics and economics of aggregate group preferences; the will of the people (whatever that might be); social choice theory

September 22, 2014 — April 21, 2022

Figure 1

There’s lots of interesting mathematics around this democracy business, and its shortcomings. Insert disclaimers about the complicated relationship between is and ought, and model and actuality. Anyway… I’ll look at that here. Whining about modern democratic failure I’ll leave to capitalism’s end game and practical analysis to psephology.

1 Alternatives to/improvements upon voting for deciding things

Utopian mechanisms.

Figure 2: Tom Gauld, Voting system

2 References

Buchanan, James M. 1954. Social Choice, Democracy, and Free Markets.” Journal of Political Economy.
Buchanan, James M, and Tullock. 1962. The Calculus of Consent: Logical Foundations of Constitutional Democracy.
Chau, Gonzalez, and Sejdinovic. 2022. Learning Inconsistent Preferences with Gaussian Processes.” In Proceedings of The 25th International Conference on Artificial Intelligence and Statistics.
Chaum. n.d. “Far Lower Cost, Better Quality and More Democratic.”
Duggan, and Schwartz. 2000. Strategic Manipulability Without Resoluteness or Shared Beliefs: Gibbard-Satterthwaite Generalized.” Social Choice and Welfare.
Gajdos, Tallon, and Vergnaud. 2008. Representation and Aggregation of Preferences Under Uncertainty.” Journal of Economic Theory.
Geanakoplos. 1996. Three Brief Proofs of Arrow’s Impossibility Theorem.” Cowles Foundation Discussion Paper 1123R3.
Ingham. 2019. Why Arrow’s Theorem Matters for Political Theory Even If Preference Cycles Never Occur.” Public Choice.
List, and Pettit. 2004. Aggregating Sets of Judgments: Two Impossibility Results Compared 1.” Synthese.
Masuda, and Redner. 2011. “Can Partisan Voting Lead to Truth?” Journal of Statistical Mechanics: Theory and Experiment.
Perony, Pfitzner, Scholtes, et al. 2013. Enhancing Consensus Under Opinion Bias by Means of Hierarchical Decision Making.” Advances in Complex Systems.
Risse. 2001. Arrow’s Theorem, Indeterminacy, and Multiplicity Reconsidered.” Ethics.
———. 2003. Democracy and Social Choice: A Response to Saari.” SSRN Scholarly Paper.
Saari. 2003. Capturing the ‘Will of the People’.” Ethics.
Satterthwaite. 1975. Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions.” Journal of Economic Theory.
Taylor. 2002. The Manipulability of Voting Systems.” The American Mathematical Monthly.