Probabilistic electoral methods, representative probability, and maximum entropy

Roger Sewell, David MacKay, Iain McLean

A probabilistic electoral system is described in a context accessible to readers not familiar with social choice theory. This system satisfies axioms of: identical treatment of each voter and of each candidate; universal domain; fair representation of the pairwise preferences of the electorate; independence of irrelevant alternatives; and clarity of voting for pairwise outcomes; and hence Arrow's other axioms (weak Pareto and no dictator) are also satisfied. It produces in an information-theoretic sense the least surprising outcome given any candidate-symmetric prior beliefs on the voters' prefer- ences, and is shown to be able to compromise appropriately in situations where a Condorcet winner would not be elected top under many other systems. However, difficulties can arise with this system in situations where one political party is permitted to flood the candidate list with large numbers of their own candidates.

The empirical properties of this system are explored and compared with the systems known as "Majority (or Plurality) Rule" and "Random Dictator".

We also make the case for using a probabilistic system even in the simple 2-candidate case.

This paper was accepted (Dec 2008) for publication in Voting Matters. The published paper (Issue 26, January 2009) is available as a pdf file.

[This paper was formerly titled 'A maximum entropy approach to fair elections']

David MacKay
Last modified: Sat Jan 24 22:36:57 2009