# 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