Social Choice

August 11th, 2011

Combinatorial, probabilistic and algorithmic methods in social choice theory

It has been shown in the last several decades that every reasonable voting rule is susceptible to various “paradoxes” (undesirable behaviour such as being strategically manipulable, failing to elect a Condorcet winner, etc). It therefore makes sense to quantify the extent to which this behaviour can occur, and this brings in probability theory. Important issues to be dealt with include the probability distribution on the space of opinions (“culture”), and whether to use random sampling, asymptotic analysis, or exact counting.

The aim of this project is to use more sophisticated methods than have typically been used so far in order to understand the quantitative behaviour of voting rules. Our main ideas are

  • The area would benefit from a more rigorous and elegant mathematical treatment. Several mathematical errors are found in the existing literature, and results are often insufficiently general and/or presented in a confusing way.
  • The measures used, such as the indicator of manipulability, are often extremely crude. We intend a much more detailed study.
  • Some families of rules can be quite well studied analytically in much more generality than has been done so far.
  • Most calculations have been restricted to computing the probability of certain simple events, or the mean of some random variables. More detailed information on the probability distributions is desirable.
People involved: Geoffrey Pritchard, Mark Wilson. Publications can be found under the category Social Choice.

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