The Mediancentre Rule for Many Alternatives

Union College research fellowship, summer 2009
Advisor: Prof. William Zwicker
Based upon work by Ari Morse and Andy Mackenzie

Official abstract:

We continue research into the mediancentre voting rule, the recently introduced variant of the Borda count. In particular, we extend the investigation of this rule to beyond 3 alternatives. We have determined that at up to 4 alternatives, the mediancentre rule seems to outperform the mean rule in terms of manipulability, as expected. We have also found that it seems to have a higher Condorcet efficiency. Finally, we have continued work on finding reliable ways to find ties, and we have found two classes of profiles that we believe describe all 2-way ties for 3 alternatives.

To describe it in less esoteric terms: this project was a continuation of a long line of student research in voting theory, a discipline of mathematics that is much more interesting than it sounds due to some surprising limitations on what a voting system can do. This project involved writing and using a set of programs to probe the properties of the mediancentre rule, a voting system invented by Prof. William Zwicker. This line of research is certainly incomplete; the final report represents the results from the first attempts to expand our investigation to 4 candidates or more. Much remains to be explored, and many problems remained to be resolved (e.g. we are yet to find a reliable way to detect ties).

• Final report [pdf]
• Data, programs, source files [tar.gz]

For space reasons, the data files I generated with these programs are not included in the above tarball. If you want these files (i.e. to continue my research without recomputing all data from scratch), try contacting me to see if we can arrange for me to send the data to you.

This work is licensed under a Creative Commons Attribution 3.0 United States License.