2015-2016 AP Football Poll Using Alternative Voting Methods

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College football polls such as the AP Poll are perhaps the most familiar real-world examples of nonplurality voting systems. The AP Poll comprises roughly sixty members of the media; each week, voters submit their personal rankings of the top 25 football teams. The rankings are calculated using a Borda count, in which a first-place vote is worth 25 points, a second-place vote is worth 24 points, and so on. However, the rankings may be different depending on the voting method used. This Demonstration contains complete AP Poll voter data for the 2015–2016 season and uses this data to rank the top football teams under alternative voting methods.

Contributed by: Vivek Kaushik, Aubrey Laskowski, Matthew Romney, Yukun Tan (April 2016)
Based on an undergraduate research project at the Illinois Geometry Lab directed by A. J. Hildebrand.
Open content licensed under CC BY-NC-SA


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Details

The AP Poll could have used alternative voting methods. An obvious question is to what extent the resulting rankings depend on the choice of voting method. This Demonstration considers what are called positional voting methods, in which a fixed weight is assigned for a vote of each type. For example, the actual AP Poll assigns points for a vote of rank . This Demonstration lets you prescribe your own voting method by individually choosing the weight of each vote type. For convenience, it also includes several predefined voting methods.

We have included complete AP Poll voter data for the 2015–2016 season. The data used here was obtained from www.collegepolltracker.com.

References

[1] D. G. Saari, Basic Geometry of Voting, New York: Springer-Verlag, 1995.

[2] D. G. Saari and F. Valognes, "Geometry, Voting, and Paradoxes," Mathematics Magazine, 71(4), 1998 pp. 243–259. www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1999/0025570x.di021206.02p0091u.pdf.



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