Voting Systems - Prüfungsnummer 9958387

Why is the US President elected in a completely different way than the President of France? Why does Ireland use yet another completely different method? Why is there not just the one universally accepted method for such elections?

How could it happen that Jesse Ventura was elected Governor of Minnesota in 1998 even though more than 60% of the voters considered him to be the worst of the three major candidates?

This is the kind of questions that we will discuss during this course. Our first step will be to analyse the “usual” voting systems and to establish their main properties. To this end we will essentially use mathematical techniques. The required mathematical prerequisites will however be elementary and thus the material will be accessible to students of all faculties without special preparations. In this process, we will find out that every known voting system behaves in a very unexpected (and usually undesired) way in certain circumstances. In this respect, the course will culminate with the insight derived by Kenneth Arrow in the 1950s that all voting methods have undesired properties. Thus, in every election scenario, one has to decide which disadvantages must be avoided at all costs and which one is prepared to accept. (The mathematical proof of this result was one of the main reasons why Arrow was awarded the Nobel Prize for Economics in 1972.)

At the end of the semester, you will have an overview of available voting methods and their properties. You will know which method can be reasonably used in which situation. Furthermore, you will be able to recognize potential manipulations that are possible when certain methods are used under specific conditions and you can work towards preventing such manipulations.

Literature:
C. Börgers: Mathematics of Social Choice. SIAM, Philadelphia (2010).
K. Diethelm: Gemeinschaftliches Entscheiden - Untersuchung von Entscheidungsverfahren mit mathematischen Hilfsmitteln. Springer, Berlin (2016), ix+138 pp., ISBN 978-3-662-48779-2.
J. K. Hodge, R. E. Klima: The Mathematics of Voting and Elections: A Hands-On Approach. Amer. Math. Soc., Providence (2005).
D. G. Saari: Chaotic Elections. Amer. Math. Soc., Providence (2001).

Dozent: Prof. Dr. Diethelm Kai

Stand: 10.08.2023