Fibonacci sequences and the golden number in voting systems

Title data

Freixas, Josep ; Kurz, Sascha:
Fibonacci sequences and the golden number in voting systems.
2014
Event: 16th International Conference on Fibonacci Numbers and their Applications , 20.-26.07.2014 , Rochester, New York.
(Conference item: Conference , Speech )

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Abstract in another language

Binary voting systems, or simple games, are structures that, up to isomorphism, are countable as a function of the number of voters and / or dierent additional parameters. In the late nineteenth century, Dedekind investigated the problem of counting certain Boolean functions (simple games) and got some seminal results, in the mid-twentieth century May enumerated the class of symmetric games, in which all voters play an equivalent role and therefore belong to the same equivalent class. For certain voting systems some scholars have been determined upper bounds for their number; however it is very dicult in general to determine the exact number of them. Slightly surprising, Fibonacci sequences appear regularly for games with few types of equivalent players and many of the counts dier asymptotically by a multiplicative factor which turns out to be the golden number or a power of it. It is nice to observe that these voting systems are very common in practice and are frequently used to govern many democratic institutions, as councils, counties, parliaments, but also in the boards of many private companies. The paper summarizes the known counts for signicant classes of binary voting systems that follow Fibonacci sequences.