Complete voting systems with two classes of voters: weightedness and counting
We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.
KeywordsVoting systems Simple games Weighted games Complete simple games Fibonacci sequence
Unable to display preview. Download preview PDF.
- Boros, E., Hammer, P. L., Ibaraki, T., & Kawakawi, K. (1991). Identifying 2-monotonic positive boolean functions in polynomial time. In W. L. Hsu & R. C. T. Lee (Eds.), LNCS: Vol. 557. ISA’91 algorithms (pp. 104–115). Berlin: Springer. Google Scholar
- Cameron, P. J. (1994). Combinatorics: topics, techniques, algorithms. Cambridge: Cambridge University Press. Google Scholar
- Dunlap, R. A. (1998). The golden ratio and Fibonacci numbers. Singapore: World Scientific. Google Scholar
- Hu, S. T. (1965). Threshold logic. Berkeley: University of California Press. Google Scholar
- Taylor, A. D., & Zwicker, W. S. (1992). A characterization of weighted voting. In Proceedings of the American mathematical society (Vol. 115, pp. 1089–1094). Google Scholar
- Taylor, A. D., & Zwicker, W. S. (1999). Simple games: desirability relations, trading, and pseudoweightings. Princeton: Princeton University Press. Google Scholar