 The golden number and Fibonacci sequences in the design of voting structuresJosep Freixas and Sascha Kurz European Journal of Operational Research, 2013, vol. 226, issue 2, 246-257 Abstract: Some distinguished types of voters, as vetoes, passers or nulls, as well as some others, play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power. In this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters. With this purpose in mind we enumerate these special classes of games and find out that its number always follows a Fibonacci sequence with smooth polynomial variations. As a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor which is the golden number or its square. From a more general point of view, our studies are related with the design of voting structures with a predetermined importance ranking. Keywords: 91A12; 91A80; 91B12; Game theory; Voting systems; Complete simple games; Enumeration and classification; Operational research structures (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:226:y:2013:i:2:p:246-257 DOI: 10.1016/j.ejor.2012.10.017 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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