Nature and statistics of majority rankings in a dynamical model of preference aggregation

Details Nature and statistics of majority rankings in a dynamical model of preference aggregation Nature and statistics of majority rankings in a dynamical model of preference aggregation

2007-09-19

arxiv.org/abs/0709.3018v1

Physics

Physics and Society

11 pages

Scientific paper

10.1016/j.physa.2007.10.046

We present numerical results on a complex dynamical model for the aggregation of many individual rankings of S alternatives by the pairwise majority rule under a deliberative scenario. Agents are assumed to interact when the Kemeny distance between their rankings is smaller than a range R. The main object of interest is the probability that the aggregate (social) ranking is transitive as a function of the interaction range. This quantity is known to decay fast as S increases in the non-interacting case. Here we find that when S>4 such a probability attains a sharp maximum when the interaction range is sufficiently large, in which case it significantly exceeds the corresponding value for a non-interacting system. Furthermore, the situation improves upon increasing S. A possible microscopic mechanism leading to this counterintuitive result is proposed and investigated.

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