TY - GEN
T1 - Noise sensitivity and chaos in social choice theory
AU - Kalai, Gil
PY - 2010
Y1 - 2010
N2 - In this paper we study the social preferences obtained from monotone neutral social welfare functions for random individual preferences. It turns out that there are two extreme types of behavior. On one side, there are social welfare functions, such as the majority rule, that lead to stochastic stability of the outcome in terms of perturbations of individual preferences. We identify and study a class of social welfare functions that demonstrate an extremely different type of behavior which is completely chaotic: they lead to a uniform probability distribution on all possible social preference relations and, for every ε > 0, if a small fraction e of individuals change their preferences (randomly) the correlation between the resulting social preferences and the original ones tends to zero as the number of individuals in the society increases. This class includes natural multi-level majority rules.
AB - In this paper we study the social preferences obtained from monotone neutral social welfare functions for random individual preferences. It turns out that there are two extreme types of behavior. On one side, there are social welfare functions, such as the majority rule, that lead to stochastic stability of the outcome in terms of perturbations of individual preferences. We identify and study a class of social welfare functions that demonstrate an extremely different type of behavior which is completely chaotic: they lead to a uniform probability distribution on all possible social preference relations and, for every ε > 0, if a small fraction e of individuals change their preferences (randomly) the correlation between the resulting social preferences and the original ones tends to zero as the number of individuals in the society increases. This class includes natural multi-level majority rules.
UR - http://www.scopus.com/inward/record.url?scp=84880275854&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-13580-4_8
DO - 10.1007/978-3-642-13580-4_8
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AN - SCOPUS:84880275854
SN - 9783642135798
T3 - Bolyai Society Mathematical Studies
SP - 173
EP - 212
BT - Fete of Combinatorics and Computer Science
T2 - Meeting on Fete of Combinatorics and Computer Science
Y2 - 11 August 2008 through 15 August 2008
ER -