David A. Meyer and Thad A. Brown,
``Statistical mechanics of voting'',
Physical Review Letters 81 (1998) 1718-1721,
cond-mat/9806359.
Decision procedures aggregating the preferences of multiple agents can
produce cycles and hence outcomes which have been described
heuristically as `chaotic'. We make this description precise by
constructing an explicit dynamical system from the agents' preferences
and a voting rule. The dynamics form a one dimensional statistical
mechanics model; this suggests the use of the topological entropy to
quantify the complexity of the system. We formulate natural
political/social questions about the expected complexity of a voting
rule and degree of diversity among agents in terms of random matrix
models--ensembles of statistical mechanics models--and compute
quantitative answers in some representative cases.
PlainTeX (9 pages): PostScript (193K),
PDF (160K).
Reported in:
-
Phillip F. Schewe and Ben Stein,
Physics
News Update, Number
385,
3 August 1998;
``Chaos in
group decisions'',
Physics
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4 August 1998;
Physical Review
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-
Javier Crúz,
``La teoría de decisiones es un puritito caos'',
Reforma,
Ciencia, 13 August 1998
[local image].
-
``Chaos
at the polls'',
New Scientist,
News,
15 August 1998, p. 25.
-
Mario Aguilera,
``Chaos
at the polls: mathematicians prove that group decisions can be impossible
to predict'',
UCSD News &
Information,
Science and
Engineering News Releases,
1 September 1998;
UC NewsWire,
1 September 1998
[local image];
ScienceDaily,
9 September 1998
[local image].
-
Amanda Onion,
``Math experts find the formula for electoral chaos'',
Fox News Online,
Sci-Tech, 17 September 1998
[local image].
-
Malcolm W. Brown,
``Science
squints at a future fogged by chaotic uncertainty'',
The New York Times,
National
Science, 22 September 1998
[local image].
-
Paul Arnold, interview,
BBC Radio 5,
The Formula, 27 September 1998.
-
Aloísio Araújo,
``Regras eleitorais e comportamento caótico'',
Ciência Hoje,
vol.24, no.144, November 1998, pp. 13-14.
Last modified: 30 november 1998