20,773 research outputs found
Statistical mechanics of voting
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 cohesion/diversity among agents in terms of random matrix
models---ensembles of statistical mechanics models---and compute quantitative
answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages
Social choice theory, game theory, and positive political theory
We consider the relationships between the collective preference and non-cooperative game theory approaches to positive political theory. In particular, we show that an apparently decisive difference between the two approachesthat in sufficiently complex environments (e.g. high-dimensional choice spaces) direct preference aggregation models are incapable of generating any prediction at all, whereas non-cooperative game-theoretic models almost always generate predictionis indeed only an apparent difference. More generally, we argue that when modeling collective decisions there is a fundamental tension between insuring existence of well-defined predictions, a criterion of minimal democracy, and general applicability to complex environments; while any two of the three are compatible under either approach, neither collective preference nor non-cooperative game theory can support models that simultaneously satisfy all three desiderata
Voting and the Cardinal Aggregation of Judgments
The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections
Incorporating stakeholders’ knowledge in group decision-making
International audienc
Perspectives on Preference Aggregation
For centuries, the mathematical aggregation of preferences by groups, organizations or society has received keen interdisciplinary attention. Extensive 20th century theoretical work in Economics and Political Science highlighted that competing notions of “rational social choice” intrinsically contradict each other. This led some researchers to consider coherent “democratic decision making” a mathematical impossibility. Recent empirical work in Psychology qualifies that view. This nontechnical review sketches a quantitative research paradigm for the behavioral investigation of mathematical social choice rules on real ballot, experimental choice, or attitudinal survey data. The paper poses a series of open questions. Some classical work sometimes makes assumptions about voter preferences that are descriptively invalid. Do such technical assumptions lead the theory astray? How can empirical work inform the formulation of meaningful theoretical primitives? Classical “impossibility results” leverage the fact that certain desirable mathematical properties logically cannot hold universally in all conceivable electorates. Do these properties nonetheless hold in empirical distributions of preferences? Will future behavioral analyses continue to contradict the expectations of established theory? Under what conditions and why do competing consensus methods yield identical outcomes?
Anyone but Him: The Complexity of Precluding an Alternative
Preference aggregation in a multiagent setting is a central issue in both
human and computer contexts. In this paper, we study in terms of complexity the
vulnerability of preference aggregation to destructive control. That is, we
study the ability of an election's chair to, through such mechanisms as
voter/candidate addition/suppression/partition, ensure that a particular
candidate (equivalently, alternative) does not win. And we study the extent to
which election systems can make it impossible, or computationally costly
(NP-complete), for the chair to execute such control. Among the systems we
study--plurality, Condorcet, and approval voting--we find cases where systems
immune or computationally resistant to a chair choosing the winner nonetheless
are vulnerable to the chair blocking a victory. Beyond that, we see that among
our studied systems no one system offers the best protection against
destructive control. Rather, the choice of a preference aggregation system will
depend closely on which types of control one wishes to be protected against. We
also find concrete cases where the complexity of or susceptibility to control
varies dramatically based on the choice among natural tie-handling rules.Comment: Preliminary version appeared in AAAI '05. Also appears as
URCS-TR-2005-87
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