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

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure

An 'exception culturelle'? French sensationist political economy and the shaping of public economics

This paper examines some ideas developed in the field of public economics by French Sensationist political economists, from Turgot and Condorcet to the young Jean-Baptiste Say. An ideal-typical account of their position is based on the fact that issues raised by public expenditure and revenue are not dealt with independently. Instead, a strong link between the two sides of the budget is emphasized, an approach arising out of political considerations concerning human rights and equity. Following on from this they develop a theory of public expenditure based on public goods�-�national and local�-�and externalities, and a theory of taxation culminating in a justification of progressive taxation. The central section of the paper forms a kind of pivotal point in the analysis, showing how the above political and ethical requirements of the theory lead to the first estimation of the optimal amount of public expenditure and revenue�-�involving an equilibrium at the margin.History of public economics, Turgot, Condorcet, Roederer, Say, public goods, externalities, equity in taxation, progressive taxation, optimal amount of public expenditure and revenue, equilibrium at the margin,

Disentangling Referendums and Direct Democracy: A Defence of the Systemic Approach to Popular Vote Processes

What is the relationship between referendum and initiative processes and democracy? The dominant understanding is that these popular vote processes are institutions associated with a model of direct democracy that stands in opposition to representative democracy. However, this pervasive approach is rarely justified and appears to limit the study of popular vote processes by focusing on implausible ideals, obscuring that many democratic institutions face similar challenges, and encouraging overgeneralising claims that neglect institutional variation in referendum and initiative processes. Previous criticisms of the association of popular vote processes with direct democracy have failed to clearly articulate an alternative. We trace the emergence of a democratic systems approach to popular vote processes and argue that it provides a better conceptual framework to empirically study and normatively discuss these processes

Dynamics of strategic three-choice voting

In certain parliamentary democracies, there are two major parties that move in and out of power every few elections, and a third minority party that essentially never governs. We present a simple model to account for this phenomenon, in which minority party supporters sometimes vote ideologically (for their party) and sometimes strategically (against the party they like the least). The competition between these disparate tendencies reproduces the empirical observation of two parties that frequently exchange majority status and a third party that is almost always in the minority. Copyright (C) EPLA, 200