626 research outputs found

    Approval Voting: Three Examples

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    As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions

    The Trembling Chairman Paradox

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    The Chairman Paradox (Farquharson, 1969) is a classical observation in voting games showing that a Chairman endowed with tie-breaking power might end up with her worst outcome. The analysis posits three players whose preferences build a Condorcet cycle and invokes Iterated Elimination of Weakly Dominated Strategies (IEWDS) to select a unique equilibrium. However, IEWDS is a controversial procedure which exhibits well-known weaknesses. This work relies on non-controversial equilibrium refinements instead. For any cardinal payoffs representing the preferences, two pure-strategy equilibria are trembling-hand perfect, the paradoxical one and another one where the Chairman attains her best outcome. The original paradox is restored (and shown not to actually depend on IEWDS) if one considers the stronger concept of proper equilibrium. The analysis casts new light on a classical paradox and illustrates the difference between properness and trembling-hand perfection in a relevant example

    A Local-Dominance Theory of Voting Equilibria

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    It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting

    Preference Intensity Representation : Strategic Overstating in Large Elections

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    International audienceIf voters vote strategically, is it useful to offer them the possibility of expressing nuanced opinions, or would they always overstate the intensity of their preferences? For additive voting rules, say that a ballot is extremal if it is neither abstention-like nor can be expressed as a mixture of the available ballots. We give a sufficient condition for strategic equivalence: if two rules share the same set of extremal ballots (up to an homothetic transformation), they are strategically equivalent in large elections. This condition is also necessary for the strategic equivalence of positional rules. These results do not hold for small electorates

    Implementation Theory

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    This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered

    The Spatial Analysis of Elections and Committees: Four Decades of Research

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    It has been more than thirty five years since the publication of Downs's (1957) seminal volume on elections and spatial theory and more than forty since Black and Newing (1951) offered their analysis of majority rule and committees. Thus, in response to the question "What have we accomplished since then?" it is not unreasonable to suppose that the appropriate answer would be "a great deal." Unfortunately, reality admits of only a more ambiguous response

    Social choice theory, game theory, and positive political theory

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    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

    Models of Political Economy

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    Models of Political Economy will introduce students to the basic methodology of political economics. It covers all core theories as well as new developments including: decision theory game theory mechanism design games of asymmetric information. Hannu Nurmi's text will prove to be invaluable to all students who wish to understand this increasingly technical field

    Strategic Manipulability is Inescapable: Gibbard-Satterthwaite without Resoluteness

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    The Gibbard-Satterthwaite Theorem on the manipulability of collective-choice procedures treats only of resolute procedures. Few real or reasonable procedures are resolute. We prove a generalization of Gibbard-Satterthwaite that covers the nonresolute case. It opens harder questions than it answers about the prediction of behavior and outcomes and the design of institutions
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