A dynamic model of democratic elections in multidimensional policy spaces

We propose a general model of repeated elections. In each period, a challenger is chosen from the electorate to run against an incumbent politician in a majority-rule election, and the winner then selects a policy from a multidimensional policy space. Individual policy preferences are private information, whereas policy choices are publicly observable. We prove existence and continuity of equilibria in "simple" voting and policy strategies; we provide examples to show the variety of possible equilibrium patterns in multiple dimensions; we analyze the effects of patience and office-holding benefits on the persistence of policies over time; and we identify relationships between equilibrium policies and the core of the underlying voting game. As a byproduct of our analysis, we show how equilibrium incentives maylead elected representatives to make policy compromises, even when binding commitments are unavailable. We provide an informational story for incumbency advantage. Finally, we give an asymptotic version of the median voter theorem for the one-dimensional model as voters become-arbitrarily patient

A General Bargaining Model of Legislative Policy-making

We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be bad for all legislators, and delay may be Pareto efficient. We prove existence of stationary equilibria. We show that if all legislators are risk averse or if even limited transfers are possible, then delay is only possible if the status quo lies in the core. Thus, we expect immediate agreement in multidimensional models, where the core is typically empty. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. Our comparative statics analysis yield two noteworthy insights: moderate status quos imply moderate policy outcomes, and legislative patience implies policy moderation

Electoral Competition with Uncertainty Averse Parties

The nonexistence of equilibria in models of electoral competition involving multiple issues is one of the more puzzling results in political economics. In this paper, we relax the standard assumption that parties act as expected utility maximizers. We show that equilibria often exist when parties with limited knowledge about the electorate are modeled as uncertainty-averse. What is more, these equilibria can be characterized as a straightforward generalization of the classical median voter result.Uncertainty Aversion, Multiple Priors, Median Voter, Electoral Competition over many Issues

Laboratory Experiments in Political Economy

Most of the laboratory research in political science follows the style that was pioneered in experimental economics a half-century ago by Vernon Smith. The connection between this style of political science experimentation and economics experimentation parallels the connection between economic theory and formal political theory.

Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle versus Stackelberg

We study majority voting over a bidimensional policy space when the voters' type space is either uni- or bidimensional. We show that a Condorcet winner fails to generically exist even with a unidimensional type space. We then study two voting procedures widely used in the literature. The Stackelberg (ST) procedure assumes that votes are taken one dimension at a time according to an exogenously specified sequence. The Kramer-Shepsle (KS) procedure also assumes that votes are taken separately on each dimension, but not in a sequential way. A vector of policies is a Kramer-Shepsle equilibrium if each component coincides with the majority choice on this dimension given the other components of the vector. We study the existence and uniqueness of the ST and KS equilibria, and we compare them, looking e.g. at the impact of the ordering of votes for ST and identifying circumstances under which ST and KS equilibria coincide. In the process, we state explicitly the assumptions on the utility function that are needed for these equilibria to be well behaved. We especially stress the importance of single crossing conditions, and we identify two variants of these assumptions: a marginal version that is imposed on all policy dimensions separately, and a joint version whose definition involves both policy dimensions.

Ideology and existence of 50% majority equilibria in Multidimensional spatial voting Models .

When aggregating individual preferences through the majority rule in an n-dimensional spatial voting model, the ‘worst-case’ scenario is a social choice configuration where no political equilibrium exists unless a super-majority rate as high as 1 — 1/(n+1) is adopted. In this paper we assume that a lower d-dimensional (dideology, mean voter theorem, spatial voting, super majority;

Ideology and existence of 50%-majority equilibria in multidimensional spatial voting models

When aggregating individual preferences through the majority rule in an n-dimensional spatial voting model, the `worst-case' scenario is a social choice configuration where no political equilibrium exists unless a super majority rate as high as 1-1/n is adopted. In this paper we assume that a lower d-dimensional (d smaller than n) linear map spans the possible candidates' platforms. These d `ideological' dimensions imply some linkages between the n political issues. We randomize over these linkages and show that there almost surely exists a 50%-majority equilibria in the above worst-case scenario, when n grows to infinity. Moreover the equilibrium is the mean voter. The speed of convergence (toward 50%) of the super majority rate guaranteeing existence of equilibrium is computed for d=1 and 2.

A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces

We propose a general model of repeated elections. In each period, a challenger is chosen from the electorate to run against an incumbent politician in a majority-rule election, and the winner then selects a policy from a multidimensional policy space. Individual policy preferences are private information, whereas policy choices are publicly observable. We prove existence and continuity of equilibria in “simple” voting and policy strategies; we provide examples to show the variety of possible equilibrium patterns in multiple dimensions; we analyze the effects of patience and office-holding benefits on the persistence of policies over time; and we identify relationships between equilibrium policies and the core of the underlying voting game. As a byproduct of our analysis, we show how equilibrium incentives may lead elected representatives to make policy compromises, even when binding commitments are unavailable. We provide an informational story for incumbency advantage. Finally, we give an asymptotic version of the median voter theorem for the one-dimensional model as voters becomes arbitrarily patient.

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

A MODEL OF ENDOGENOUS POLITICAL PARTY PLATFORMS

We develop a model of endogenous party platform formation in a multidimensional policy space. Party platforms depend on the composition of the parties? primary electorate. The overall social outcome is taken to be a weighted average of party platforms and individuals vote strategically. Equilibrium is defined to obtain when no group of voters can shift the social outcome in its favor by deviating and the party platforms are consistent with their electorate. We provide sufficient conditions for existence and study the robustness properties of the sorting equilibria.Political Economy, Endogenous Party Formation, Multimensional Space.