Peter C. Ordeshook

An Expository Development of a Mathematical Model of the Electoral Process

The fundamental process of politics is the aggregation of citizens preferences into a collective—a social—choice. We develop, interpret, and explain non-technically in this expository essay the definitions, assumptions, and theorems of a mathematical model of one aggregative mechanism—the electoral process. This mechanism is conceptualized here as a multidimensional model of spatial competition in which competition consists of candidates affecting turnout and the electorates perception of each candidates positions, and in which the social choice is a policy package which the victorious candidate advocates.This approach, inaugurated by Downss An Economic Theory of Democracy, and falling under the general rubric “spatial models of party competition,†has been scrutinized, criticized, and reformulated. To clarify the accomplishments of this formulation we identify and discuss in section 2 the general democratic problem of ascertaining a social preference. We review critically in section 3 the definitions and assumptions of our model. We consider in sections 4 and 5 the logic of a competitive electoral equilibrium. We assume in section 4 that the electorates preferences can be summarized and represented by a single function; the analysis in section 5 pertains to competition between two organizational structures or two opposed ideologies (i.e., when two functions are required to summarize and represent the electorates preference). Finally, we suggest in section 6 a conceptualization of electoral processes which facilitates extending and empirically testing our model.

Game Theory and Political Theory

Formal political theory seeks to develop formal, mathematical models of political and economic processes. This book attempts to integrate the last twenty years of development in this field. Professor Ordeshook uses the modern developments in the theory of games (decision making with multiple, interactive decision makers) as the basis for the synthesis. Topics covered include models of elections and of committee processes, the demand and supply of public goods, and surveys of game theory and social-choice theory. Game Theory and Political Theory is designed as a textbook for graduate courses in formal political theory and political economy.

The Competitive Solution for N-Person Games Without Transferable Utility, With an Application to Committee Games

This essay defines and experimentally tests a new solution concept for n-person cooperative games-the Competitive Solution. The need for a new solution concept derives from the fact that cooperatie game theory focuses for the most part on the special case of games with transferable utilii v, even though, as we argue here, this assumption excludes the possibility of modelling most interesting political coalition processes. For the more general case, though, standard solution cotlcepts are inadequate either because they are undefined or they fail to exist, and even if they do exist, theyfocus on predicting payoffs rather than the coalitions that are likely to form. The ComPetitive Solution seeks to avoid these problems, but it is not unrelated to existent theory in thit we can establish some relationships (see Theorems 1 and 2) between its payoff predictions and those of the core, the V-solution and the bargaining set. Additionally, owing to its definitio~i and motivation, nontrivial coalition predictions are made in conjunction with its payoff pt edictions. The Comb ptitive Solutions definition is entirely general, but a special class of gamesmajority ru: Kspatial games-are usedfor illustrations and the experimental test reported here consists of .ight plays of a 5-person spatial game that does not possess a main-simple Vsolution or i bargaining set. Overall, the data conform closely to the Competitive Solutions predictions.

Information, Electoral Equilibria, and the Democratic Ideal

A considerable literature argues that poor information among voters produces an elitist or class bias in public policy. Owing to the complexity of public issues and their generally slight impact on outcomes, citizens fail to invest in information, and in their voting decisions rely instead on cues such as party labels, the opinions of friends, and interest group endorsements. As a result, political entrepreneurs are unable to mobilize effectively the general electorate to vote in their own self-interest. This essay takes issue with some theoretical premises of this argument. Using a rational expectations approach to modeling elections with incomplete information, we show first that citizens require only very general information to vote correctly. Second, this information can be deduced from exactly those cues that are commonly interpreted as substitutes for voting on the issues. Finally, even if interest groups attempt to influence candidate positions with money, equilibria exist to the election game that are identical to what occurs under full information, provided some strong symmetry conditions hold with regards to the resources of such groups. Thus, popular control of public policy is not precluded per se by lower levels of voter information about the candidates positions on issues.

Plurality Maximization vs Vote Maximization: A Spatial Analysis with Variable Participation

Spatial models of party competition constitute a recent and incrementally developing literature which seeks to explore the relationships between citizens decisions and candidates strategies. Despite the mathematical and deductive rigor of this approach, it is only now that political scientists can begin to see the incorporation of those considerations which less formal analyses identify as salient, and perhaps crucial, features of election contests. One such consideration concerns the candidates objectives. Specifically, spatial analysis often confuses the distinction between candidates who maximize votes and candidates who maximize plurality. Downs and Garvey, for example, assume explicitly that candidates maximize votes, though plurality maximization is clearly the assumption which Garvey actually employs, while Downs frequently assumes that vote maximization, plurality maximization, and the goal of winning are equivalent. Downs, nevertheless, attempts to disentangle these objectives, observing that plurality maximization is the appropriate objective for candidates in a single-member district, while vote maximization is appropriate in proportional representation systems with many parties. All subsequent spatial analysis research, however, assumes either implicitly or explicitly that candidates maximize plurality. If Downs is correct, therefore, this research may not be relevant for a general understanding of electoral competition in diverse constitutional or historical circumstances. The question then is whether those strategies that maximize votes differ from those strategies that maximize plurality.

A Theory of Electoral Equilibrium: A Spatial Analysis Based on the Theory of Games

Two areas of political science that utilize rigorous deductive formulations are: (1) the paradox of voting, and (2) spatial analysis of election competition. It is not surprising that the analysis of the paradox and the development of spatial theory occur simultaneously because the concerns of both endeavors are parallel: we study the paradox to ascertain conditions under which majority-rule equilibria exist, that is, conditions under which at least one alternative exists that cannot be

Election Goals and Strategies: Equivalent and Nonequivalent Candidate Objectives *

This essay ascertains some general conditions for equivalence and nonequivalence among six election objectives: 01, maximizing expected plurality; 02, maximizing proportion of expected vote; 02, maximizing expected vote; 04, maximizing probability that plurality exceeds some level; 05, maximizing probability that proportion of vote exceeds some level; 06, maximizing probability that vote exceeds some level. The major findings are these: (1) 01, 02, and 03 are equivalent if the election is zero-sum-like in expected vote; (2) 01 and 02 are equivalent if competition is strongly symmetric. A necessary condition for this equivalence is also presented for 2-candidate elections: (3) 01 and 04 are equivalent, as are 03 and 06, if the candidates forecasting error is independent of all strategies; (4) 01 and 04 are equivalent for two-candidate elections, and for n-candidate elections 02 and 05 are equivalent, as are 03 and 06, if the distribution of a candidates forecasting error is multivariate normal, and if the level of plurality, proportion, or vote to be exceeded is the minimax value of the election game under 01, 02, or 03; (5) findings of equivalence and nonequivalence depend upon the definition of equivalence (findings 1 and 2 rely upon an election with all candidates at equilibrium strategies, while findings 3 and 4 do not); (6) equivalence and nonequivalence among election objectives may be sensitive to the candidates attitude toward risk, i.e., to the functional form of his utility function in pluraliy, vote proportion, or vote; election objectives depend on information, competitive environment, and constitutional arrangements. Hence, statements of preference for alternative election systems, laws, and reforms perforce entail reasonable theoretical expectations about the way in which these systems, laws, and reforms affect the candidates campaign objectives, as well as about equivalence and nonequivalence among these objectives.

Campaign Resource Allocations Under the Electoral College

This essay addresses the question: Why does the Electoral College bias campaign resource allocations in favor of large states? Using data on candidate trips as well as estimates of the time candidates spend in states, we conclude, first, that much of the apparent empirical support for Brams and Daviss 3/2s hypothesis is an artifact of the candidates consideration of each states relative competitiveness and the statistical relationship between size and competitiveness. There is some evidence, however, for a residual bias. That is, after controlling for each states competitiveness, campaign allocations still appear to favor larger states—at least for the two competitive elections of 1960 and 1968. We attribute that bias to corner solutions to the candidates maximization problem and to the effects of sequential campaign planning. Thus, while we do not dispute the existence of bias over the course of the entire campaign, the data are consistent with a modified (albeit complex) proportional rule that each candidate applies sequentially during the campaign. Our conclusion is that the unit rule feature of the Electoral College, rather than weighted voting, is the predominant cause of bias.

A Decade of Experimental Research on Spatial Models of Elections and Committees

The Euclidean representation of political issues and alternative outcomes, and the associated representation of preferences as quasiconcave utility functions, is by now a staple of formal models of committees and elections. This theoretical development, moreover, is accompanied by a considerable body of experimental research. We can view that research in two ways: as a test of the basic propositions about equilibria in specific institutional settings, and as an attempt to gain insights into those aspects of political processes that are poorly understood or imperfectly modeled, such as the robustness of theoretical results with respect to procedural details and bargaining environments. This essay reviews that research so that we can gain some sense of its overall import.

Agendas, Strategic Voting, and Signaling with Incomplete Information *

The literature on agendas with sincere and strategic voting represents an important contribution to our understanding of committees, of institutions, and of the opportunities to manipulate outcomes by the manipulation of institutions. That literature, though, imposes an assumption that may be unrealistic in many situations; namely, that everyone knows the preferences of everyone else. In this essay we apply Bayesian equilibrium analysis to show that the properties of agendas that others derive by assuming complete information do not hold necessarily under incomplete information. First, a Condorcet winner need not be selected, even if nearly everyone on the committee most prefers it. Second, the two-step theorem, that any outcome reachable in n voting stages via some amendment agenda is reachable in two stages under sophisticated voting, need not hold. Third, nonbinding votes, such as straw polls, can critically affect final outcomes.