Robert P. Parks

PREFERENCES WHICH HAVE OPEN GRAPHS

Gale and Mas-Collel and Shafer and Sonnenschein introduced powerful new theorems on the existence of competitive equilibrium which used the assumption that the graph of the strict preference relation P is an open set. We show when this condition is satisfied and when it is not.

Deriving public sector preferences

Abstract Many analyses of the public sector use preferences which are defined on public sector allocations. We relate these preferences to the primitive preferences defined on the consumption space. Many properties of consumption preferences are inherited by derived public sector preferences but not all. We also question whether public sector preferences can be independent of prices with a negative conclusion. Also different definitions of derived public sector preferences are related.

Existence of voting-market equilibria

Abstract We show the existence of an equilibrium in a model where private goods are allocated by markets and the public good (bad) is allocated by majority rule voting.

Nash equilibrium in a spatial model of coalition bargaining

Abstract In the model presented here, n parties choose policy positions in a space Z of dimension at least two. Each party is represented by a “principal” whose true policy preferences on Z are unknown to other principals. In the first version of the model the party declarations determine the lottery outcome of coalition negotiation. The coalition risk functions are common knowledge to the parties. We assume these coalition probabilities are inversely proportional to the variance of the declarations of the parties in each coalition. It is shown that with this outcome function and with three parties there exists a stable, pure strategy Nash equilibrium, z∗ for certain classes of policy preferences. This Nash equilibrium represents the choice by each party principal of the position of the party leader and thus the policy platform to declare to the electorate. The equilibrium can be explicitly calculated in terms of the preferences of the parties and the scheme of private benefits from coalition membership. In particular, convergence in equilibrium party positions is shown to occur if the principals’ preferred policy points are close to colinear. Conversely, divergence in equilibrium party positions occurs if the bliss points are close to symmetric. If private benefits (the non-policy perquisites from coalition membership) are sufficiently large (that is, of the order of policy benefits), then the variance in equilibrium party positions is less than the variance in ideal points. The general model attempts to incorporate party beliefs concerning electoral responses to party declarations. Because of the continuity properties imposed on both the coalition and electoral risk functions, there will exist mixed strategy Nash equilibria. We suggest that the existence of stable, pure strategy Nash equilibria in general political games of this type accounts for the non-convergence of party platforms in multiparty electoral systems based on proportional representation.

Pareto irrelevant externalities

Abstract Cases in which competitive equilibrium is efficient and unbiased in the presence of externalities are analyzed. Necessary and sufficient conditions for efficiency and unbiasedness are proved. It is shown that these conditions imply that utility must be interdependent; i.e., each individual must have a Bergson utility function that aggregates all individuals private utilities. In the interdependent case, unbiasedness requires non-negative externalities but efficiency is more complicated not quite requiring non-positive externalities.

Residential preferences, neighborhood filtering and neighborhood change : Comment and corrections

Abstract The purpose of this Comment is to correct the estimating technique used by Little in “Residential Preferences, Neighborhood Filtering and Neighborhood Change.” Little uses the factor load matrix rather than the factor score matrix in his computations of the implicit regression coefficients. We correct Littles estimates and also present additional results to compare his corrected results with principal component estimates and ordinary least squares.