Debraj Ray

On the measurement of polarization

Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the generation of social tensions, to the possibilities of revolution and revolt, and to the existence of social unrest in general. The authors take special care to distinguish their theory from the theory of inequality measurement. They derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth. Copyright 1994 by The Econometric Society.

Polarization: Concepts, Measurement, Estimation

The purpose of this paper is two-fold. First, we develop the measurement theory of polarization for the case in which asset distributions can be described using density functions. Second, we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities. Distribution-free statistical inference results are also derived in order to ensure that the orderings of polarization across entities are not simply due to sampling noise. An illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice.

A Noncooperative Theory of Coalitional Bargaining

We explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on the efficiency properties of stationary equilibria of strictly superadditive games, when the discount factor δ is sufficiently large; we do, however, consider examples of other games where subgame perfectness alone is employed. It is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium, the latter for some or all orders of proposer. However, efficient stationary equilibrium payoffs converge to a point in the core, as δ → 1. Strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high δ. This vector converges as δ → 1 to the egalitarian allocation of Dutta and Ray (1989).

Collective Action and the Group Size Paradox

According to the Olson paradox, larger groups may be less successful than smaller groups in furthering their interests. We address the issue in a model with three distinctive features: explicit intergroup interaction, collective prizes with a varying mix of public and private characteristics, and nonlinear lobbying costs. The interplay of these features leads to new results. When the cost of lobbying has the elasticity of a quadratic function, or higher, larger groups are more effective no matter how private the prize. With smaller elasticities, a threshold degree of publicness is enough to overturn the Olson argument, and this threshold tends to zero as the elasticity approaches the value for a quadratic function. We also demonstrate that these results are true, irrespective of whether we examine group sizes over the cross-section in some given equilibrium or changes in the size of a given group over different equilibria.

Collective Dynamic Consistency in Repeated Games

We formalize the notion of collective dynamic consistency for noncooperative repeated games. Intuitively, we require that an equilibrium not prescribe any course of action in any subgame that players would jointly wish to renegotiate, given the restriction that any alternative must itself be invulnerable to subsequent deviations and renegotiation. While the appropriate definition of collective dynamic consistency is clear for finitely repeated games, serious conceptual difliculties arise when games are repeated infinitely. We investigate several alternative solution concepts, and establish existence (under reasonably general conditions) for each.

Group Formation in Risk-Sharing Arrangements

We study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. However, such deviations must be credible, in the sense that the subgroup must pass exactly the same test that we apply to the entire group; it must itself employ some self-enforcing risk-sharing agreement. We observe that the stability of subgroups is inimical to the stability of the group as a whole. Two surprising consequences of this analysis are that stable groups have (uniformly) bounded size, a result in sharp contrast to the individual-deviation problem, and that the degree of risk-sharing in a community is generally non-monotonic in the level of uncertainty or need for insurance in the community. Copyright 2003, Wiley-Blackwell.

Farsighted network formation

This paper studies a model of dynamic network formation when individuals are farsighted : players evaluate the desirability of a “current” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account far-sighted behavior of agents and allows for limited cooperation amongst agents. We show that an equilibrium process of network formation exists. We also show that there are network structures in which no equilibrium strategy profile can sustain efficient networks. We then provide sufficient conditions under which the equilibrium process will yield efficient outcomes.

Inequality, Control Rights, and Rent Seeking: Sugar Cooperatives in Maharashtra

This paper presents a theory of rent seeking within farmer cooperatives in which inequality of asset ownership affects relative control rights of different groups of members. The two key assumptions are constraints on lump‐sum transfers from poorer members and disproportionate control rights wielded by wealthier members. Transfers of rents to the latter are achieved by depressing prices paid for inputs supplied by members and diverting resulting retained earnings. The theory predicts that increased heterogeneity of landholdings in the local area causes increased inefficiency by inducing a lower input price and a lower level of installed crushing capacity. Predictions concerning the effect of the distribution of local landownership on sugarcane price, capacity levels, and participation rates of different classes of farmers are confirmed by data from nearly 100 sugar cooperatives in the Indian state of Maharashtra over the period 1971–93.

Polarization, Fractionalization and Conflict

This article provides a theoretical framework that distinguishes between the occurrence of conflict and its severity, and clarifies the role of polarization and fractionalization in each of these cases. The analysis helps in ordering the various definitions, and in providing explanations for the empirical observations on the relationship between conflict, on the one hand, and polarization or fractionalization, on the other. The behaviour of players in conflict is described as a game, and equilibrium payoffs to all players are computed. The status quo is characterized by a set of political institutions that channel the different opposing interests and turn them into a collective decision, with a second set of payoffs. Groups rebel against the status quo political institution whenever the latter set of payoffs is dominated by the former. When society is highly polarized, the potential cost of rebellion is extremely high, and this cost may serve as the guarantor of peace. So, in highly polarized societies, the occurrence of open conflict should be rare but its intensity very severe, whenever it happens. On the other hand, highly fractionalized societies are prone to the occurrence of conflict, but its intensity will be moderate. It matters, therefore, whether one studies the intensity of conflict, conditional on conflict breaking out, or the likelihood that conflict actually occurs. Specifically, it is shown that: (i) measures of fractionalization and polarization tend to run in opposite directions, (ii) the onset of conflict critically depends on the political system in place, (iii) the occurrence of conflict and the intensity of conflict also tend to move in opposite directions, (iv) the relationship between polarization or fractionalization and conflict is non-monotonic and (v) the intensity of conflict depends positively on the degree of polarization.

Coalitional Power and Public Goods

We study the provision of public goods when all agents have complete information and can write binding agreements. This framework is in deliberate contrast to a traditional view of the free‐rider problem based on hidden information or voluntary provision. We focus on coalition formation as a potential source of inefficiency. To this end, we develop a notion of an equilibrium coalition structure, based on the assumption that each coalition that forms does so under a rational prediction of the society‐wide coalition structure. In a simple model, we characterize the (unique) equilibrium coalition structure. Only in some cases does the equilibrium involve full cooperation, resulting in efficient provision of the public good. In other cases, the equilibrium consists of several coalitions and inefficient provision. However, the degree of inefficiency and the number of possible coalitions are bounded.