Group Structure and Public Goods Provision in Heterogeneous Societies

• DOI: http://doi.org/10.1111/jpet.12213
• Date: 01 April 2017
• Published date: 01 April 2017
• Author: JO THORI LIND

GROUP STRUCTURE AND PUBLIC GOODS PROVISION

IN HETEROGENEOUS SOCIETIES

JO THORI LIND

University of Oslo

Abstract

I consider a society with heterogeneous individuals who can form or-

ganizations for the production of a differentiated public good. A de-

centralized arrangement of organizations is said to be split-up stable

whenever there is no majority to split any of the organizations. Com-

pared to the social optimum, decentralization yields too few organiza-

tions if they provide broad services and potentially too many if they are

highly specialized. Conclusions are broadly similar in the presence of

an outside opportunity where only some individuals join organizations.

1. Introduction

Organizations are everywhere in society, providing a huge range of services and ranging

in scope from the local football club to nationwide unions and international organiza-

tions. Most fields have a multitude of organizations providing comparable but still differ-

entiated services. This is to accommodate the heterogeneous needs and tastes of their

users. A large number of organizations guarantee each user access to services closely

suited to her particular needs and desires. The flip side is higher total costs.

Do we get the appropriate number of organizations when they are allowed to form

freely? In the celebrated papers by Salop (1979) and Alesina and Spolaore (1997), the

answer is no. But this depends on how organizations form. I argue that under reason-

able assumptions, we may actually achieve an optimal organizational structure in an

unregulated economy.

My analysis applies to many categories of organizations. Economically, the most im-

portant may be the organization in the “third sector,” the voluntary organizations pro-

viding welfare services complementing those provided by the public and private sectors.

These organizations are responsible for providing health care, education, and many

other services, and accounts for as much as 20% of GDP in some countries (Evers and

Jo Thori Lind, Department of Economics, University of Oslo, PB 1095 Blindern, 0317 Oslo, Norway

(j.t.lind@econ.uio.no).

I am grateful for comments from two anonymous referees, an associate editor, Maren Elise Bachke,

B˚

ard Harstad, TapasKundu, Anthony McGann, Kalle Moene, and Fredrik Willumsen as well as seminar

participants at the University of Oslo and at the EPCS and EEA conferences. While carrying out this

research I have been associated with the center Equality,Social Organization, and Per formance (ESOP)

at the Department of Economics at the University of Oslo. ESOP is supported by the Research Council

of Norway through its Centres of Excellence funding scheme, project number 179552.

Received October 16, 2014; Accepted June 21, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (2), 2017, pp. 377–408.

377

378 Journal of Public Economic Theory

Laville 2004). Then efficiency matters. Most other organizations providing excludable

public goods and services are also relevant examples, for instance churches (cover-

ing different denominations or religions), interest groups (advocating anything from

stronger environmental protection to less strict gun regulation), newspapers (with dif-

ferentiated focus and political orientation), sports and recreation facilities (for different

sports, with different equipment, and at different location in space), housing cooper-

atives (different types of housing and location), and rotating savings groups (different

income groups and risk profiles). Other applications are to the number of political

parties (several differentiated parties may be required to get a properly functioning

democracy) and the variety of unions (to accommodate different interests of workers in

different sectors and different types of firms). In all of these cases, there are good rea-

sons to entrust provision to private actors. But the efficiency of an unregulated market

for organizations is an open question—there may be cases where the government can

improve efficiency through subsidies or taxes.

I consider a population of heterogeneous individuals that can join organizations

providing a unique public good. The utility derived from the public good depends on

how well it matches the needs of the individual as well as on the cost of membership in

the organization. In more heterogeneous societies where preferences are more diverse,

a larger number of organizations is required to provide suitable services for everybody.

Hence the socially optimal number of organizations is larger.

In the model, new organizations are formed by splitting old ones. If a majority of the

members of an organization prefer a split, it splits. This can be seen as the organization

holding a vote on whether to split, but a more natural interpretation is that a secessionist

group leaves the organization if the support for maintaining unity is absent.1

As organizations are split and the number of organizations increases, support for

further splits declines. This is both because organizations become smaller and hence

closer to the needs of all its members, and because the financial burden on each mem-

ber increases. When the splitting process has reached a state where only a minority of

members in each organization prefers further split-ups, the organizational structure is

stable. I label this stable structure the split-up stable equilibrium.

I go on to study the efficiency properties of decentralized equilibria where the num-

ber of organizations is given by the smallest split-up stable number of organizations.

The welfare properties depend on the utility loss from an imperfect match between the

member’s ideal point and the public good provided by the organization. If this disutility

is linear in distance, the members with median and average types coincide within each

organization. As the median members are pivotal in the split-up decision and the social

optimum entails maximization of the utility of the member of average type, this implies

that the split-up stable outcome is almost efficient.

When preferences are concave in the distance from the ideal type, so organizations

cater to a broader range of potential members, the median and average types no longer

coincide. I show that in this case the decentralized solution yields fewer organizations—

and potentially too few organizations. Finally, if preferences are convex so organizations

are specialized at providing services to a narrow segment of society, preferences for

organizational splits become more involved as we get a coalition of the center and the

remote periphery, both in favor of the old organizational structure, against the close

1One could also imagine the center evicting the periphery, but in the class of models I consider this

typically does not happen as the periphery pays membership fees and hence keep the costs down for

individuals in the center.

Group Structure and Public Goods Provision 379

periphery, who would be the winners in case of a split. The final outcome may be both

too many and too few organizations.

Membership in organizations is voluntary in several interesting cases. Then it is

unsatisfactory to require all individuals to belong to an organization. To model an en-

rollment decision, I give all agents an outside opportunity with heterogeneous value.

Individuals with good outside opportunities stay outside the organizations, whereas in-

dividuals with bad outside opportunities join. This introduces a number of new features.

First, the number of agents joining an organization depends on their types; agents who

can find an organization close to their own preferences are more attracted to the or-

ganization, and join even when they have good outside opportunities. Among agents

who are less satisfied with the organization’s choice of public goods, only those with

bad outside opportunities join. As it is now optimal that some agents, those with good

outside options, stay outside the organizations, it follows that the optimal number of

organizations is lower than with compulsory membership.

The main result from this extension is that with linear preferences the smallest

split-up stable number of organizations still corresponds to the socially optimal num-

ber of organizations. There are three new factors pulling in different directions. First,

with voluntary membership, agents whose ideal type of service is close to the one actu-

ally provided by the organization tend to be overrepresented within the organization

as they are more likely to prefer the organization over the outside opportunity. These

are less inclined to favor a split of the organization, reducing the pressure for splitting

it. Second, as the cost of running the organization is split between the actual members,

this also tends to limit the incentives to form new organizations. These two factors tend

to give too few organizations. However, organizations are composed of agents with rela-

tively bad outside opportunities, and when deciding on whether to spilt the organization

or not, they do not take the preferences of agents with good outside opportunities into

account. This third factor tends to give too many organizations. Under the conditions

studied here, these factors almost perfectly balance, typically canceling out the effect of

voluntary membership and hence restoring efficiency.

There are three major novelties in this paper. First, the split-up stability criterion

has not been used before. This solution concept is interesting because it is a reasonable

criterion for the study of organization formation, because it provides a useful bench-

mark as the decentralized solution corresponds closely to the social optimum in certain

cases, and because it by its transparency yields analytically tractable expressions. Second,

the paper provides an analysis of how the decentralized solution compares to the social

optimum under different assumptions on the cost of the difference between the agent’s

and the organization’s type. Finally, this is to the best of myknowledge the first paper to

consider the issue of endogenous membership in this context.

The paper is related to several strands of literature. First, the formation of organiza-

tions may be seen as specific case of coalition formation, studied at length in cooperative

game theory and related literature. It may also be seen as a special case of the literature

on club goods, starting with Buchanan (1965); see, e.g., Cornes and Sandler (1996),

Scotchmer (2002), and Wooders (2012) for overviews. This literature focuses more on

crowding and less on optimal diversification than the present work. Also, the dominant

competitive approach of Ellickson et al. (1999) focuses on infinitely many small clubs

whereas I consider a finite number of infinitely large organizations.

The modeling is closely related to Hotelling’s (1929) model of choice of location,

and the extensions by, e.g., Salop (1979). But as this literature focus on competition and

price mechanisms, both analyses and outcomes differ substantially. The paper is also

closely related to Cremer, De Kerchove, and Thisse’s (1985) model of the location of