FAIR ALLOCATION OF DISPUTED PROPERTIES

• Author: Biung‐Ghi Ju,Juan D. Moreno‐Ternero
• DOI: http://doi.org/10.1111/iere.12251
• Published date: 01 November 2017
• Date: 01 November 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 4, November 2017

FAIR ALLOCATION OF DISPUTED PROPERTIES∗

BYBIUNG-GHI JUAND JUAN D. MORENO-TERNERO1

Seoul National University, Korea; Universidad Pablo de Olavide, Spain, and CORE, Universit ´

e

catholique de Louvain, Belgium

We model problems of allocating disputed properties as generalized exchange economies. Therein, agents

have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient

to satisfy all individual claims. We focus on market-based allocation rules that impose a two-step procedure:

assignment of rights based on claims first and voluntary exchange based on the assigned rights afterward. We

characterize three focal egalitarian rights-assignment rules that guarantee that the allocation rules are fair.We

apply our results to problems of greenhouse gas emissions and contested water rights.

1. INTRODUCTION

Fairness and distributive justice are primary concerns in practical procedures for property

rights disputes. If a rule is not perceived as fair, its adoption might be jeopardized. Failures to

agree on a new international framework dealing with greenhouse gas (GHG) emissions after

the Kyoto protocol are a point in case. Countries at different stages of economic development

have different perceptions of fairness and support different rules. Closing the gap to reach

a final resolution is a political economy problem. However, the core issue is an ethical one,

and investigating it from the perspective of normative economics will facilitate its political

resolution.

Resolving property rights disputes usually involves three general principles, namely, equal

division,proportional division, and equal sacrice. Examples can be found in numerous insti-

tutional setups (including laws and social and religious norms) or agreed conventions (such

as court settlements for accident damages or international resolutions on environmental prob-

lems). The three principles also underlie the three prominent proposals for the allocation of

GHG emission rights.2

The normative foundation of allocation schemes, such as the above three principles, has been

a key subject in the literature of fair allocation. Nevertheless, most studies in this literature either

focus on allocating a single good (money), dismissing the issue of fair initial allocation and its

influence on the final allocation of the other goods after the subsequent interactions among

∗Manuscript received October 2014; revised July 2016.

1We are grateful to Masaki Aoyagi (coeditor of this journal), three anonymous referees, Younghwan In, Herv´

e

Moulin, and William Thomson for detailed comments and suggestions. We also thank Yuki Funaki, Francois

Maniquet, John Roemer, and Roberto Veneziani as well as the participants at seminars and conferences where ear-

lier versions of this article have been presented, at Albany, Alicante, Bergen, Bilbao, Brussels, Kaifeng, Lisbon,

London, Madrid, Odense, Rochester, Salamanca, Seoul, Seville, Taipei, Tokyo, and Valencia. All remaining errors are

ours. Financial supports from the National Research Foundation of Korea Grant funded by the Korean Government

(NRF-2016S1A3A2924944), from the Center for Distributive Justice, Institute of Economic Research at Seoul National

University, and from the Spanish Ministry of Economics and Competitiveness (ECO2011-22919, ECO2014-57413-P)

are gratefully acknowledged. Please address correspondence to: Biung-Ghi Ju, Department of Economics, Seoul Na-

tional University, 1 Ganwak-ro, Gwanak-gu, Seoul 08826, Korea. Phone: +82 28802879. Fax: +82 28864231. E-mail:

bgju@snu.ac.kr.

2The proposal to allocate on an “equal per capita basis” (e.g., Neumayer, 2000) corresponds to equal division, the

polluter pays principle (paraphrased as “you broke it, you fix it”; e.g., Singer, 2002) to proportional division, and the

principle of equal burden sharing (e.g., Posner and Weisbach, 2010) to equal sacrifice.

1279

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1280 JU AND MORENO-TERNERO

claimants (e.g., O’Neill, 1982; Thomson, 2003, 2015), or assume a fixed initial distribution of

property rights, without dispute, and investigate end-state fairness (e.g., Pazner and Schmeidler,

1974; Thomson, 2011).3Therefore, they are somewhat limited for the investigation of (end-state

and procedural) fairness in some environments with conflicting claims or property rights dispute.

We provide in this article a comprehensive framework to investigate fairness in the initial

assignment of rights on disputed properties, fairness in the transaction of rights, and fairness of

the end-state allocation as well as the implications of the three categories of fairness and their

relations. Our model is an extended model of exchange economies, the extension allowing for

conflicts over properties. More precisely, agents have preferences over a finite number of goods,

and they also have initial claims on those goods. Furthermore, the available endowment of each

good may not be sufficient to satisfy all claims; i.e., the sum of individual claims exceeds the

endowment. In other words, we consider rationing problems with multiple goods where agents

can have various homogeneous or heterogeneous preferences over those goods.4

Our model is flexible enough to accommodate a variety of real-life problems involving prop-

erty rights disputes. A running interpretation of the model is as cap-and-trade systems to deal

with GHG emissions.5For such an interpretation, agents should be considered as GHG-emitting

entities, goods as energy and money (with the latter being used to produce the former), claims

as their energy consumptions on a base year and their incomes, and the social endowment as

the targeted amount for total energy consumption, below the total energy consumption on a

base year, and the net total endowment of money after paying the cost of energy production.

Another interpretation of our model is as problems of contested water rights.6In those cases,

water supply falls short of satisfying the regular amounts of water usage by the entities who

share a water source. There are two goods: water and money. Claims consist of the amount

of water used in a base year and the monetary endowment. Here, dispute exists only over the

water rights, not over money.

Various forms of markets have been developed throughout human history. Two fundamental

elements encompassing them are private property rights and voluntary exchange.7We precisely

define in our context market-based allocation rules as those rules determined by these two

elements, formalized in our model by the consecutive procedures of rights-assignment and

voluntary exchange. Our main results characterize market-based allocation rules that lead to

fair (and efficient) end-state allocations.

End-state fairness is formalized in this context as three variants of no-envy, probably the

concept with the longest tradition in the theory of fair allocation (e.g., Foley, 1967; Kolm,

1972; Varian, 1974).8No-envy is satisfied if no agent prefers anyone else’s consumption to her

own. A parallel comparative notion of fairness, defined through interpersonal comparisons of

(absolute) sacrifices, gives rise to the notion of sacrice-no-envy. Likewise, we define relative-

no-envy through interpersonal comparison of relative sacrifices (or rewards).

The rights-assignment procedure assigns property rights by means of adjudicating claims un-

der resource constraints.9Voluntary exchange yields individually rational end-state allocations,

3There exist generalizations of the rationing model introduced by O’Neill (1982) to a multidimensional setting, but

therein, even though claims refer to multiple types of assets, the endowment to be allocated is still unidimensional (e.g.,

Ju et al., 2007).

4This is the main difference with respect to bankruptcy problems dealing with the allocation of a single good (e.g.,

Thomson, 2003, 2015) where all agents are presumed to have the same monotonic preferences over the single good.

5The term is broadly used to describe a policy that sets caps on the emissions of (GHG-emitting) entities and allows

trading in the resulting emissions allowances (e.g., Stavins, 2008).

6A different analysis of these problems is Ansink and Weikard (2009).

7For instance, as Hodgson (2008, p. 326) puts it, “Together these specifications (put forward by the Austrian school

economist Ludwig van Mises) amount to a definition of the market that embraces all forms of trade or exchange that

involve private property, defined loosely as assets under private control.” This view is also shared by Adam Smith, Karl

Marx, Friedrich Hayek, etc. (see Hodgson, 2008).

8It was also used in moral philosophy as a basic test for resource egalitarian allocations (e.g., Dworkin, 1981).

9We impose solidarity in this procedure, modeled by the combination of two axioms, known as resource monotonicity

and consistency, as suggested by Moreno-Ternero and Roemer (2006, 2012), among others.