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URIEL PROCACCIA and UZI SEGAL

SUPER MAJORITARIANISM AND THE ENDOWMENTEFFECT

ABSTRACT. The American and some other constitutions entrenchproperty rights by requiring super majoritarian voting as a condition foramending or revoking their own provisions. Following Buchanan andTullock [The Calculus of Consent, Logical Foundations of ConstitutionalDemocracy (University of Michigan Press, Ann Arbor), 1962], this paperanalyzes individuals’ interests behind a veil of ignorance, and shows thatunder some standard assumptions, a (simple) majoritarian rule should beadopted. This result changes if one assumes that preferences are consistentwith the behavioral phenomenon known as the ‘‘endowment effect.’’ It thenfollows that (at least some) property rights are best defended by supermajoritarian protection. The paper then shows that its theoretical results areconsistent with a number of doctrines underlying American ConstitutionalLaw.

KEY WORDS: Endowment effect, Super majoritarianism

1. INTRODUCTION

Parts of the legal system can be interpreted as an allocation ofproperty rights among different claimants. Such an allocationcan, and often is, put in place by regular statutes as well as bydecisional law. Certain property entitlements, however, areconstitutionally entrenched. Thus, the Fifth Amendment of theAmerican Constitution protects certain property rights of thecitizens and forbids the government from taking them withoutjust compensation. By entrenching these property rights withinthe Constitution, the citizenry denies itself the opportunity tochange course and reshuffle entitlements by majoritarian reso-lution. The process of Constitutional amendment commits thecitizenry to the arduous path of super majoritarian regulation.Some other constitutions, like those of Germany, The Neth-erlands, and Spain, offer similar protection.1 In this paper wewant to offer a decision theoretic insight to this phenomenon.

Theory and Decision 55: 181–207, 2004.� 2004 Kluwer Academic Publishers. Printed in the Netherlands.

The most important contribution to understanding consti-tutional entrenchment of property rights was offered by Bu-chanan and Tullock (1962). They suggested to analyze rules forfuture redistributions by positioning a set of players behind aveil of ignorance. Acting in their own personal interests,members of society are threatened with the possibility of a fu-ture majority taking away from them something which is theirs;or not wishing to give them something that they do not cur-rently own. The expected cost of the first contingency isdeclining with the number of voters necessary for its attain-ment, while the expected cost of the second contingency isincreasing with the number of voters. Let n be the number ofplayers. If the minimum of the aggregate cost function is ob-tained at a number k > n

2 þ 1, this may serve as a normativejustification for the super majoritarian constitution. Theproblem with this analysis is that there is nothing in it to sug-gest that the ideal number, k, is larger than a simple majority. Itis, perhaps, the realization of this fact that caused a decline inthe influence of Buchanan and Tullock’s work (see Tullock,1988).

Following Buchanan and Tullock, we too discuss a modelwhere a set of subjects are positioned behind a veil of igno-rance. We assume that these subjects know their preferences,but not their future endowments. We prove in Section 2 thatunder a standard assumption of risk aversion, these subjectswould prefer future society to adopt fully egalitarian principles.We then show that this result can be obtained by adopting asimple majoritarian rule, i.e., without a super majoritarianconstitution. In other words, according to these assumptions,super majoritarian protection of property rights is sub-optimal.The main contribution of our paper is to show (in Section 3)that this analysis does not hold if we assume that preferencesare consistent with the behavioral phenomenon known as the‘‘endowment effect.’’ This effect records a gap between whatsubjects are willing to accept, as their minimum price, forparting with something that is already theirs, and what they arewilling to pay, as their maximum price, for the same object, ifthey do not already possess it. Numerous experiments show

URIEL PROCACCIA AND UZI SEGAL182

that for most subjects, the former far exceeds the latter. This isconsistent with the hypothesis that subjects develop a specialsense of attachment to their existing endowment. However, thisdifference exists only in tangible objects intended for personalconsumption and not in monetary wealth or other forms offungible or tradable goods.2 It follows from the analysis ofSection 2 that if all wealth were defined in cash and tradablecommodities, the case for constitutional entrenchment ofproperty rights would have been rather unclear, and undersome plausible assumptions, no entrenchment would have beenoptimal. But as we show in Section 3, assuming the endowmenteffect, the case for constitutional entrenchment becomesstronger as a measure of protecting endowed property.

To illustrate our claims by means of an example, we thenturn to show that the American Constitution consistently ap-plies super majoritarian voting rules to protect tangible enti-tlements in property rights, but fails to extend the sameprotection to general wealth (money) in which no gap existsbetween the willingness to accept and the willingness to pay (seeSection 4). Furthermore, we show that the constitutional pro-tection of wealth in America is constantly shifting, in tandemwith the composition of typical asset-portfolios in differenthistorical periods. When most people held their wealth in tan-gible assets with little trading activity, the protection of prop-erty rights offered by the American Constitution reached itsapex. When wealth became more concentrated in cash, corpo-rate securities and other tradable or negotiable goods, thisprotection lost ground.

There are many other explanations of the super-majoritarianrequirement, at least in its American version. Tushnet (1984),Sunstein (1993), and Przeworski (1971) explain that the Con-stitution was intended to secure to its drafters, a distinct class ofland and slave owners, a measure of protection for their vestedinterests, without which the initial passage of the constitutioncould not have been secured. Black (1999) argues that theConstitution is not really counter majoritarian, because itadapts itself to the changing mores of time, and thus reflects thetrue will of the constituency in every given generation. Strauss

SUPER MAJORITARIANISM AND THE ENDOWMENT EFFECT 183

(2001) claims that the constitutional amendment process iscompletely illusory, as all important modifications of theexisting Constitution are judge-made, while formal amend-ments are nothing but ratifications of the more profoundchanges already forged within the body politick. Olson (1971)claims that minorities often possess an inordinately stronginfluence on the legislative process, given their tight organiza-tion and lower costs of forming winning coalitions. From this itcan be inferred that super majorities are needed to overcomeminority clout, and to bar simple majorities from acting againstthe interests of their own constituencies. Finally, Cooter (2000)made a recent attempt to explain the Constitution in gametheoretic terms, arguing that a simple majority is always acoreless solution; each given distribution is dominated by amajority of players who have an incentive to toss the systeminto an endless cycle of changes, thereby creating economicinstability and political chaos.

We do not wish to claim that these explanations are notvalid. Moreover, our analysis clearly ignores important issueslike the discouraging effect of egalitarianism on individualincentives to generate wealth (see Section 5 below). However,we want to show that certain kinds of super majoritarianism arecompatible with recent developments in the decision theoreticliterature. Rather than viewing our paper as an exclusiveexplanation for the entrenchment of some property rights, wewish to emphasize its conformity with the modern decisiontheoretic literature. As suggested in Section 4, this addedexplanation has a surprisingly good fit with some major trendsin the historical development of American constitutional law.

In our quest for a fit between legal rules and decision theo-retic insights we certainly do not wish to imply that the sup-pliers of rules, legislatures and courts, were consciously awareof the economic literature or its policy implications. To do sowould be particularly bizarre when the fit in question is soughtbetween recent results and legal rules crafted about two cen-turies ago, at the formative stages of the American Constitu-tion. The standard wisdom in the law and economic literature isthat players (including the suppliers of legal rules) often behave


as if they were bent on promoting efficient results, although, inactual fact, they are not.3

2. SELFISH VOTERS AND FUTURE UTILITARIANISM

In this section we show that although individuals may be as-sumed to act selfishly, there are circumstances in which it isrational for all of them to seek an egalitarian social outcome.

Suppose society has n members, living for two periods, thepresent (period 1) and the future (period 2), and suppose thatthere are k commodities. Individuals do not know their futureendowments, and evaluate uncertain outcomes by using anexpected utility functional V, where for ~x ¼ ðx1; p1; . . . ; xm; pmÞ,x1; . . . ; xm 2 <k, Vð~xÞ ¼

Ps psuðxsÞ, with a utility function

u : <k ! <. We assume that V satisfies risk aversion in thesense that the average of a non-degenerate distribution isstrictly preferred to the distribution itself.

Risk Aversion: Let ~x ¼ ðx1; p1; . . . ; xm; pmÞ, where x1; . . . ;xm 2 <k. Then ðE½~x�; 1Þ � ~x, where E½~x� ¼

Ps psxs, and indif-

ference is obtained only if ~x ¼ ðx; 1Þ.

At period 1, person i is facing three sources of uncertainty.He does not know what future social resources will be avail-able, nor does he know the allocation of possible socialendowments among individuals. Moreover, he does not knowwhat will be his position in each possible future society. That is,he does not know what part of the social resources of anyfuture realization he will possess. We restrict this third source ofuncertainty, and assume that his beliefs are that he has an equalchance to be any member of future society. That is, he believesthat whatever the future social resources and allocation will be,with probability 1

n he will receive each of the social allocation’s npossible bundles.

Formally, he has a probability distribution over future re-sources and their allocations, and conditional on the realizationof allocation x2 ¼ ðx2

1; . . . ;x2nÞ he believes he has 1

n chance ofreceiving each of the bundles x2

j (where for every j, x2j 2 <k). A


social policy is a reallocation of these goods, that is, an allo-cation of the form ðx21; . . . ; x2nÞ such that

Px2j ¼

Px2

j .4 It

follows from the properties of expected utility theory thatregardless of other possible realizations of future socialendowments and their likelihood, person i prefers, in period 1,that society should select, in period 2, a distribution ðx21; . . . ; x2nÞthat maximizes his expected utility Viðx21; 1n ; . . . ; x2n; 1nÞ. By riskaversion, this is the egalitarian distribution, the one that giveseveryone 1

n

Px2

j . In other words, if person i could decide inperiod 1 what allocation society should adopt in the future, hewould have selected the egalitarian distribution, the one thatgives everyone the same bundle of commodities. Moreover, hewould like society to choose this allocation in all possiblerealizations of its future endowments.5

The same holds true for everyone else in society. That is,even though individuals i and j may have different preferencesand different beliefs about aggregate future wealth and itsdistribution, they will nevertheless agree that given their presentselfish preferences, it is best for future society to reallocate fu-ture wealth in an egalitarian manner. This is true even if theyhave different beliefs about the level of the future average in-come.

Note the importance of the assumption that individuals be-lieve that all the n possible future wealth distributions areequally likely for themselves. Without it, it is not necessarilytrue that the average income is superior to the distribution. Onemay object to this assumption by claiming that even thoughwealthier persons may realize that their luck may run its course(and if they are poor, Fortune may still grace their future),wealthy persons and their descendants are more likely to re-main wealthier than poor people and their offspring, and oursymmetry assumption may well be violated. However, if this isthe case, and if each person wishes to maximize his stake in thefuture, the rich should be interested in entrenching their richesand the poor should be interested in wealth redistribution.Assuming that the latter outnumber the former, it is hard to seewhy the majority of voters consent to constitutional entrench-ments of property rights in the first place.


There is a difference between this kind of egalitarian prin-ciple and some alternative theories of justice that depend onutilities. Harsanyi (1953) suggested axioms leading to the util-itarian social welfare function

Pui, while Rawls (1971) sug-

gested maxminfuig. To be sure, if all individuals in society havethe same utility function u, then both Harsanyi’s and Rawls’social welfare functions are maximized at the egalitarian dis-tribution. We, on the other hand, do not need to assume that allindividuals have the same utility function to obtain the desir-ability of the egalitarian solution, and our focus of attention isnot individual utilities, but income levels. Moreover, and this isthe major difference between the present analysis and standardmodels of social choice, individuals in our model are motivatedby selfishness and not by social justice. All the calculations ofindividual i are made with respect to his (known) utility func-tion ui.

6 The only two assumptions needed are symmetryregarding beliefs about future income distribution, and riskaversion.

We have shown that under our assumptions, selfish indi-viduals living in the present would wish future social decisionmakers to act as if they were guided by an egalitarian principle.But how can they achieve this purpose? We now add an axiomunder which a future set of decision-makers will satisfy egali-tarian desiderata by effecting transfers by a simple majorityvote. The meaning of this result is that no current entitlementshould ever be entrenched, or, in other words, a constitutionalprotection of property rights against taking is not needed. Thisresult will be re-examined as we relax the axioms in the sub-sequent section.

We defer to a latter section the question whether it isadvisable for society to actually reach an egalitarian distribu-tion, and deal here only with the question of how can societyreach such a distribution if it desires to do so. The problem isthat future voters are not bound by their previous preferences.In other words, once they know who they are, it is no longertrue that decision makers prefer the average bundle to theiractual holding, even if they are risk averse. In fact, it may evenhappen that everyone will strictly prefer his holding to the


average bundle. For example, suppose n ¼ k ¼ 2, and let per-son 1 have the nonstochastic utility function u1ðx1; x2Þ ¼x1 þ 2x2 and the bundle ð1; 3Þ, and let person 2 have the utilityfunction u2ðx1; x2Þ ¼ 2x1 þ x2 and the bundle (3,1). Both prefertheir holding to the average (2, 2). To prevent such examples,we assume that the endowments of more than half of thepopulation is less, in all commodities, than the social average.Formally:

Skewed Distributions: The number of individuals i whoseallocation x2

i satisfies x2i 2 �x2 ¼ 1

n

Px2

j is more than n2.

For empirical evidence supporting this assumption seeAtkinson (1983). It holds for income, and more significantly,for wealth distribution.

Suppose that in the second period, when they know howwealthy they are, individuals are selfish. It follows that whenasked to vote whether or not they would like society to imposethe egalitarian distribution �x2, person i will vote favorably iffx2

i 2 �x2. Since more than half of the population satisfies thiscondition, if follows that a simple majority rule will implyegalitarian income distribution in the next period.

Our structure does not imply that society will necessarilyreach an egalitarian distribution. Suppose for example thatsociety is composed of three members, and there is one goodonly. The initial distribution of this good is given byx ¼ ð11; 4; 0Þ. A majority of selfish individuals will vote infavor of replacing this distribution with ~x ¼ ð7; 6; 2Þ. Once thisnew distribution is obtained, no simple majority will ever votefor the egalitarian distribution (5, 5, 5). We do not claim thatmajority rule necessarily leads to an egalitarian distribution,and we do not claim that there are no social mechanisms thatmay lead to such a future allocation. What we do claim is thefollowing. Under the constraint that future societies can vote toreallocate their resources, but face severe difficulties in changingthe voting rules themselves, the only majoritarian rule underwhich the egalitarian distribution may win regardless of theactual initial distribution of social resources (subject to the


skewed distributions assumption) is the simple majority rule.For any other special majority rule, one can find a distributionof the social resources that will not be replaced by the egali-tarian distribution even after many rounds of voting. Supposewe impose a 0:5þ e majority rule. Assume for simplicity onegood only, and consider the initial distribution where 0:5þ e

2 ofthe population receive a, while the remaining 0:5� e

2 of thepopulation receive b > a. Assuming that the only relevantparameter for a reallocation is personal wealth, no money canbe taken from either group, as it can blocked by more than0:5� e of the population.

3. THE ENDOWMENT EFFECT AND THE ENTRENCHEDCONSTITUTION

Under the assumptions we outlined in the previous section,future simple majority enables society to reach what at presenteveryone considers to be the best outcome. In other words, nospecial voting devices are needed to entrench property rights,and they should not be secured beyond the measure of pro-tection they receive by the simple majority rule. But this con-clusion may change once we introduce the possibility of moregeneral preferences for uncertain prospects.

The psychological literature documents the existence of whatcame to be known as the ‘‘endowment effect’’. Tversky andKahneman (1991) suggested that preferences over bundles ofcommodities should depend on a reference point. Formally,preferences over <k given the reference point y should be de-noted �y and the utility function representing these preferencesuð�jyÞ. Their main definition and assumption regarding theendowment effect is the following:

Loss Aversion: Let x; y; r; s 2 <k such that for good ‘,s‘ ¼ y‘ > r‘ ¼ x‘, and for all m 6¼ ‘, rm ¼ sm. Then y �r x im-plies y �s x.

The intuition is clear. If, when having as a reference point r,with the lower quantity of good ‘, the decision maker was


willing to exchange y�‘ for x�‘ so that the quantity of good ‘will increase from x‘ to y‘, then he would certainly be willing tokeep y�‘ over x�‘ so that the quantity of good ‘ will not de-crease from y‘ to x‘ when the reference point is s with the higherlevel of good ‘.7 For a further discussion of this phenomenon,experimental evidence, and axiomatization see Thaler (1980);Kahneman and Tversky (1979); Tversky and Kahneman (1991;1992); Bateman et al. (1997) and Knetsch and Sinden (1984).As is evident from Tversky and Kahneman (1991), this effectrelates to goods, and not to money.8 We show now how theendowment effect may change the desirability of simplemajoritarian rules.

REMARK 1. Strictly speaking, goods for which endowmenteffects exist must be idiosyncratic. If identical goods can bebought in the market, there is a much weaker reason for thedecision maker to get attached to the specific units he has. Thetypical protection against taking of property is indeed appliedto assets like land, which is probably the extreme case of idi-osyncratic goods.9

For our purposes, we assume that there are two goods,money (m) and land (x), and that the utility function is sepa-rable, that is, it is of the form Vðm; xÞ ¼ vðmÞ þ uðxjyÞ. Themeaning of the expression uðxjyÞ is that when the decisionmaker’s current holding of land is y, he evaluates x with thevalue obtained from uðxjyÞ. Assuming a separable utilityfunction is of course restrictive, but as long as one of the goodsif money, it has a simple interpretation – enjoyment of good xdoes not depend on wealth level. Unlike consumption goodswhere complementarity or substitutability may be natural (e.g.,bread and butter, or bread and cakes), such effects seem muchless natural between money and other goods.

We will assume the following:

1. v is concave, and for every y, uð�jyÞ is concave.2. uðxjyÞ has a kink at the point x ¼ y.3. Let y < y0 be two reference points. For x < y < y0, uðxjyÞ ¼

uðxjy0Þ, and for x > y0 > y, uðxjy0Þ ¼ uðxjyÞ þ ½uðy0jy0Þ �


uðy0jyÞ�. Moreover, for x 2 ðy; y0Þ, u0ðxjy0Þ > u0ðxjyÞ (seeFigure 1).

The first assumption, that uðxjyÞ is concave, is directly im-plied by risk aversion. The second assumption implies a sig-nificant difference between gains and losses. Not only is it true,as follows by the concavity of u, that gaining a certain amount eof land generates less utility than the the drop in utility when eis lost, but this holds even for infinitesimally small quantities ofland.

The third assumption suggests that changing the referencepoint from y to y0 affects marginal utility (from land) only foroutcomes between y and y0. (In Figure 1, the utilities uð�jyÞ anduð�jy0Þ coincide up to y, and parallel beyond y0). We find thisrestriction quite plausible, and it is trivially satisfied whenpreferences do not depend on reference points. The introduc-tion of such dependency implies different attitudes to unitsabove and below of the reference point. But as long as a unit isabove this point, its evaluation should be the same.

The third assumption also implies that u0ðy�jyÞ and u0ðyþjyÞare decreasing functions of y. That is, the marginal utility froma small gain that is added to the endowment is decreasing withthe size of the endowment, and the marginal loss in utility from

Figure 1. Assumption 3.


a small increment taken away from the endowment isdecreasing with the size of the endowment. In other words, thedamage from losing e, measured in terms of utility, is less severeto the rich than it is to the poor. Similarly, the gain in utilityfrom winning e is larger to the poor than to the rich. We explainthe implications of this assumption in Section 5 below.

Functions satisfying these three requirement are consistentwith the loss aversion assumption. Formally:

LEMMA 1. If the function Vðm; xÞ satisfies the above threeassumptions, then the preferences represented by this functionsatisfy loss aversion.

Proof. We want to show that if y > x and Vðm; yjm00; xÞ �Vðm0; xjm00; xÞ, then Vðm; yjm00; yÞ > Vðm0; xjm00; yÞ. But Vðm;yjm00; xÞ ¼ vðmÞ þ uðyjxÞ, Vðm0; xjm00; xÞ ¼ vðm0Þ þ uðxjxÞ, Vðm;yjm00; yÞ ¼ vðmÞ þ uðyjyÞ, and Vðm0; xjm00; yÞ ¼ vðm0Þ þ uðxjyÞ.Now Vðm; yjm00; xÞ � Vðm0; xjm00; xÞ implies vðmÞ þ uðyjxÞ �vðm0Þ þ uðxjxÞ, hence vðm0Þ � vðmÞ � uðyjxÞ � uðxjxÞ. Byassumption, uðyjxÞ � uðxjxÞ < uðyjyÞ � uðxjyÞ, hence vðmÞþuðyjyÞ > vðm0Þ þ uðxjyÞ, and it follows that Vðm; yjm00; yÞ >Vðm0; xjm00; yÞ. (

Consider now once again the optimization problem faced byindividual i during the first period. He does not know what willbe the social endowments in the next period, nor does he knowthe distribution of these endowments. But whatever these willbe, he believes that he has an equal chance of being any of the nmembers of society. Once the actual distribution is known,society will reallocate its resources, so that the individual who isinitially allocated x2

j will receive x2j ðx2j Þ instead. The budget

constraint isP

x2j ðx2j Þ ¼

Px2

j . For simplicity, we omit thesecond period superscript. The question now is, what allocationðx1ðx1Þ; . . . ; xnðxnÞÞ would person i like future society tochoose?

It is possible to argue that there should be no differencebetween the analysis of Section 2 and the analysis of the presentsituation, as the relevant reference point should be the decisionmaker’s current holding. At period 1, when individual i knowshis current endowment, and is trying to evaluate future


uncertainty, he acts as an expected utility maximizer (albeitwith a non-differential utility at his current holding), hence weshould still obtain the same result, namely, that a simplemajority rule is optimal. But this argument ignores the fact thatonce the decision maker realizes actual future distribution ofsocial endowments, his actual bundle of commodities will de-fine his reference point. Therefore, when selecting a constrainton future social policies, this new reference point should beconsidered. Since he is an expected utility maximizer, hisanalysis of each possible realization of social endowments isseparable from other possible realizations. We turn now to spellout individual i’s optimal strategy, assuming his familiarity withthe distribution of future endowments but ignorance of hisown.

Unlike standard analysis of uncertainty with referencepoints, where the decision maker knows his reference point butnot the outcome he will receive, in this case his major source ofuncertainty is his reference point. Once this uncertainly is re-solved, he knows his outcome as well. We therefore suggest thateach decision maker would be interested in maximizing hisexpected utility-gain (which may, in fact, be negative). For-mally, let xj ¼ ðm0

j; yjÞ, j ¼ 1; . . . ; n be a possible realization andallocation of future endowments. Individual i prefers futuresociety to choose the allocation

ððm1ðx1Þ; x1ðx1ÞÞ; . . . ; ðmnðxnÞ; xnðxnÞÞ ð1Þthat is, to replace each of his possible future bundles xj ¼ðm0

j; yjÞ with ðmjðxjÞ; xjðxjÞÞ, where the vector in Equation (1)solves

maxXj

1

n½ViðmjðxjÞ; xjðxjÞjxjÞ � Viðm0

j; yjjxjÞ�

s:t:Xj

xjðxjÞ ¼Xj

yj

Xj

mjðxjÞ ¼Xj

m0j

ð2Þ

Here ViðmjðxjÞ; xjðxjÞjxjÞ is the utility of person i from thebundle ðmj; xjÞ that will be reallocated to him if his true second


period outcome is xj, given the reference point xj. From this wesubtract Viðm0

j; yjjxjÞ ¼ ViðxjjxjÞ, which is his utility from theoutcome xj with the same reference point. Note that expectedutility implies separable analysis of each possible realization ofsecond period endowments and their distribution. Therefore,even though the allocation of Equation (1) is by itself uncertain(and not only person i’s position in it), we can analyze themaximization problem (2) independently on any other possiblerealization of social endowments.

Since Vjðm; xjm0; yÞ ¼ vjðmÞ þ ujðxjyÞ, it is easy to verify, bythe concavity of vj, that the solution to this optimizationproblem implies m1 ¼ � � � ¼ mn ¼ m0 ¼ 1

n

Pm0

j. For the optimalvalues of the x good, person i sets the values x�i and xi� suchthat

xjðxjÞ ¼xi� yj � xi�yj xi� < yj < x�ix�i yj � x�i

8<:

where

1.P

j:yj�xi�ðxi� � yjÞ ¼

Pj:yj�x�

iðyj � x�i Þ.

2. For yj < xi� and y0j > x�i , u0iðxi�jyjÞ ¼ u0iðx�i jy0jÞ. Denote this

common derivative d.3. For yj 2 ½xi�; x�i �, u0iðy�j jyjÞ � d � u0ðyþj jyjÞ.

The first condition, which follows directly from the firstconstraint, implies that the net transfer of the non-money goodis zero. The second condition suggests that person i would likehis marginal utility from this good to be the same for all thosecases where his ultimate allocation will be different from hissecond period initial endowment. This is an obvious condition,since for these cases the utility function ui is differentiable at hisoutcome. (Of course, the fact that for all yj < xi� , the derivativeu0iðxi�jyjÞ is the same follows by the third assumption we madeconcerning the nature of the function V). The third conditionstates that for those cases j where his endowment does notchange, the common marginal utility of the rest of the cases dmust be between his marginal utility from loss and the marginalutility from gain at yj. Obviously if this condition is violated,


(say, d is above the marginal utility from loss at yj which isbetween xi� and x�i and will therefore not change), then it wouldbe better for person i, in terms of expected gains and losses ofutility, to have less of the non-money good if yj is its realization,and to have more of it in the cases where the above conditionsimply that the marginal utility from it is d.

Observe that the second and the third conditions are ob-tained with respect to u0i, the derivative of the utility function ofperson i, and not with respect to the marginal utilities of allindividuals. As in the previous section, we assume that person iknows his identity (and hence, his utility function), but isuncertain what bundle he will initially own in the second per-iod.

As before, the desired result for the reallocation of moneycan be obtained by a simple majority rule. But the same rulewill take too many units of x from the rich and transfer them tothe poor. Clearly, individual i would like in period 1 to entrenchthe property rights of those whose future x endowment will beless than x�i , which is of course larger than the average quantityof x, �x.

Two conclusions follow immediately from this analysis.First, money and land need different entrenchments. Note thatgiven the additively separable structure of the functions Vi, theoptimal entrenchment of each of the two goods is independentof the actual entrenchment of the other. Secondly, simplemajority is not enough to offer the kind of protection forproperty rights in land individuals living in period 1 want forthe future. Suppose that under all circumstances society agreesthat if any plot of land is to be transferred, then it should betransferred from those who have more to those who have less.Then even those individuals whose endowment is not threa-tened, will agree to such reallocations. The simplest way toprevent ‘‘too much’’ land from being reallocated, that is, toprevent taking from a rich person j more than yj � x�, is byimposing a super majoritarian rule. Of course, the opti-mal values of x� and x� depend on the utility functions u, onsociety’s future endowments, and on their allocation. Sinceindividual utilities and individual beliefs regarding these


eventualities may differ, so will the optimal values of x� and x�differ from one person to another. But all members of societywill agree that more than a simple majority is needed toexpropriate land from their future possessors in order to benefitother members of society.

We conclude this section with a numerical example. We as-sume here that there is only one possible allocation of secondperiod endowments, and the only source of uncertainty relatesto the identity of the different individuals in this allocation.

EXAMPLE 1. Let n ¼ 3, and suppose that all three individualshave the same utility function Vðm; xjm0; yÞ ¼ vðmÞ þ uðxjyÞ,where uðxjyÞ is given by

uðxjyÞ ¼ffiffiffix

px � y

12 ½

ffiffiffix

pþ ffiffiffi

yp � x > y

�

Suppose y1 ¼ 1600, y2 ¼ 1200, and y3 ¼ 900. Clearly,u0ðy�1 jy1Þ ¼ 1

80 while u0ðyþ3 jy3Þ ¼ 1

120. There is therefore no reasonfor individuals in period 1 to wish to have any transfers of landin the second period. On the other hand, if y1 ¼ 4900, thenu0ðy�1 jy1Þ ¼ 1

140, and following our analysis, individuals in thefirst period would like future society (that is, the second periodsociety) to transfer land from the rich to the poor. It is easy toverify that the optimal amount of land transferred is 260. (

4. EXAMPLE: THE AMERICAN CONSTITUTION

In this section we discuss two fundamental legal doctrines thatseem to be consistent with our analysis. The discussion is in-tended to shed some new light on the analysis of propertyprotection in American Constitutional Law.

4.1. Constitutional Protection of Property Rights

The Fifth Amendment to the American Constitution providesthat ‘‘no person shall be . . . deprived of . . . property withoutdue process of law; nor shall private property be taken forpublic use, without just compensation’’. The first part of thecited passage could be interpreted as a constitutional


entrenchment of all forms of wealth, but in reality it is not sointerpreted. The most straightforward method of wealthredistribution, direct taxation, is obviously not banned by theconstitution, and is commonly practiced with the avowedpurpose of taking from the rich and giving to the poor.10 Thesecond part of the cited passage, commonly referred to as the‘‘Taking Clause,’’ stipulates that property cannot be takenwithout due compensation.11 Why can the government tax thegeneral resources of taxpayers, without compensating them fortheir losses, but it is banned from doing so if the object of itsintentions falls within the ambit of the Taking Clause? Oneobvious distinction is that ‘‘taking,’’ unlike taxation, is neverpracticed on money or other tradable goods. It is practiced onreal objects, and most commonly on land. ‘‘Taking’’ forcespeople to part with endowed objects, while general taxationdoes not. The analysis of the previous sections suggests thatsince taxpayers do not endow their overall wealth, wealthredistribution ought to be voted on by employing the simplemajority rule. Since property owners do endow, on the otherhand, their real estate and other takable assets, a redistributionof these assets ought to be voted on by employing a supermajoritarian mechanism.

A further examination of this hypothesis reveals someadditional insights. Suppose people did not have money andother tradable goods and all their wealth were invested in en-dowed objects. If this were the case, general taxation wouldhave destroyed the taxpayers’ sense of endowment, because tofinance their tax obligations, taxpayers would have to sell theirendowed assets. In a situation like this general taxation oughtto have been banned as well, unless ratified by a super major-itarian constituency. But at some historical periods this situa-tion was exactly the case. By the end of the 18th century, whenthe American Constitution was drafted, and for a long timethereafter, a typical portfolio representing the citizens’ wealthconsisted of tangible assets like land, plantations, and slavesand not of ready cash, corporate securities, and other tradableassets (see Goldsmith, 1985). This situation was faithfullymirrored in the constitutional treatment of the subject of


general taxation. Although the Constitution, in its originalform, declares (Article I, Section 8) that ‘‘the Congress shallhave Power to lay and collect Taxes, Duties, Imposts and Ex-cises . . .’’ it was widely believed that it lacked power to impose ageneral income tax, and, indeed, it was so held by the SupremeCourt.12 This constitutional ruling was partly based on someidiosyncratic considerations relating to the American form offederalism, but it was also consciously made to reflect a deeplyfelt antipathy to the redistribution of wealth. Redistributionwas bound to generate, in the words of one of the Justices, ‘‘thespecter of Socialism,’’ and was bound to result in ‘‘an assault oncapital,’’ which was nothing short of ‘‘a war of the poor againstthe rich’’. Not until the Sixteenth Amendment, introduced in1913, did Congress get the power to impose general taxation.There are, of course, other reasons why the Sixteenth Amend-ment was introduced, which have to do with a shift in thepopular understanding of the role of government. However,one cannot ignore the fact that by the second decade of the 20thcentury it was no longer necessary to sell land and other en-dowed assets to finance the typical taxpayer’s tax bills;13 hencethe optimal constitutional protection of moneyed wealth be-came the simple majority rule.

The Taking Clause in itself merits a closer look. When someproperty is condemned for public use, the language of theConstitution is straightforward and due compensation ispromptly paid. But there are many more ways to take some-thing away from someone without expropriating it. The mostcommon form of government interference with ownership is byregulating it away, e.g. by zoning decisions that diminish thevalue of land. Arguably, there should be little difference be-tween, say, taking 50% of someone’s land for the purpose ofconstructing a railroad track, and rezoning an area in a waythat reduces the value of all affected real estate by 50%. From adoctrinal perspective, however, there is a great deal of differ-ence. A few years after the passage of the 16th Amendment, theSupreme Court ruled that mere regulation is not ‘‘taking’’,14

although in extreme cases, where the effects of the regulatorymeasure are indistinguishable from straightforward condem-


nation for public use, regulation could be tantamount to‘‘taking’’.

For example, in one case,15 the Supreme Court held that azoning decision turning parts of Penn Central Station in NewYork into a city landmark, which severely limited its owners’freedom to develop their own real estate, was not a ‘‘taking.’’ Inanother case,16 the owners of real estate were forced to give thepublic a right of way on their property as a condition forgranting them permit to expand their house. The SupremeCourt held that this amounted to ‘‘taking’’. The apparentcontradiction between these two outcomes has puzzled com-mentators for a long time. In conformity with our main argu-ment it can be pointed out that in the first case the possession ofthe regulated area remained in the hands of its owners. Thedetrimental regulation merely affected its monetary value andtherefore did not violate the owners’ sense of endowment. Inthe second case, the effect of the regulation was to condemnendowed assets and to convert them into public use. Theowners could no longer enjoy exclusive possession of a strip ofland on which the public had a right of way.

4.2. Contractual Freedom

Another major shift in the doctrinal attitude to property rightsoccurred in relation to contractual freedom. To what extent arefirms free to contract with labor for oppressive work conditions(say, extremely long shifts, unrestrained work conditions forunderage employees, or a ban on organization and unioniza-tion)? To what extent are firms free to exploit market condi-tions in their favor without constraint (for example, set‘‘excessive’’ prices or flood the market with substandardproducts or services)? The privilege of doing so, and the cor-relative duty of the other party to abide by such stipulations, isan important property right of firms, and one that was largelyimmune from majoritarian (that is, statutory) interference wellinto the 20th century. Thus, in the well known case of Lochnerv. New York (198 U.S. 45 (1905)) the Supreme Court struckdown, on constitutional grounds, a state statute purporting to


limit the maximum working hours for bakers. It was held thatsuch a statute infringed the right of the employer and the em-ployee to freely negotiate and forge their own agreements ex-actly as they wished. Many similar statutes (some 200 of them)were held unconstitutional during the so-called Lochner era.17

The turning point did not occur until the mid-1930’s, whenLochner was reversed and contractual freedom lost its inde-pendent constitutional immunity.18

A straightforward explanation of the post Lochner juris-prudence is by direct reference to the New Deal philosophy,which turned its back on laissez faire economics and embraceda regulatory approach instead. Nor did the post Lochner jus-tices have much of a real choice in this matter, given PresidentRoosevelt’s threat to restore majoritarianism by packing theSupreme Court. Here we add another explanation. Berle andMeans (1932) introduced the idea that corporate ownership andcorporate control became, for all practical purposes, separatedfrom each other. This peculiarity is not typical of other forms ofwealth (land, machinery, intellectual property) and it was a newapparition on the corporate scene as well, since most 19thcentury enterprises were essentially family businesses. Clearly,there is a difference between owning a controlled enterprise(a closely held corporation) and holding a financial stake in apublicly held firm. One does endow a close corporation(alongside with whatever the company possesses) as ‘‘one’sown’’.19 On the other hand, one presumably treats financialassets in public firms according to their true nature, as fungible,tradable units of wealth. Like cash, corporate securities do notcreate in their owners any noticeable endowment effect (seenote 2 above). In protecting the firm’s right to contractualfreedom, the Lochner era courts recognized the entrenchedstatus of endowed wealth. In the later repudiation of that en-trenched status, the post Lochner courts were simply subjectingunendowed forms of wealth to the rigors of majoritariandemocracy.

Other examples for the difference between legal protection ofendowed assets and financial assets can be found in variousinsolvency statutes, which typically exempt debtors’ home-


steads from the reach of their creditors. Some wages are exemptas well, but to a dramatically lesser extent. Another example isthe fact that when debtors collateralize an asset as security for adebt, they always enjoy the so-called ‘‘equity of redemption,’’meaning that regardless of any agreement to the contrary, adebtor has an option to redeem the collateralized asset in pri-ority to all other persons.

5. SOME ADDITIONAL CLARIFICATIONS

In this section we discuss some possible objections to ouranalysis.

Is it money versus property or arbitrary versus non-arbitrarytaking? Our analysis depends strongly on the distinction be-tween protection against property taking, and the lack of suchprotection when financial assets are taken. One can argue thatsuch lack of protection is merely due to the fact that it is a loteasier to take away money, rather than property, and theconstitutional protection is against random taking, rather thanagainst taking of property.

As we have explained above, when personal assets were heldmostly in property, it was indeed much harder for the gov-ernment to impose taxes. A modern day echo of the income taxcontroversy of a century ago can be found in the debate relatingto the estate tax. One objection to this tax centers on theimplications of the tax for families who own most of theirwealth in endowed assets, like farms, homesteads and a varietyof family businesses.

The two most important modern taxes are income tax andsales tax. Although it is true in principal that income in goodsand services is taxable, it is certainly the case that almost all ofthe taxed income is monetary, being either income from workor from financial assets. Sales taxes may affect consumerswillingness to buy goods, but typically it does not force them toliquidate assets.

What super majority? This question concerns the identifica-tion of the ideal super majority. We did show that the redistri-bution of wealth ought not to be conducted by using the simple


majority rule, but we failed to identify what kind of supermajority to employ. Our model is not rich enough to answer thisquestion. Using the notations of Section 3, each member ofsociety has an individual value for x�, the lower boundary belowwhich property is not to be seized, which depends on the indi-vidual’s utility function and on his beliefs regarding futureendowments and their distributions. As before, denote thesepersonal values x�i . For each such value there is a correspondingsize of super majority, given by the proportion of futureendowments that are below x�i . If society were to select by votinga particular super majority rule, then a simple majority wouldpresumably choose the median value of these individuallyoptimal super majority rules. There is no logical inconsistency ina simple majority entrenching future rights by requiring a supermajority, as everyone in our model wants some super majori-tarian defense for future reallocations.20

Clearly, the more concave the individuals’ utility functionsare, the greater is the justification for an egalitarian distribu-tion, which can best be achieved by weaker super majoritarianprerequisites. On the other hand, the fonder are the members ofa given society of their initial endowments, the greater is theneed for a stronger constitutional entrenchment. Each societymay have its special traits with regard to these two parameters,and may well need its own custom-made majority rule.

What is the endowment? Consider again the utility functionsof Example 1. After 260 units are transferred from person 1 toperson 3, their corresponding wealth levels become 4640 and1160. Should these numbers be now used as the new endow-ments and should the calculations now be done again withrespect to these wealth levels?

We do not have a general answer to this question, but givenour assumptions, the question is irrelevant. In Section 3 weassumed that for every i and for x < y < y0, uiðxjyÞ ¼ uiðxjy0Þ,and for x > y > y0, uiðxjyÞ ¼ uiðxjy0Þ þ ½uiðyjyÞ � uiðyjy0Þ�. Inour example it is indeed the case that u01ð4640�j4640Þ ¼u01ð4640j4900Þ, and u03ð1160þj1160Þ ¼ u03ð1160j900Þ. There istherefore no need to transfer any more land from person 1 toperson 3.


This third assumption implies that the dependency of themarginal utility at x on the endowment y relates only towhether x is above or below y. For all levels of y below x, themarginal utility at x is the same, and the same holds true forall levels of y above x. Of course, these two levels are differ-ent.21

Why does not society redistribute wealth above x�? Given thefact that the poor outnumber the rich, one wonders why doesnot a simple majority of the voters redistribute all moneyedwealth equally among the entire population, and why does nota special majority redistribute at least some of the endowedwealth. Egalitarian redistribution is not a reasonable alterna-tive because of the negative incentives it creates. The votersrealize that it might be better to get a smaller percentage of alarger pie than the other way around. With this said, a lot ofmoney distribution, and a fair amount of property redistribu-tion, takes place through tax transfers. The object of taxation ismoney, but financing it often requires a marked diminution ofendowed assets. Finally, one must not underestimate the vigorof the existing constitutional entrenchment. Consider oncemore the American example. Securing a majority vote of twothirds in the House, two thirds in the Senate and ratification by75% of the states (where every state imposes its internal supermajoritarian requirements) is almost tantamount to imposing aconstraint of unanimity.

ACKNOWLEDGEMENTS

We wish to thank Jennifer Arlen, Kit Baum, Ehud Kamar, EdiKarni, Daniel Klerman, John McGinnis, Joe Ostroy, EdwardRock, David Rudenstine, Alan Schwartz, Menny Shalom, DanSimon, Stewart Sterk, Richard Tresch and Dan Vincent forhelpful comments on previous drafts.

NOTES

1. Germany: Section 14(3); The Netherlands: Section 14(1); Spain: Section33(3).


2. For analysis of this phenomenon and some experimental evidence (seeThaler, 1980; Kahneman and Tversky, 1979; Tversky and Kahn-eman, 1991,1992; Bateman et al., 1997; Knetsch and Sinden, 1984;Kahneman et al., 1993; Knez et al., 1985; Singh, 1991; McClelland andSchulze, 1991; Arlen et al., 2002). However, most studies indicate thatsubjects develop a much stronger attachment to unique objects (such asland) or to objects intended for their personal consumption; there is nosuch attachment, or almost none, when it comes to fungible goods (suchas money) or to tradable assets (such as corporate securities). Indeed, itmakes some sense to expect individuals to ask for a larger amount ofmoney in exchange for a farm inherited from their parents than theamount of money they would have been willing to pay for the samefarm if it were not theirs; it makes no sense for anyone to exhibit a gapbetween his willingness to accept and his willingness to pay, if the objectin question is a twenty dollar bill.

3. It is commonly believed that judges, for instance, do not understand thesubtleties of economic discourse, but nevertheless develop common-sensical intuitions that help them identify efficient results (see Posner,1998). Some theorists suggest that the Common Law might be efficientfor evolutionary reasons, where inefficient norms do not ‘‘survive’’ (seeRubin, 1977; Posner, 1998). A straightforward application of the fitargument to statutory (as opposed to Common Law) legal rules,assumes that like all regulators, legislators ‘‘sell’’ statutory products inimplicit markets, and are rewarded by the affected constituency in theballot (see Stigler, 1971. For further, more modern, cites, see Posner,1998). Although legislators are often ‘‘captured’’ by special inter-est groups and craft statutory products to appease their cravings, it isclear in the context discussed in this paper that the universality ofendowment effects ensures a good alignment between the commonpreferences of the entire constituency and the contents of the resultingstatutory products.

4. We assume here that the reallocation mechanism is not wasteful.Otherwise, one can only assume

Px2j 2

Px2

j (for x; y 2 <k, x2 ymeans that for every m ¼ 1; . . . ; k, xm � ym). See section 5 bellow.

5. This is not true if preferences are not expected utility. In that case it mayhappen that even if the decision maker is risk averse, the conditionalaverages will be dominated by the original distribution. This is of coursenot the case if there is only one possible future distribution.

6. The importance of this point becomes evident in Section 3 below.7. x�‘ stands for ðx1; . . . ; x‘�1; x‘þ1; . . . ; xkÞ.8. Strictly speaking, this effect is stronger with respect to goods than with

respect to money. The experiment reveals higher asking monetary pricefor endowed goods than the price subjects are willing to pay to purchasethe same goods.


9. In terms of notation, such goods should be indexed by the agent whoholds them. To simplify notation, we skip this formality.

10. If the purpose of taxation is to provide government funding of publicgoods, taxpayers do get some return for their tax dollars; but even inthis case there is a clear repudiation of the quid pro quo philosophy asmany taxpayers are contributing more than their share in the funding ofthe common good.

11. Although linguistically the Taking Clause is not limited in scope, andcould be directed against any form of wealth, in practice it appliesmainly to property and not to money.

12. See, for example, Pollock v. Farmers’ Loan and Trust Co. 158 U.S. 601(1895).

13. For the distribution of wealth between financial and tangible assets (seeGoldsmith, 1985).

14. The taking-regulation distinction was articulated in Pennsylvania CoalCo. v. Mahon, 260 U.S. 393 (1922).

15. Penn Central Transportation Co. v. New York City, 438 U.S. 104(1978).

16. Nollan v. California Coastal Commission, 483 U.S. 825 (1987).17. The identification of the Lochner style doctrine of contractual freedom

with the allocation of property rights, and thus of political power, to therich at the expense of the poor, has become a major tenet of the criticallegal studies movement (see Horwitz, 1992).

18. For example, in Nebbia v. New York, 291 U.S. 502 (1934), the SupremeCourt upheld, for the first time, the right of state legislatures to fix maxi-mumorminimumprices (in this particular case the commodity in questionwas milk containers). Later on, the court took even a more extreme po-sition. In Williamson v. Lee Optical Co., 348 U.S. 483 (1955) the Courtupheld a state statute regulating opticians away from the frame fittingbusiness. This was done to accommodate the interests of the ophthal-mology profession; the court reached this outcome although it did notendorse the policy behind the statute and even considered it detrimental.

19. For the law’s detailed response to the sense of endowment in closecorporations, see, for example, O’Neal and Thompson, 2000.

20. Incidentally, this insight lays to rest a common objection to constitu-tional entrenchment of entitlements which is obtained by a baremajority of the voters; the bare majority relates to the particular supermajority selected by the constituency, but the very principle of supermajoritarian entrenchment enjoys a universal support.

21. Sunstein, 1993 seems to have the opposite intuition. He appears to claimthat once the endowment structure is altered, all individuals develop anew allegiance to the new structure, and thus there is no good reason tobe opposed to judicial review, which tends to overrule the original senseof endowment.


REFERENCES

Arlen, J., M. Spitzer and E. Talley: 2002, ‘Endowment effects within cor-porate agency relationships’, Journal of Legal Studies 31, pp. 1–38.

Atkinson, A.B.: 1983, The Economics of Inequality, 2nd edn (ClarendonPress, Oxford).

Bateman, I., A. Munro, B. Rhodes, C. Starmer and R. Sugden: 1997, ‘A testof the theory of reference-dependent preferences’, Quarterly Journal ofEconomics 112, pp. 479–505.

Berle, A.A. and G.C. Means: 1932, The Modern Corporation and PrivateProperty (Macmillan, New York).

Black, C.: 1999, A New Birth of Freedom (Yale University Press, NewHaven, CT).

Buchanan, J.M. and G. Tullock: 1962, The Calculus of Consent, LogicalFoundations of Constitutional Democracy (University of Michigan Press,Ann Arbor).

Cooter, R.: 2000, The Strategic Constitution (Princeton University Press,Princeton).

Goldsmith, R.W.: 1985, Comparative National Balance Sheets (Universityof Chicago Press, Chicago).

Harsanyi, J.C.: 1953, ‘Cardinal utility in welfare economics and in thetheory of risk-taking’, Journal of Political Economy 61, pp. 434–435.

Horwitz, M.: 1992, The Transformation of American Law 1870–1960: TheCrisis of Orthodoxy (Oxford University Press, New York).

Kahneman, D., J. Knetsch and R. Thaler: 1993, ‘The endowment effect, lossaversion and status quo bias’, Economic Perspective, 5, pp. 193–206.

Kahneman, D. and A. Tversky: 1979. ‘Prospect theory: An analysis ofdecision under risk’, Econometrica 47, pp. 263–291.

Knetsch, J.L. and J.A. Sinden: 1984, ‘Willingness to pay and compensationdemanded: Experimental evidence of an unexpected disparity in measuresof value’, Quarterly Journal of Economics 99, pp. 507–521.

Knez, P., V. Smith and A. Williams: 1985, ‘Individual rationality, marketrationality and value estimation’, American Economic Review 75, pp.397–402.

McClelland, G. and W. Schulze: 1991, ‘The disparity between willingness topay versus willingness to accept as a framing effect’, in D. Brown and K.Smith (eds.), Frontiers of Mathematical Psychology: Essays in Honor ofClyde Coombs 166–192.

Olson, M.: 1971, The Logic of Collective Action (Harvard University Press,Cambridge, MA).

O’Neal, H. and R. Thompson: 2000, Close Corporations (West Group, St.Paul, MN).

Posner, R.A.: 1998, Economic Analysis of Law, 5th edn (Aspen Law &Business, New York).


Przeworski, A.: 1971, ‘Democracy as a contingent outcome of conflicts’, inJ. Elster and R. Slagstand (eds.), Constituionalism and Democracy(Cambridge University Press, Cambridge), p. 59.

Rawls, J.: 1971, A Theory of Justice (Harvard University Press, Cambridge,MA).

Rubin, P.: 1977, ‘Why is the common law efficient?’ Journal of Legal Studies6, pp. 51–63.

Singh, H.: 1991, ‘The disparity between willingness to pay and compensa-tion demanded: Another look at laboratory evidence’, Economic Letters35, pp. 263–266.

Stigler, G.: 1971, ‘The theory of economic regulation’, Bell Journal ofEconomics and Management Science 3, pp. 3–21.

Strauss, D.: 2001, ‘The irrelevance of constitutional amendments’, HarvardLaw Review 114, pp. 1457–1505.

Sunstein, C.: 1993, The Partial Constitution (Harvard University Press,Cambridge, MA).

Thaler, R.: 1980, ‘Toward a positive theory of consumer choice’, Journal ofEconomic Behavior and Organization 1, pp. 39–60.

Tullock, G.: 1988, ‘The calculus – postscript after 25 years’, in J. Gwartneyand R. Wagner (eds.), Public Choice and Constitutional Economics (JAIPress, Greenwich, CT), p. 139.

Tushnet, M.: 1984, ‘An essay on rights’, Texas Law Review 62, pp. 1363–1403.

Tversky, A. and D. Kahneman: 1991, ‘Loss aversion in riskless choice: Areference-dependent model’, Quarterly Journal of Economics 106, pp.1039–1061.

Tversky, A. and D. Kahneman: 1992, ‘Advances in prospect theory:Cumulative representation of uncertainty’, Journal of Risk and Uncer-tainty 5, pp. 297–323.

Addresses for correspondence: Uriel Procaccia, Inter-Disciplinary Center,Herzeliya, Israel, 46150 and Center for Rationality, Hebrew University,Givat Ram, Jerusalem, 91904, Israel. E-mail: [email protected] Segal, Department of Economics, Boston College, Chestnut Hill, MA02467, USA. E-mail: [email protected]


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