(1) Since the exemption from a burden (e.g. from military service) can always be viewed as a good, I shall henceforward refer only to the allocation of scarce goods.

(2) For one such case study, see, in this issue, Herpin, Nicolas, le don du sperme, Archives européennes de sociologie, XXXI (1990), 141–173.CrossRefGoogle Scholar

(3) Walzer, M., Spheres of Justice (New York, Basic Books, 1983).Google Scholar

(4) Useful comparative studies of singlearena issues in different countries include Yemin, E. (ed.), Workforce Reductions in Undertaking (Geneva, International Labour Office, 1982)Google Scholar and Aaron, H. J. and Schwartz, W. B., The Painful Prescription (Washington, D.C., The Brookings Institution, 1984)Google Scholar. The first of these compares layoff policies in seven industrialized countries, the second allocation of medical goods in the United States and Britain. Within-country comparisons of several arenas are virtually non-existent. Nobody, for instance, seems to have compared the process of being exempted from military service with the process of being admitted to college in the United States. A fortiori, simultaneous comparisons of countries and arenas have, to my knowledge, never been carried out.

(5) The following draws on Stouer, S. et al. , The American Soldier (Princeton, Princeton University Press, 1949).Google Scholar

(6) Strictly speaking, the problem differs from the one Arrow set out to study. He examined the problem of transforming individual rankings of alternatives into a social ranking. The demobilization scheme raised the problem of transforming individual comparisons of individuals into an overall social comparison. Hylland, A. has shown (‘Subjective interpersonal comparison’, to be published in Elster, J. and Roemer, J. (eds.), Interpersonal Comparisons of Well-Being, forthcoming from Cambridge University Press) that this aggregation problem is only slightly less serious than Arrow's original one.Google Scholar

(7) Although the medical literature is divided, this statement appears to remain true even after the introduction of cyclosporin. See notably Opelz, , Allocation of cadaver kidneys for transplantation, Transplantation Proceedings, XX (1988), 1028–32.Google Scholar

(8) For a fuller description, see United Network for Organ Sharing, Articles of Incorporation, Bylaws and Policies (effective 05 31, 1988) [Richmond, Virginia]Google Scholar. Recently, the point system has changed in the direction of assigning more points for good antigen matching. There also exist local variants, which, however, have to be approved by unos centrally.

(9) H. P. Young, On the use of priority formulas for determining organ transplant recipients, unpublished manuscript, 1988.

(10) Antibody formation and antigen matching do not vary independently of each other. ‘Widely reacting cytotoxic antibodies often have specificity against the class 1 antigens of the A and B histocompatibility loci; because of this, the demonstration of a negative cytotoxic cross match for a highly sensitized patient should predict a good antigen match. Thus, the antibody and antigen credits tend to be reinforcing’. (Starzl, T.E. et al. , A multifactorial system for equitable selection of cadaver kidney recipients, Journal of the American Medical Association, CCLVII (1987), 3073–75.CrossRefGoogle Scholar

11. Ibid.

(12) Petersen, R., Rationality, ethnicity and military enlistment, Social Science Information, XXVIII (1989), 563–598.CrossRefGoogle Scholar

(13) For a study of such allocation problems, see Hylland, A. and Zeckhauser, R., The efficient allocation of individuals to positions, Journal of Political Economy, LXXXVII (1979), 293–314.CrossRefGoogle Scholar

(14) Calabresi, G. and Bobbit, P., Tragic Choices (New York, Norton, 1978).Google Scholar

(15) Cahn, E., The Moral Decision (Bloomington, Indiana University Press, 1955), p. 61 ff.Google Scholar; Jakobovits, I., Jewish Medical Ethics (New York, Bloch, 1975, p. 98Google Scholar; Rosner, F., Modern Medicine and Jewish Ethics (New York, Yeshiva University Press, 1986).Google Scholar

(16) Gilbert, H. and Larson, E. B., Dealing with limited resources: The Oregon decision to curtail funding for organ transplantation, The New England Journal of Medicine, 07 21, 1988, 171–73, at p. 171Google Scholar. For a partially similar policy in Massachusetts, see Havighurst, C. M. and King, N. M., Liver transplantation in Massachusetts: Public policymaking as a morality play, Indiana Law Review, XIX (1986), 955–987.Google Scholar

(17) Democracy in America (New York, Anchor Books, 1969), pp. 651–652.Google Scholar

(18) For an extensive survey of the use of lotteries to allocate resources, see Ch. II of my Solomonic Judgements (Cambridge, Cambridge University Press, 1989).Google Scholar

(19) For details, see Hans, V. P. and Vidmar, N., Judging the Jury (New York, Plenum Press, 1986).CrossRefGoogle Scholar

(20) For details about the American draft lotteries, see Fienberg, S., Randomization and social choice, Science, CLXXI (1971), 255–261CrossRefGoogle Scholar. For the French case, see Choisel, F., Dutirage au sort au service universel, Revue historique des armées, XXXVII (1981), 43–60.Google Scholar

(21) See U.S. Department of State, Bureau of Consular Affairs, Visa Bulletin Number 19, Volume VI (1989).

(22) Simpson, A. W., Cannibalism and the Common Law (Chicago, University of Chicago Press, 1984).Google Scholar

(23) Johansen, L., Queues (and ‘rent-seeking’) as non-cooperative games, in his Collected Papers, vol. II (Amsterdam, North-Holland, 1987), pp. 827–876.Google Scholar

(24) This analogy is explored in Holt, C. A. and Sherman, R. S., Waiting-line auctions, Journal of Political Economy, XC (1982), 280–294.CrossRefGoogle Scholar

(25) Under certain (unrealistic) conditions, the inefficiency may be eliminated by ‘inverse queueing’—last in, first out; see Hassin, R., On the optimality of first come last served queues, Econometrica, LIII (1985), 201–2.CrossRefGoogle Scholar

(26) In January 1987, American newspapers reported the queueing by mail for non-restrictive immigrant visas to the United States.

(27) The following draws on Iversen, T., A simple model of waiting list generating incentives (Unpublished manuscript 1988).Google Scholar

(28) This follows from the fact that getting ill and needing treatment are events governed by a stochastic process.

(29) For a survey, see Yemin, E. (ed.), Workforce Reductions in Undertakings (Geneva, International Labour Office, 1982).Google Scholar

(30) On age as an allocative criterion, see Chs. 4 and 5 of Esposito, J. L., The Obsolete Self: Philosophical dimensions of aging (Berkeley, University of California Press, 1987).Google Scholar

(31) For a recent case study, see Oren, D. A., Joining the Club: a history of Jews and Yale (New Haven, Yale University Press, 1985).Google Scholar

(32) This statement does not refer to the hidden or even unconscious prejudices that may still operate, but to more explicit forms of discrimination.

(33) Tsuang, G. W., Assuring equal access of Asian Americans to highly selective universities, Yale Law Journal, XCVIII (1989), 659–678.CrossRefGoogle Scholar

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(35) Winslow, G., Triage and Justice (Berkeley, University of California Press, 1982), Ch. 1.Google Scholar

(36) Dequn, J., Criteria for land distribution during the second revolutionary civil war period (1927–37), Social Sciences in China (1981).Google Scholar

(37) Klitgaard, R., Choosing Elites (New York, Basic Books, 1985), pp. 61–71Google Scholar, has a good discussion of this criterion and the objections to it.

(38) Beecher, H. K., Scarce resources and medical advancement, in Freund, P. (ed.), Experimentation with Human Subjects (New York, George Braziller, 1970), pp. 66–104.Google Scholar

(39) Boyes, W. J. and Happel, S. K., Auctions as an allocation mechanism in academia: The case of faculty offices, Journal of Economic Perspectives, III (1989), 37–40.CrossRefGoogle Scholar

(40) This proposal is due to P. Van Parijs (unpublished work).

(41) Walder, A., Communist Neo-Traditionalism (Berkeley, University of California Press, 1986).Google Scholar

(42) Gennard, Great Britain, in E. Yermin (ed.), Workforce Reductions… op. cit. p. 129–30.

(43) Two studies of implicit weights are Bazerman, M., Norms of distributive justice in interest arbitration, Industrial and Labor Relations Review, XXXVIII (1985), 558–570CrossRefGoogle Scholar, and Taylor, R. et al. , Individual differences in selecting patients for regular hemodialysis, British Medical Journal, XVII (1975), 38–81Google Scholar. The former of these studies also compares the implicit weights of the various criteria with the explicit weights assigned to them by the decision-makers.

(44) Keeney, R. and Raifa, H., Decisions with Multiple Objectives (New York, Wiley, 1976), p. 78.Google Scholar

(45) Hofstee, W., The case for compromise in educational selection and grading, in Anderson, S. B. and Helmick, J. S. (eds.), On Educational Testing (San Francisco, Jossey-Bass, 1983).Google Scholar

(46) Wilms, D. C., Georgia's land lottery of 1832, The Chronicles of Oklahoma, LII (1974), 52–60.Google Scholar

(47) Brock, D., Ethical issues in recipient selection for organ transplantation, in Matthieu, D. (ed.), Organ Substitution Technology (Boulder, Westview Press, 1988), pp. 86–99, at p. 97.Google Scholar

(48) Cwartosz, Z., On queueing, Archives européennes de sociologie, XXIX (1988), 3–11.CrossRefGoogle Scholar

(49) Scarce medical resources, Columbia Law Review, LXIX (1969), p. 665.Google Scholar

(50) V. P. Hans and N. Vidmar, Judging the Jury, op. cit.

(51) Simpson, Cannibalism and the Common Law, op. cit. p. 131.

(52) de Bohigas, N., Some opinions on exemption from military service in nineteenth-century Europe, Comparative Studies in Society and History, X (1968).Google Scholar

(53) See Chalmers, J. W. III, To Raise an Army (New York, Macmillan, 1987)Google Scholar, index under ‘substitution’ and ‘commutation’.

(54) Sah, R. K., Queues, rations, and market: Comparisons of outcomes for the rich and the poor, American Economic Review, LXXVII (1987), 69–77.Google Scholar

(55) The following draws on and cites from Ch. 2 of Klitgaard, Choosing Elites, op. cit.

(56) For these claims, see Freeman, R. B. and Medoff, J. L., What do Unions do? (New York, Basic Books, 1984).Google Scholar

(57) Chalmers III, Raising an Army, op. cit..

(58) Le don du sperme, loc. cit.

(59) Childress, J. F., Some moral connections between organ procurement and organ distribution. Journal of Contemporary Health Law and Policy, III (1987), 85–110.Google Scholar

(60) Russell, P. S., Organ allocation: how can we assure equitable distribution?, Transplantation Proceedings, XX (1988), 1022–24Google Scholar; G. Opelz, Allocation of cadaver kidneys for transplantation, Ibid. 1028–32.

* The research reported in this article has been supported by a grant from the Russell Sage Foundation.