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Voting Systems, Honest Preferences and Pareto Optimality Author(S): Richard Zeckhauser Source: the American Political Science Review, Vol Voting Systems, Honest Preferences and Pareto Optimality Author(s): Richard Zeckhauser Source: The American Political Science Review, Vol. 67, No. 3 (Sep., 1973), pp. 934-946 Published by: American Political Science Association Stable URL: https://www.jstor.org/stable/1958635 Accessed: 27-05-2020 22:08 UTC REFERENCES Linked references are available on JSTOR for this article: https://www.jstor.org/stable/1958635?seq=1&cid=pdf-reference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms American Political Science Association is collaborating with JSTOR to digitize, preserve and extend access to The American Political Science Review This content downloaded from 206.253.207.235 on Wed, 27 May 2020 22:08:36 UTC All use subject to https://about.jstor.org/terms Voting Systems, Honest Preferences and Pareto Optimality* RICHARD ZECKHAUSER Harvard University "In a capitalist democracy there are essentially A Desirable Voting Scheme two methods by which social choices can be made: In the market, an individual indicates his pref- voting, typically used to make 'political' decisions, erences through his purchases and sales. In and the market mechanism, typically used to make general, these tracings are insufficient to define an 'economic' decisions."' To economists, the freely individual's complete preference mapping, but functioning competitive market mechanism has from the standpoint of efficiency this creates no alluring structural properties.2 If each individual difficulties. With merely the limited amounts of follows his own self-interest in making his market information fed to it, the market leads to a decisions, an efficient outcome is achieved. Pareto-optimal outcome. (It should be noted that What of the possibility of constructing a voting no individual has an incentive to disguise his mechanism that would achieve a collective politi- preferences.) cal outcome that would have desirable properties A voting system in theory could operate in the that parallel those of the competitive market out- same decentralized fashion. Each individual come? Can a voting system be impersonal and would feed in some indication of his preferences, decentralized, allow each individual to act on his and the processing mechanism would employ this own behalf, and guarantee that a Pareto-optimal information to yield an outcome. To see whether outcome will be achieved? such a procedure should be established as an * Kenneth Arrow, Robert Klitgaard, Pamela Memi- ideal, we must determine how it can perform along shian, Howard Raiffa, Thomas Schelling, Michael a number of significant dimensions. Spence, Milton Weinstein, and a referee for the Ameri- can Political Science Review provided me with helpful Major Characteristics of Social comments. This research was supported by NSF grants GS-28626x and Gr-58. Decision Procedures I Kenneth Arrow, Social Choice and Individual Values The flow diagram below provides the context (New York: John Wiley and Sons, Inc., 1964), p. 1. for the major topics discussed in this paper. (At a 2 It is with some discomfort that I leave aside the problem of distribution in this paper. The issue is at- later juncture, it will serve to summarize its princi- tacked directly in a later effort, "Risk Spreading and pal results.) These topics are indexed A through F. Distribution," Kennedy School of Government, Discus- Social decision problems are first classed as sion Paper No. 10 (August, 1972). There I argue that a economic or political. Economic decisions are profound belief in the efficacy of the outcome of a per- fect market gives one insights into distributional ques- handled by the market mechanism. Under the ap- tions. One can consider the problem of drawing the propriate competitive conditions, the market out- social contract equivalent to that of a group of future come will meet some preassigned standards of ac- citizens starting in some initial position of equal poten- ceptability. The principal standard to be met is tial (they face the same lottery on future possibilities). efficiency. The measuring rod for this standard is They draw up a contingent claims agreement, the mag- nitudes of payment to depend on their future fortune in Pareto optimality. securing endowments of goods and capabilities (that is There are myriad situations in which the very the states of the world). In retrospect, we may decide restrictive competitive assumptions are not met. that it is our duty to redistribute in the manner that For these situations, much the subject of current would be prescribed by the hypothetical agreement that antedated our present position. For a philosophically economics debate, the unhindered play of the compatible, but perhaps policy inconsistent view, see market will not lead to an attractive outcome. John Rawls, The Theory of Justice (Cambridge, Mass., Perhaps the establishment of new areas of prop- Harvard University Press, 1971). erty rights, or innovative additions to present 'Thomas Schelling has commented at great length, interpreting and questioning the significance of Pareto market mechanisms will set things right. What- optimality as a criterion for social choices. He states, ever, this is not material to the present discussion. 'the significance of failure to achieve Pareto-optimality These situations would be of import for this merely means that the situation is improvable . it is paper if they were treated as political decisions. the degree of improvability that determines how impor- They then would be carried down the lower tant the nonoptimality is. Pareto optimality is not like virginity or justice. Small departures are of small branch of the flow diagram, where they could interest, large departures are of large interest." Personal serve as further exemplars for the analysis of that communication, July 12, 1972. branch. Economists have long recognized that Pareto optimal- ity by itself is a hopelessly incomplete guide to norma- Political Decisions and the tive and descriptive considerations of social choice. An Individualist Approach indication of this author's response is given by the con- clusion to this paper. In evaluating outcomes in the economic arena, 934 This content downloaded from 206.253.207.235 on Wed, 27 May 2020 22:08:36 UTC All use subject to https://about.jstor.org/terms 1973 Voting Systems, Honest Preferences and Pareto Optimality 935 Market decentralized, ordinal, unique, _ ___ X U mechanism |[ . / ~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~ ~~~~~~~~Dictatorial |Inefficient Democratic ] Cr\ r D~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~effcet Context and Summary Diagram we rely on consumer sovereignty. Each individual success. Yet Kenneth Arrow, in a much celebrated is entitled to judge what is best for himself, work, and has demonstrated that there is no general these individual judgments form the basis for procedure as- to pass from individuals' preferences sessments of social welfare. This paper carries to social orderings that meets certain standards of over this individualist ethic to the evaluation of attractiveness.4 The power of the Arrow result de- all social choices, including those that are con- rives from the fact that the standards he imposed ventionally considered to be of a political nature. were both innocuous in appearance and intui- Thus individuals' preferences form the basis for tively appealing. the social decisions considered here. In social de- Arrow sets forth four standards. In unrigorous cisions more than one individual is involved. language, they are: (1) The procedure must in- Together, social decision and consumer sover- clude all logically possible combinations of indi- eignty exclude from consideration any form of viduals' orderings. (2) It must lead to Pareto- paternalistic rule. optimal outcomes. (3) The choice between any two The ground rules then are set. We are searching alternatives cannot be influenced by the presence for a procedure that enables us to proceed from or nonpresence of a third alternative. (4) No indi- information on individuals' preferences to a social vidual can always secure his choice regardless of outcome that meets some conditions of accept- the preferences of others. A later expositor has ability. The ultimate objective is to discover a de- provided a mnemonic for these properties:' un- centralized procedure, one which consciously or restricted domain, U; Pareto principle, P; inde- automatically takes the (perhaps incomplete) in- pendence of irrelevant alternatives, I; nondictator- formation provided by individuals' ballots and ship, D. Dealing with the simplest case of interest yields an acceptable social outcome. (at least two individuals and at least three alterna- tives), the famous Arrow result is that there is no Centralized Decision Procedures social welfare function that satisfies U, P, I, and D. For purposes of comparison, I shall begin with Let us stop for a moment to get our bearings a look at the success or nonsuccess of centralized in the flow chart. We should like all of our social procedures. With centralized decision, a single de- decisions to apply over an unrestricted domain. cision authority with accurate knowledge of in- Condition U is imposed at all nodes in the flow dividuals' preferences selects an outcome. diagram and throughout this paper. Next observe Centralized Decision, Ordinal Preferences (A) 4 For the conditions, see K. Arrow, Social Choice, pp. 22-33. At first glance it would seem that centralized 5Amartya K. Sen, Collective Choice and Social Wel- decision procedures hold out promise of great fare (Holden-Day, Inc., San Francisco), pp. 41-42. This content downloaded from 206.253.207.235 on Wed, 27 May 2020 22:08:36 UTC All use subject to https://about.jstor.org/terms 936 The American Political Science Review Vol.
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