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The Misguided Renaissance of Social Choice

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The Misguided Renaissance of Social Choice The Misguided Renaissance of Social Choice Maxwell L. Stearns' CONTENTS I. INTRODUCTION ........................................... 1221 A. The Intellectual History of Social Choice ...................... 1221 B. Social-Choice-BasedNormative Proposals ..................... 1225 C. The Nirvana, Isolation, and Composition Fallacies ............... 1229 II. MARKETS, LEGISLATURES, AND THE EMPTY CORE ................... 1233 A. The Case of the Polluting Firms ............................ 1234 B. Location of Toxic-Waste Disposal Facility ..................... 1240 FIGURE 1. Proposed Locations of Toxic Waste Dump .......... 1241 C. Alice, Bob, and Carole as Siblings .......................... 1246 Il. DEFINING THE "IDEAL" NORM ................................. 1247 A. The Arrow's Theorem Criteria ............................. 1247 B. The Condorcet-Winner Criterion ............................ 1252 IV. THE SUPREME COURT AND CONGRESS THROUGH AN ARROVIAN LENS ..... 1257 A. Range .............................................. 1258 B. Universal Domain ..................................... 1271 C. Unanimity and Independence of Irrelevant Alternatives ............ 1276 D. Nondictatorship ....................................... 1281 E. Rationality ........................................... 1283 F. Summary ............................................ 1285 TABLE 1. The Supreme Court and Congress Through an Arrovian Lens ................................ 1286 t Assistant Professor of Law, George Mason University School of Law. B.A. 1983, University of Pennsylvania; J.D. 1987, University of Virginia School of Law. I would like to thank the following for their helpful comments and suggestions: Lawrence Baxter, Lloyd Cohen, Harold Demsetz, Einer Elhauge, Hehry Hansmann, Bruce Kobayashi, Bill Kovacic, Aaron Krauss, Saul Levmore, Nelson Lund, Henry Manne, Richard McAdams, Timothy Muris, Jeffrey Parker, Larry Ribstein, Glen 0. Robinson, Linda Schwartzstein, David Skeel, and Gordon Tullock. I would also like to thank the participants in the GMUSL brown bag lunch series for their helpful comments, the GMUSL library staff for their assistance in tracking down hard-to-find source materials, Wendy Payton for her assistance in creating the tables that appear in the text, and Melissa Austin for her research assistance. Finally, I wish to acknowledge the generous research funding provided by the John M. Olin and Sarah Scaife Foundations. 1219 1220 The Yale Law Journal [Vol. 103: 1219 V. COLLECTIVE DECISIONMAKERS THROUGH A WIDE-ANGLE ARRovLAN LENS . 1287 A. Markets ............................................. 1287 B. Legislatures and Appellate Courts .......................... 1288 C. Agencies ............................................ 1289 D. Summary ............................................ 1290 TABLE 2. Collective DecisionmakersThrough a Wide-Angle Arrovian Lens ........................ 1290 VI. CONCLUSION ............................................. 1291 VII. APPENDIX ............................................... 1291 A. Arrow's Theorem Proof .................................. 1291 B. Arrow's Theorem Explanation ............................. 1292 1994] Social Choice 1221 I. INTRODUCTION A. The Intellectual History of Social Choice In a world in which relatively few people were formally educated and fewer still could honestly describe themselves as intellectuals, it is perhaps not surprising that both Thomas Jefferson and James Madison were familiar with the noted French philosopher and mathematician,' the Marquis de Condorcet.2 As Minister to France, Jefferson personally knew Condorcet.3 Jefferson owned several of Condorcet's works, including the famous Essai sur l'applicationde l'analyse atla probbbilitgdes dicisions rendues i la pluralitgdes voix written in 1785.4 The Essai describes what has become known as the "Condorcet Paradox,"5 the seminal insight underlying what Condorcet described as "social 6 mathematics" and what is presently known as social choice theory. The paradox is fairly straightforward. Consider the plight of three law firm associates, Alice, Bob, and Carole, who need to decide which flavor to order for an ice cream cake that they intend to serve at a party honoring their departing colleague Diane. Three flavors are available: coffee, chocolate, and 1. H.P. Young, Condorcet's Theory of Voting, 82 AM. POL.SCi. REV. 1231 (describing Condorcet as a "mathematician and social philosopher"); DUNCAN BLACK, THE THEORY OF COMMrrIEES AND ELECTION 159 (1963) (describing Condorcet as a "mathematician, philosopher, economist and social scientist"). Describing the Marquis de Condorcet as a philosopher and mathematician is a bit misleading. In the late 18th century, spheres of knowledge were not delineated with the precision that they are today. Instead, intellectuals of the day, including the three men identified in the text, were well versed across a wide variety of what we today call mathematics, philosophy, history, law, architecture, and the natural sciences. 2. See lain McLean & Arnold B. Urken, Did Jefferson or Madison Understand Condorcet's Theory of Social Choice?, 73 PUB. CHOICE 445, 445, 453 (1992). 3. See 8-12 THE PAPERS OF THOMAS JEFFERSON (Julian P. Boyd ed., 1950); Arnold B. Urken, The Condorcet-Jefferson Connection and the Origins of Social Choice Theory, 72 PUB. CHOICE 213, 215, 218 (1991). 4. McLean & Urken, supra note 2, at 447 ("Jefferson owned a copy of Condorcet's 1785 Essai and several of Condorcet's other works in social choice."); Urken, supra note 3, at 215, 218. 5. McLean & Urken, supra note 2, at 446 ("Condorcet's standing as the principal founder of social choice rests largely, but not entirely, on his Essai sur l'application de l'analyse a la probabilitJ des decisions rendues a la pluralitj des voix of 1785 ....This work investigates the logical relationship between voting procedures and collective outcomes."). 6. The name social choice theory is derived from the title of Kenneth Arrow's famous book, Social Choice and Individual Values, for which, along with other works, he was awarded a Nobel Prize in 1972. See Noiman Macrae, Towards Smaller Government, ECONOMIST, Dec. 23, 1978, at 48 ("Professor Kenneth Arrow won a Nobel Prize in economics by trying to discover a 'social welfare function,' designed to be useful in guiding the planning authority for a society-and then discovering to his surprise and chagrin that it is logically impossible for any such function to exist."); KENNETH J. ARROW, SOCIAL CHOICE AND INDIVIDUAL VALUES (1951). Arrow initially set out to determine a method of aggregating collective welfare and instead proved mathematically that the Condorcet Paradox was an intractable problem in collective decisionmaking. See DENNIS C. MUELLER, PUBLIC CHOICE H12-3 (1989). The Marquis de Condorcet was not the first to identify the voting paradox that bears his name. Some fifteen years earlier, Jean Charles de Borda read a paper to the French Academy of Sciences demonstrating the paradox and proposing a different solution from that which Condoret offered in his 1785 Essai. See Young, supra note 1, at 1236-39 (describing and evaluating Borda method); BLACK, supra note 1, at 178- 80 (describing relationship between the theories of Condorcet and Borda). See infra note 124 for a description of the Borda method. 1222 The Yale Law Journal [Vol. 103: 1219 vanilla. Assume further that each announces his or her preferences in advance. Alice ranks her preferences "coffee, chocolate, vanilla;" Bob ranks his "chocolate, vanilla, coffee;" and Carole ranks hers "vanilla, coffee, chocolate." Bob suggests that they put the choice of flavor to a series of votes, two flavors at a time. Carole, amused by the suggestion, remains silent. In the first vote, vanilla versus coffee, vanilla prevails two to one, with Alice losing to Bob and Carole. In the second vote, vanilla versus chocolate, chocolate prevails two to one, with Carole losing to Alice and Bob. Carole explains that she truly dislikes chocolate and asks for one final vote, this time chocolate versus coffee. Alice and Bob, a bit surprised at the suggestion of their colleague, whom they had always considered to be quite bright, explain that the final vote is obviously unnecessary; given that chocolate prevailed over vanilla and that vanilla prevailed over coffee, chocolate would obviously prevail over coffee. Carole, who double majored in French and intellectual history before going to law school, asks her friends to indulge her. Much to the surprise of Alice and Bob, in a final pairwise vote between chocolate and coffee, coffee prevails, with Bob losing to Alice and Carole. Carole then explains that if everyone voted sincerely in accordance with his or her preannounced set of preferences, there was no rational means of choosing a flavor through pairwise voting.7 This fundamental insight, that absent clear majority support for one of three or more options presented to a collective decisionmaking body there may be no rational means of aggregating individual preferences, contributed to what Condorcet hoped would become a social science, founded upon the laws of probability, no less rigorous than the natural sciences.8 While Madison did not know Condorcet personally, he received copies of the Essai from at least two independent sources, Thomas Jefferson and Philip Mazzei.9 In addition, in a 7. As shown in infra notes 223-24 and accompanying text, there may be other rational ways for Alice, Bob, and Carole to choose a flavor, including strategic voting and logrolling.
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