Skip to main content icon/video/no-internet

Social choice theory studies the differences between individual and group (or social) decision making and the implications of these differences for the structure and outputs of institutions. Social choice begins with the insight that while it is reasonable to assume as a condition of rationality that individuals hold transitive preference orderings (A preferred to B preferred to C implies that A is preferred to C), this assumption cannot be extended to groups of three or more when they are selecting among three or more options. Three people, each holding the following transitive preference orderings (P1: ABC; P2: BCA; P3: CAB), will reveal a collective intransitivity, or cycle, if they vote sincerely in the three possible direct binary comparisons. Thus, while P1 and P3 prefer A to B, and P1 and P2 prefer B to C (implying A preferred to C, had an individual held these preferences), P2 and P3 instead prefer C to A, thus presenting a cycle.

One implication of collective intransitivity is that if participants vote sincerely based on individual preferences, and if the number of votes is fewer than the number of options, the order in which choices are presented will control the outcome. In the prior example, but for the final vote (C versus A), which revealed the cycle, the series of two votes produced C. The sequence C versus A followed by C (the winner) versus B would instead produce B; and the sequence B versus C followed by B (the winner) versus A would instead produce A. Thus, if the members vote sincerely in accordance with their ordinal preferences when presented with binary comparisons (thus adhering to independence of irrelevant alternatives or independence), an agenda setter can produce any result given two paired votes over three options.

Arrow's Impossibility Theorem

In a famous essay for which he received the Nobel Prize in Economics, Kenneth Arrow demonstrated the impossibility of developing rules for a decisionmaking body that would simultaneously guarantee transitive group outputs, meaning that the rules would prevent cycling, and ensure adherence to a set of norms that he considered fundamental to fair or democratic decision making. The fairness factors include independence (demanding sincere voting in direct binary comparisons), nondictatorship (not vindicating the preferences of one member against the contrary preferences of the group as a whole), unanimity (the Pareto criterion), and range (requiring that the outcome be consistent with the unrestricted ranking by all members of the three available options in any order). Arrow's Theorem ultimately establishes that the price for guaranteeing noncyclical outcomes is to violate at least one of Arrow's fairness norms.

Legislatures versus Appellate Courts

Several economists and legal scholars have suggested that because legislatures are collective decisionmaking bodies, Arrow's Impossibility Theorem demonstrates their incompetence or irrationality and thus justifies shifting substantial control over legal policy to appellate courts, and in particular the U.S. Supreme Court. Of course, appellate courts are also collective decision-making bodies, and this insight has led some scholars to claim that Arrow's Theorem leaves legal policy makers nowhere to turn. Because a critical feature of judicial decision-making rules involves when to leave the resolution of questions of public policy to the political branches, it is important to evaluate such claims. A rigorous appreciation of the implications of social choice reveals the limits of these broad claims by demonstrating important synergies between legislatures and courts that together improve their overall rationality and fairness.

...

  • Loading...
locked icon

Sign in to access this content

Get a 30 day FREE TRIAL

  • Watch videos from a variety of sources bringing classroom topics to life
  • Read modern, diverse business cases
  • Explore hundreds of books and reference titles

Sage Recommends

We found other relevant content for you on other Sage platforms.

Loading