The Simpler, the Better: A New Challenge for Fair-Division Theory

The Simpler, the Better: A New Challenge for Fair-Division Theory Nicolas Dupuis-Roy (nicolas@dupuis.ca) Universite de Montreal, Department de Psychologie, C.P. 6128, succ. Centre-ville, H3C 3J7, Montreal, QC, Canada Frederic Gosselin (frederic.gosselin@umontreal.ca) Universite de Montreal, Department de Psychologie, C.P. 6128, succ. Centre-ville, H3C 3J7, Montreal, QC, Canada Abstract According to John Rawls, there exists a perfect procedural justice for which there is no conflict between process and outcome. One such procedure is the Divide and Choose. Recently, the mathematical theory of fair-division extended this idea by developing procedures that offer fairer outcomes and a better guarantee of justice. Here, we tested the extent to which the distributive and procedural properties of these perfect and improved division procedures were perceived as more satisfactory and fairer than imperfect division procedures. Thirty-nine pairs of participants divided six $10 gift certificates between them using seven division procedures. They rated their satisfaction and their perceived fairness before and after they executed each division procedure. Contrarily to our hypothesis, the results show that perfect procedural justice does not really translate into the perception of a fairer and more satisfactory outcome and process. The most sophisticated division procedures failed to select fair and satisfactory solutions. Keywords: Fair-division theory, fair-division procedures, satisfaction, perceived fairness, procedural and distributive justice, John Rawls. Introduction Social psychological studies on justice distinguish between the perception of the outcome and the perception of the process that leads to the outcome (Lind & Tyler, 1988). The former concerns issues of distributive justice such as the criteria under which an outcome is considered fair or unfair (e.g., equitability or envy-freeness), whereas the latter relates to issues of procedural justice such as voicing—to express oneself in the process of justice. Perception of distributive and procedural justice does not always coincide: for instance, a procedure seen as fair can lead to undeserved outcomes (e.g., an innocent individual found guilty by a court of justice) and conversely, an outcome perceived as fair can result from an unjust procedure (e.g., a monarch applying a just sentence). According to Rawls (1971), there exists a perfect procedural justice for which there is no conflict between process and outcome. This idea is based on an age-old fair- division procedure termed Divide and Choose. A first player divides a ‘cake’ (or any divisible object) in what she considers to be two equal pieces, and a second player chooses the piece she sees as the largest. This procedure exemplifies perfect procedural justice because it has an independent criterion for what constitutes a fair outcome and a process that guarantees that such an outcome will be reached. More specifically, the solution derived from Divide and Choose is envy-free since both players will have no incentive to exchange their share with the other player’s share. Also, its process always leads to such solution given that the players comply with the rules and adhere to specific mathematical assumptions. Nonetheless, Divide and Choose has weaknesses. First, it only applies to conflicts that involve two parties and a divisible good (e.g., money). Second, it is vulnerable to strategic manipulation (Crawford & Heller, 1979). Third, it does not guarantee that the divider will cut the cake in the most efficient way. A division is efficient if no other division can make one participant better off without hurting another. The mathematical theory of fair-division extended Rawls’ idea of a perfect procedural justice mainly by focusing on solutions that are fair and efficient, and by strengthening the guarantee of fairness with game-theoretic tools. In the context of game theory, a procedure’s fair and efficient solution is said to be guaranteed when the strategy it prescribes (e.g., “cut the cake in what you consider two equal pieces”) is optimal for rational and self-regarding players. Following these improvements, mathematicians have recently designed dozens of fair-division procedures presenting sophisticated mechanisms (for a review, see Barbanel, 2004; Brams, 2008; Brams & Taylor, 1996a; Moulin, 2003; Robertson & Webb, 1998; Young, 1994). One of such algorithms, called the Adjusted Winner (Brams & Taylor, 1996a), has recently been patented in the United