The Limitations of Fair Division

Abstract

Mathematical procedures that promise an envy-free, equitable, and efficient solution to distributional conflicts have received widespread attention. Two fair-division mechanisms, adjusted Knaster and proportional Knaster, which are similar to the well-known adjusted-winner procedure, are compared with the less fair divide-and-choose mechanism. Results show that participants largely prefer the adjusted-Knaster procedure to the two alternatives. Adjusted Knaster, closely followed by proportional Knaster, also promises the highest average payoff. Yet the sophisticated mechanisms cease to perform better than divide-and-choose once actors receive the possibility to deviate from the mandatory bargaining protocols of fair-division procedures. The preference for adjusted and proportional Knaster is found to be a partial function of the participants'psychological profile. The more "antisocial" a participant, the more likely this respondent is to opt for a procedure with a compensatory mechanism.When negotiating over Belfort after the Franco-German War, Chancellor Bismarck experienced an outburst from Foreign Minister Thiers. Reminding his counterpart that the disputed town never belonged to Germany, the French diplomat shouted, You admit with your behavior that you have settled on a course of total destruction. Lead it! Demolish our provinces, burn our houses, strangle our innocent people! With one word: Finish your work. We will fight until the last breath. We will lose, but we will at least not be dishonored. (Quoted in Uthmann 1985, 178, authors' translation)

Fair cake-cutting algorithms with real land-value data

“…The experimenters then compare different division procedures according to various criteria, such as: perceived fairness, economic efficiency, etc. [23,46]. Other experiments test what desiderata are more important to the subjects when there is a conflict, e.g.…”

Fair Cake-Cutting in Practice

“…In particular, do users prefer the allocations generated by sophisticated and provably-fair procedures, to the allocations generated by simple and intuitive procedures? Schneider and Krämer (2004) compare the simple divide-and-choose procedure to the more sophisticated Adjusted-Knaster and Proportional-Knaster procedures, for allocating indivisible goods with monetary compensation. They find that, if the participants truthfully adhere to the protocol, then the sophisticated mechanisms perform better than divide-and-choose in terms of efficiency and fairness.…”

A simple mechanism for resolving conflict

“…The experimental literature on fair division (see for instance Daniel and Parco (2005) or Schneider and Kramer (2004)) has already shown that agents may not always reveal their information truthfully. The absence of a theoretical framework means thay cannot interpret these deviations from truthful behaviour.…”

“…those that value their most preferred issue 350 or 400). 25 We also want to analyse the behaviour of subjects that value both issues equally and hence are indifferent between possible strategies. The way they play is relevant to our welfare analysis: only when they split their votes do they allow our simple mechanism to reach the ex-ante optimal incentive compatible allocation (i.e.…”