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)
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