Mediation in claims problems

Mediation is a dispute resolution process whereby agents reach a mutually acceptable agreement among different proposals that satisfy a set of principles. This paper provides a natural way of coming to such agreements in claims problems. In our approach, mediation combines (i) a set of fair properties (legitimate principles); and (ii) a criterion for delimiting the admissible manners of distributing the endowment, that is determined by the mediator expressing the two (dual) points of view to face such problems: awards and losses. These dual views define a lower and an upper bounds on awards, which are used to implement the so-called Double Recursive Process. We find that this process concludes at the midpoint between the two dual points of view. Finally, we argue that the criterion of the mediator could be established throughout Lorenz domination. In so doing, we retrieve the average of old and well-known rules.