On preferences and reward policies over rankings

We study the rational preferences of agents participating in a mechanism whose outcome is a ranking (i.e., a weak order) among participants. We propose a set of self-interest axioms corresponding to different ways for participants to compare rankings. These axioms vary from minimal conditions that most participants can be expected to agree on, to more demanding requirements that apply to specific scenarios. Then, we analyze the theories that can be obtained by combining the previous axioms and characterize their mutual relationships, revealing a rich hierarchical structure. After this broad investigation on preferences over rankings, we consider the case where the mechanism can distribute a fixed monetary reward to the participants in a fair way (that is, depending only on the anonymized output ranking). We show that such mechanisms can induce specific classes of preferences by suitably choosing the assigned rewards, even in the absence of tie breaking.