Abstract

Robustness against strategic manipulation is a crucial topic in social choice theory. Under some social ranking solutions (SRSs), namely mappings that yield candidates’ ranking from their coalitions’ ranking, candidates can sometimes improve their own social ranking by strategically degrading the coalitions to which they belong (e.g., sabotaging the coalitions to which the candidates and their competitors both belong could damage their competitors’ social rankings). This study investigates SRSs that can prevent such sabotage and promote sincere cooperation between candidates. To this end, we introduce two axioms of SRSs by modifying the non-manipulability (NM) in the literature. An SRS is sabotage-proof (SP) if no candidate can improve their social ranking against anyone else through sabotage, and it is strongly sabotage-proof (SSP) if it is SP and is endowed with a sanction system against specific sabotage. We first demonstrate that the ceteris paribus majority (when there are at least four candidates) and lexicographic excellence solutions are SP but not SSP. We then propose a new characterization of dual lexicographic excellence solution as the unique linear SRS satisfying SSP and coalitional anonymity. Our axiomatic study provides a theoretical ground that lexicographic evaluation of coalitional performances is highly robust against strategic sabotage.