Networks of Rights in Conflict: A Talmudic Example

Many disputes involve conflicts of rights. A common view is that rights cannot really be in conflict so one of those being claimed must be a mistake. This idea leads to extreme outcomes that cut some parties out. Many studies have investigated how to choose a compromise among rights but they have focus on situations where the incompatibility comes from the degrees of the claims, as when, for example, a deceased person promised his heirs more than his total estate. I analyze a Talmudic problem where the difficulty is the pattern of the rights - each one trumps another in a cycle. The theory of non-transferable utility coalitional games suggests two solutions, one based on Shapley's and Maschler-Owen's values, which are equivalent for the problem, and the other on Harsanyi's and Kalai-Samet's, also equivalent. Each satisfies four out of five desirable properties, better than several other solutions. The NTU games are appropriate not just for power-based negotiation but for disputes over justice, fairness and rights. It is hoped that this analysis will form part of a general understanding of rights conflicts.