Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems

We analyze the problem of extending a given bilateral principle of justice to a consistent n-creditor bankruptcy rule. Based on the bilateral principle, we build a family of binary relations on the set of creditors in order to make bilateral comparisons between them. We find that the possibility of extending a specific bilateral principle of justice in a consistent way is closely related to the quasi-transitivity of the binary relations mentioned above.