The two-agent claims-truncated proportional rule has no consistent extension: A constructive proof

For resolving claims problems, we consider the rule that makes awards proportional to claims truncated at the endowment. Using a technique developed by Thomson [Thomson, W., On the existence of consistent rules to adjudicate conflicting claims: a geometric approach, mimeo, 2001.], we show that the two-claimant rule so defined has no consistent extension [Dagan, N. and O. Volij, Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems, International Journal of Game Theory 26 (1997), 11–25.].