On the Convergence of the Generalized Ibn Ezra Value

Ibn Ezra (Sefar ha-Mispar (The Book of the Number, in Hebrew), Verona (German trans: Silberberg M. (1895)). Kauffmann, Frankfurt am Main,1146), Rabinovitch (Probability and statistical inference in medieval Jewish literature. University of Toronto Press, Toronto,1973) and O'Neill (Math Soc Sci 2(4):345–371,1982)proposed a method for solving the "rights arbitration problem" (one of the historical problems of "bankruptcy") for n claimants when the estate E is equal to the largest claim. However, when the greatest claim is for less than the estate, the question of what to do with the difference between E and the largest claim is posed. Alcalde et al.'s (Econ Theory 26(1):103–114,2005) Generalized Ibn Ezra Value (GiEV), solves the problem in T iterations, of n steps. By using Monte-Carlo experiments, we show that: (i) T grows linearly with the number of claimants, which makes GiEV rapidly impracticable for real applications. (ii) The more E is close to the total claim d, themore T grows: T linearly grows when E exponentially approaches d by a factor 10. Moreover, we proved through theory that GiEV fails to provide a solution in a finite number of iterations for the trivial case E = d, whereas it should obviously find a solution in one iteration. So, even if GiEV is convergent, the sum of claims d appears as an asymptote: the number of iterations tends to infinite when the estate E approaches the claims total d. We conclude that GiEV is inefficient and usable only when: (1) the number of claimants is low, and (2) the estate E is largely lower than the total claims d.