An algorithmic rule to solve the extended Ibn Ezra – Rabad problem: recursive constrained unanimity
de Mesnard, Louis
An algorithmic rule to solve the extended Ibn Ezra – Rabad problem: recursive constrained unanimity - 2023.
67
We examine the rule of Ibn Ezra – Rabad historically used to solve the “Rights Arbitration” problem when the greatest claim is equal to the endowment. For the extended Ibn Ezra problem, i.e., when the greatest claim is less than the endowment, we propose a typology of the rules used to solve the problem according to their recursive nature: (i) non-recursive rules: Constrained Equal Awards and Constrained Equal Losses; (ii) semi-recursive rules: Unanimity on the Claim Gap, Dictatorship on the Claim Gap; (iii) the rules that combine non-recursive rules and semi-recursive rules: Minimal Overlap rule and Residual Minimal Overlap rule; (iv) recursive rules: until now the category has been empty; and (v) recursive-iterative rules: Generalized Ibn Ezra Value. We then propose a recursive rule, Recursive Constrained Unanimity. Like the Generalized Ibn Ezra Value, it extends the rule of Ibn Ezra – Rabad and fulfills the axioms of efficiency as well as claim boundedness. But unlike the Generalized Ibn Ezra Value, it does not have convergence issues whenever the value of the estate is close to the total of the claims.
An algorithmic rule to solve the extended Ibn Ezra – Rabad problem: recursive constrained unanimity - 2023.
67
We examine the rule of Ibn Ezra – Rabad historically used to solve the “Rights Arbitration” problem when the greatest claim is equal to the endowment. For the extended Ibn Ezra problem, i.e., when the greatest claim is less than the endowment, we propose a typology of the rules used to solve the problem according to their recursive nature: (i) non-recursive rules: Constrained Equal Awards and Constrained Equal Losses; (ii) semi-recursive rules: Unanimity on the Claim Gap, Dictatorship on the Claim Gap; (iii) the rules that combine non-recursive rules and semi-recursive rules: Minimal Overlap rule and Residual Minimal Overlap rule; (iv) recursive rules: until now the category has been empty; and (v) recursive-iterative rules: Generalized Ibn Ezra Value. We then propose a recursive rule, Recursive Constrained Unanimity. Like the Generalized Ibn Ezra Value, it extends the rule of Ibn Ezra – Rabad and fulfills the axioms of efficiency as well as claim boundedness. But unlike the Generalized Ibn Ezra Value, it does not have convergence issues whenever the value of the estate is close to the total of the claims.
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