Deviation from proportionality and Lorenz-domination for claims problems

Mirás Calvo, Miguel Ángel; Núñez Lugilde, Iago; Quinteiro Sandomingo, Maria Del Carmen; Sánchez Rodríguez, María Estela

doi:10.1007/s10058-022-00300-y

Mirás Calvo, Miguel Ángel

; Núñez Lugilde, Iago

; Quinteiro Sandomingo, Maria Del Carmen

; Sánchez Rodríguez, María Estela

DATE: 2023-06

UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/4810

EDITED VERSION: https://link.springer.com/10.1007/s10058-022-00300-y

UNESCO SUBJECT: 5399 Otras Especialidades económicas

DOCUMENT TYPE: article

ABSTRACT

The Lorenz order is commonly used to compare rules for claims problems. In this paper, we incorporate the average of awards rule, the mean value of the set of awards vectors for a claims problem, to the ranking of the standard rules by proving some properties that are satisfied by this rule. We define a pair of coefficients, inspired by the Gini index, aimed at measuring, for any given claims problem, the discrepancy between the awards assigned by a rule and the proportional division. We generalize the proportionality deviation indices by introducing coefficients that measure the deviation between the awards selected by any two division rules. We show how these deviation indices are related to the Lorenz order.

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