We study the problem of evaluating whether the selection from a set is close to the ordering of the set determined by an exogenously given measure. Our main result is that three axioms, two naturally capturing "dominance", and a stronger one imposing a form of symmetry in the comparison of selections, are sufficient to evaluate how close any selection from any set is to the given ordering of the set. This closeness is given by a very simple index, which is a linear function of the sum of the ranks of the selected elements. The paper ends by relating this index to the existing literature on distance between orderings, and also offers a practical application of the index.
Checchi, D., De Fraja, G., Verzillo, S. (2018). Selections from ordered sets. SOCIAL CHOICE AND WELFARE, 50(4), 677-703 [10.1007/s00355-017-1101-5].
Selections from ordered sets
De Fraja G.;
2018-01-01
Abstract
We study the problem of evaluating whether the selection from a set is close to the ordering of the set determined by an exogenously given measure. Our main result is that three axioms, two naturally capturing "dominance", and a stronger one imposing a form of symmetry in the comparison of selections, are sufficient to evaluate how close any selection from any set is to the given ordering of the set. This closeness is given by a very simple index, which is a linear function of the sum of the ranks of the selected elements. The paper ends by relating this index to the existing literature on distance between orderings, and also offers a practical application of the index.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
