Semivalues: weighting coefficients and allocations on unanimity games

This is a post-peer-review, pre-copyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590-017-1224-8.Each semivalue, as a solution concept defined on cooperative games with a finite set of players, is univocally determined by weighting coefficients that apply to players’ marginal contributions. Taking into account that a semivalue induces semivalues on lower cardinalities, we prove that its weighting coefficients can be reconstructed from the last weighting coefficients of its induced semivalues. Moreover, we provide the conditions of a sequence of numbers in order to be the family of the last coefficients of any induced semivalues. As a consequence of this fact, we give two characterizations of each semivalue defined on cooperative games with a finite set of players: one, among all semivalues; another, among all solution concepts on cooperative games.Peer ReviewedPostprint (author's final draft

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The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and conjectures.Comment: 10 page

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S'introdueixen vuit índexs de poder que admeten una interpretació probabilística per les normes de votació amb abstenció o amb tres nivells d'aprovació en l'entrada. S'analitzen les semblances i diferències entre els índexs estàndards coneguts pels jocs simples i per les extensions per aquest context més general. Es conclou la feina proporcionant procediments basats en la generació de funcions per jocs(3,2) extensibles a jocs (j,k).Preprin

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Bayesian Regression Markets

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