Nicolas Houy

Lexicographic Compositions of Multiple Criteria for Decision Making

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second binary relation, and iterates the procedure until the Mth binary relation. We show several distinct sets of conditions for the choice functions representing these two procedures to satisfy non-emptiness and choice-consistency conditions such as contraction consistency and path independence. We also examine the relationships between the outcomes of the two procedures. Finally we investigate under what conditions the outcomes of each procedure are independent of the order of lexicographic application of the criteria.

Still more on the Tournament Equilibrium Set

Schwartz (Soc Choice Welfare 3:271–291, 1990) proposed a solution concept (the Tournament Equilibrium Set) for choosing from a tournament and stated some conjectures about this solution. Laffond et al. (Math Sci Hum 123:37–44, 1993) introduced further conjectures and showed the links between some of them. In this short note, we show that one of the conjectures stated by Schwartz (1990) is false. We also complete a result given in Laffond et al. (1993).

A characterization for qualified majority voting rules

Abstract We give an axiomatization for Qualified Majority Voting Rules where one of the alternative is socially chosen if it obtains the support of 100xa0·xa0 q % of the non-abstaining voters for some q xa0∈xa0]0, 1[. These voting rules do not satisfy Neutrality in general. Instead, we introduce the axiom of Coalition Permanency.

A characterization of prudent choices

We define and axiomatize prudent choices for two criteria. Given two criteria, the alternatives chosen by the prudent choice procedure are the ones maximizing some composition of the criteria. This composition is such that (1) it contains the first criterion and a part of the second one, and (2) the new binary relation is not cyclic and cannot be enlarged with preferences of the second criterion without becoming cyclic. We also make the link between prudent choices, classical rational choices, sequentially rational choices (Manzini and Mariotti in Am Econ Rev 97(5):1824–1839, 2007a) and lexicographic binary choice rational choices (Tadenuma in J Econ Theory 104(2):462–472, 2002).

A refinement of prudent choices

We charaterize the choice correspondences that can be rationalized by a procedure that is a refinement of the prudent choices exposed in [Houy, 2008]. Our characterization is made by means of the usual expansion axiom and by a weakening of the usual contraction axiom α.

Structural holes in social networks: A remark

In a recent article, [S. Goyal, F. Vega-Redondo, Structural holes in social networks, J. Econ. Theory 137 (1) (2007) 460-492] the authors (GVR) showed the importance of stars and cycles in a given network formation game. Implicitly, in their article, a network is called an equilibrium if it is generated by an equilibrium strategy. We extend the results of GVR to the case of a stronger requirement: namely, that a network can be called an equilibrium only if all the strategies generating it are equilibria. We also show, in a dynamic framework, that both definitions differ in crucial ways.

A note on the Suzumura-consistency

Abstract In Suzumura [Suzumura K., 1976. Remarks on the theory of collective choice. Economica 43, 381–90], it is proved that a binary relation has an ordering extension if and only if it is Suzumura-consistent. We show necessary and sufficient conditions for a binary relation to have ordering extensions rationalizing a unique set of alternatives and further, for this set of alternatives to be a singleton.