Preference learning is an essential component in numerous applications, such as recommendation systems, decision-making processes, and personalized services. We propose here a novel approach to preference learning that interleaves Gaussian Processes (GP) and Robust Ordinal Regression (ROR). A Gaussian process gives a probability distribution on the latent function values that generate users’ preferences. Our method extends the traditional non-parametric Gaussian process framework by approximating the latent function by a very flexible parameterized function, that we call θ-additive function, where θ is the parameter set. The set θ reflects the degree of sophistication of the generalized additive model that can potentially represent the user’s preferences. To learn what are the components of θ, we update a probability distribution on the space of all possible sets θ, depending on the ability of the parameterized function to approximate the latent function. We predict pairwise preferences by using the parameter set θ that maximizes the posterior distribution and by performing robust ordinal regression based on this parameter set. Experimental results on synthetic data demonstrate the effectiveness and robustness of our proposed methodology.

In a coalitional game, the coalitions are weakly ordered according to their worths in the game. When moreover a power index is given, the players are ranked according to the real numbers they are assigned by the power index. If any game inducing the same ordering of the coalitions generates the same ranking of the players then, by definition, the game is (ordinally) stable for the power index, which in turn is ordinally invariant for the game. If one is interested in ranking players of a game which is stable, re-computing the power indices when the coalitional worths slightly fluctuate or are uncertain becomes useless. Bivalued games are easy examples of games stable for any power index which is linear. Among general games, we characterize those that are stable for a given linear index. Note that the Shapley and Banzhaf scores, frequently used in AI, are particular semivalues, and all semivalues are linear indices. To check whether a game is stable for a specific semivalue, it suffices to inspect the ordering of the coalitions and to perform some direct computation based on the semivalue parameters.

We investigate the issue of manipulability for social ranking rules, where the goal is to rank individuals given the ranking of coalitions formed by them and each individual prefers to reach the highest positions in the social ranking. This problem lies at the intersection of computational social choice and the algorithmic theory of power indices. Different social ranking rules have been recently proposed and studied from an axiomatic point of view. In this paper, we focus on rules representing three classical approaches in social choice theory: the marginal contribution approach, the lexicographic approach and the (ceteris paribus) majority one. We first consider some particular members of these families analysing their resistance to a malicious behaviour of individuals. Then, we analyze the computational complexity of manipulation, and complete our theoretical results with simulations in order to analyse the manipulation frequencies and to assess the effects of manipulations.

We introduce a new method to rank single elements given an order over their sets. For this purpose, we extend the game theoretic notion of marginal contribution and of Banzhaf index to our ordinal framework. Furthermore, we characterize the resulting ordinal Banzhaf solution by means of a set of properties inspired from those used to axiomatically characterize another solution from the literature: the ceteris paribus majority. Finally, we show that the computational procedure for these two social ranking solutions boils down to a weighted combination of comparisons over the same subsets of elements.

We study the problem of finding a social ranking over individuals given a ranking over coalitions formed by them. We investigate the use of a ceteris paribus majority principle as a social ranking solution inspired from the classical axioms of social choice theory. Faced with a Condorcet-like paradox, we analyze the consequences of restricting the domain according to an adapted version of single-peakedness. We conclude with a discussion on different interpretations of incompleteness of the ranking over coalitions and its exploitation for defining new social rankings, providing a new rule as an example.

A common way of dealing with the paradoxes of preference aggregation consists in restricting the domain of admissible preferences. The most well-known such restriction is single-peakedness. In this paper we focus on the problem of determining whether a given profile is single-peaked with respect to some axis, and on the computation of such an axis. This problem has already been considered in [2]; we give here a more efficient algorithm and address some related issues, such as the number of orders that may be compatible with a given profile, or the communication complexity of preference aggregation under the single-peakedness assumption.

The article discusses the use of positive and negative reasons when preferences about alternative options have to be considered. Besides explaining the intuitive and formal situations where such a bipolar reasoning is used, the article shows how it is possible to generalize the concordance/discordance principle in preference aggregation and apply it to the problem of aggregating preferences expressed under intervals. © 2008 Wiley Periodicals, Inc.