In this work, we introduce the notion of targeting for multi-criteria decision making. The problem involves selecting the best alternatives related to one particular alternative, called the target. We use an axiomatic approach to this problem by establishing properties that any targeting method should satisfy. We present a representation theorem and show that satisfying the main properties of targeting requires aggregating the evaluations of the alternatives related to the target. We propose various candidate targeting methods and examine the properties satisfied by each method.

We investigate the truth-tracking performance of iterated belief change operators. In particular, we show that a class of improvement operators is guaranteed to converge to the truth when the input sequence contains sufficiently many correct pieces of information, and we establish a corresponding convergence theorem. We also report experimental results indicating that this convergence typically occurs with relatively short input sequences.

We propose new operators for weighted propositional belief merging operators. We introduce distance-based operators that use the product as aggregation function. In social choice theory, the product, called the Nash welfare function, is known to be a more equitable social welfare function than the classical utilitarian welfare function (based on a sum). We study which properties are satisfied by the obtained corresponding weighted merging operators. In particular, we show that, unlike the Nash welfare function, distance-based operators using the product do not satisfy the Pigou-Dalton property. Then, we introduce a new family of weighted merging operators, which we call utility-based weighted merging operators, where the utility is roughly the converse of a distance for distance-based operators. For most well-known distance-based operators, it is easy to find the corresponding utility-based merging operators. But an interesting result is that the utility-based weighted merging operator based on the product does not correspond to any standard distance-based weighted merging operator, and this operator satisfies the Pigou-Dalton property.

In this work we propose a family of methods that allow to conjointly compute the reliability of a set of information sources and the confidence of the facts on a set of objects, by confronting the sources points of view. We use a (scoring-based) voting method for the evaluation of the trust of the sources, using Condorcet’s Jury Theorem arguments in order to identify the truth and the reliable sources. We discuss general theoretical properties that such operators should satisfy, and we study what are the properties satisfied by our methods. We provide an experimental study that shows that we perform better than state of the art methods on the task of finding the truth among the possible facts. We show that we can also adequately evaluate the reliability of the sources of information.

In standard propositional belief merging, one implicit assumption is that all sources have exactly the same importance. But there are many situations where the sources have different importance/reliability/expertise that have to be taken into account in the merging process. In this work we study the problem of weighted merging operators, which aimed to take these weights into account in a sensible way. We give a syntactical characterization of these operators, and then we state a representation theorem in terms of plausibility preorders on interpretations. We also propose a general method to build weighted distance-based merging operators, and provide some concrete examples, using two different weight functions.

In this work, we explore the links between the Borda voting rule and belief merging operators. More precisely, we define two families of merging operators inspired by the definition of the Borda voting rule. We also introduce a notion of cancellation in belief merging, inspired by the axiomatization of the Borda voting rule proposed by Young. This allows us to provide a characterization of the drastic merging operator.

We study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.

There are two theories of aggregation of logical formulae: merging and judgment aggregation. In this work we investigate the relationships between these theories; one of our objectives is to point out some correspondences/discrepancies between the associated rationality properties.

Belief merging is often described as the process of defining a base which best represents the beliefs of a group of agents (a profile of belief bases). The resulting base can be viewed as a synthesis of the input profile. In this paper another view of what belief merging aims at is considered: the epistemic view. Under this view the purpose of belief merging is to best approximate the true state of the world. We point out a generalization of Condorcet's Jury Theorem from the belief merging perspective. Roughly, we show that if the beliefs of sufficiently many reliable agents are merged then in the limit the true state of the world is identified. We introduce a new postulate suited to the truth tracking issue. We identify some merging operators from the literature which satisfy it and other operators which do not.

In the propositional setting, a well-studied family of merging operators are distance-based ones: the models of the merged base are the closest interpretations to the given profile. Closeness is, in this context, measured as a number resulting from the aggregation of the distances to each base of the profile. In this work we define a new familly of propositional merging operators, close to such distance-based merging operators, but relying on a set-theoretic definition of closeness, already at work in several revision/update operators from the literature. We study a specific merging operator of this family, obtained by considering set-product as the aggregation function.

Merging operators aim at defining the beliefs/goals of a group of agents from the beliefs/goals of each member of the group. Whenever an agent of the group has preferences over the possible results of the merging process (i.e., the possible merged bases), she can try to rig the merging process by lying on her true beliefs/goals if this leads to better merged base according to her point of view. Obviously, strategy-proof operators are highly desirable in order to guarantee equity among agents even when some of them are not sincere. In this paper, we draw the strategy-proof landscape for many merging operators from the literature, including model-based ones and formula-based ones. Both the general case and several restrictions on the merging process are considered.