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We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains either a veto player or a dominant veto mixed pair, or the game is a composition of these two types of special assignment games. We also show that in PMAS-admissible assignment games all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.

How can several individuals’ probability functions on a given $$\sigma $$ -algebra of events be aggregated into a collective probability function? Classic approaches to this problem usually require ‘event-wise independence’: the collective probability for each event should depend only on the individuals’ probabilities for that event. In practice, however, some events may be ‘basic’ and others ‘derivative’, so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize this idea by introducing a ‘premise-based’ approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the ‘premises’.

In this work we pursue the study of manipulability of social choice functions through “liftings”, that is, mappings which extend orderings over points to orderings over subsets of points. We discover a very weak notion of monotony which is closely related to independence of irrelevant alternatives. This allows us to establish an interesting and general theorem on manipulability. We show that this theorem is indeed equivalent to Arrow-Sen Theorem in the class of nonmanipulable social choice functions. As a consequence of this general theorem we obtain a manipulation theorem for linear profiles in the style of Gibbard-Satterthwaite Theorem but for social choice functions instead of voting schemes. We introduce the notion of nominator, which is a natural generalization of the notion of pairwise nominator introduced by Kelly. Then, we establish that, in the presence of rational properties over liftings, a social choice function is either manipulable, or it admits a nominator. In addition, we do a comparative study on different types of powerful voters (dictators, nominators, pairwise nominators and weak-dictators) present in the literature. Although, in general, they are non-equivalent notions, we show that under some natural conditions, modulo nonmanipulability, the last three are equivalent or even all the notions are equivalent.

A condition on preferences called strict Latin Square partial agreement is introduced and is shown to be necessary and sufficient for quasi-transitivity of the social weak preference relation generated by any special majority rule, under the assumption that individual preferences themselves are quasi-transitive.

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is “describable.” The “describable” coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones.

This paper studies a class of NTU coalition formation games in which every player’s payoff depends only on the members of her coalition. We identify four natural conditions on individuals’ preferences and show that, under each condition, stable (core) allocations exists.

John Broome (Proc Aristot Soc 91:87–101, 1990) has developed an influential theory of fairness, which has generated a thriving debate about the nature of fairness. In its initial conception, Broomean fairness is limited to a comparative notion. More recent commentators such as Hooker (Ethical Theory Moral Pract 8:329–52, 2005), Saunders (Res Publica 16:41–55, 2010), Lazenby (Utilitas 26:331–345, 2014), Curtis (Analysis 74:47–57, 2014) have advocated, for different reasons, to also take into account non-comparative fairness. Curtis’ (Analysis 74:47-57, 2014) theory does just that. He also claims that he furthers Broome’s theory by saying precisely what one must do in order to be fair. However, Curtis departs from Broome’s (Proc Aristot Soc 91:87-101, 1990) requirement that claims are satisfied in proportion to their strength. He neglects claim-strengths altogether and identifies claims with their amount. As a result, the theory of Curtis has limited scope. I present a theory of fairness that fulfils all three desiderata: it incorporates non-comparative fairness, it recognizes that claims have both amounts and strengths, and it tells us precisely what one must do in order to be fair.

The purpose of this article is to study two indexes, the marginal index and the Banzhaf–Coleman index. For each of these two indexes, there is a corresponding reduced game that can be used to characterize it. In addition, we consider the efficient extensions of two indexes. In comparison to each characterization of two indexes, we establish a similar characterization for each extension of two indexes through an identical approach. Finally, for each of two efficient indexes, we propose a dynamic process leading to that corresponding efficient index, starting from an arbitrary efficient payoff vector.