We consider private good economies with single-peaked preferences. We show that the uniform rule is the only allocation rule satisfying omega-continuity, no-envy, and one-sided resource-monotonicity. This result strengthens a characterization of the uniform rule due to Thomson (Soc Choice Welf...

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with singlepeaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. Most of the literature has...

We consider the problem of fairly reallocating the individual endowments of a perfectly divisible good among agents with single-peaked preferences. We provide a new concept of fairness, called position-wise envy-freeness, that is compatible with individual rationality. This new concept requires...

The paper proves the following result: every path-connected domain of preferences that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a compromise property, is single-peaked. Conversely, every single-peaked domain admits a random social choice function...

We prove a general possibility result for collective decision problems where individual allocations are one-dimensional, preferences are single-peaked (strictly convex), and feasible allocation profiles cover a closed convex set. Special cases include the celebrated median voter theorem (Black...

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended...

The assessment of income inequality can be investigated looking at the solution concepts of the cooperative game theory. We propose a multi-factorial decomposition of the Atkinson index by income sources and evaluate it as a cooperative game of the social cost of inequality. This framework...

We concentrate on the problem of the provision of one pure public good whenever agents that form the society have either single-plateaued preferences or single-peaked preferences over the set of alternatives. We are interested in comparing the relationships between different nonmanipulability...

Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule...

In this paper, we define simple measures of two properties that social choice functions may embody in different degrees in public goods environments. First, a measure of solidarity is proposed such that Thomson's (1990) replacement monotonicity property is a particular case in which the full...