Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy,one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences....

We identify in this paper two conditions that characterize the domain of single-peaked preferences on the line in the following sense: a preference profile satisfies these two properties if and only if there exists a linear order $L$ over the set of alternatives such that these preferences are...

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is...

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...

In this paper we introduce a new concept of solidarity in terms of reciprocity and characterize the set of social choice functions that are reciprocate (in both a strong and a weak sense), anonymous and efficient in a standard public good provision model when the agents have single-peaked...

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...

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 char- acterize axiomatically the family of extended...

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...

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...