Exchange of indivisible goods and indifferences: the Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems involving the exchange of indivisible goods without monetary transfers, starting from the housing market model of the seminal paper of Shapley and Scarf [10] and including other problems like the kidney exchange or the school choice problems. For many of these models, the classical solution is the application of an algorithm/mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, that generalizes the Top Trading Cycles for the general case in which individuals can report indifferences, and preserves all its desirable properties.housing market, indifferences, top trading cycles, absorbing sets

Mobility as movement: A measuring proposal based on transition matrices

In this note we introduce a family of functions that various theoretical results have revealed as useful mobility measures. These functions have enabled us to circumvent an impossibility result obtained by Shorrocks (1978), by adapting one of his axioms to the context of mobility as movement. A particular case belonging to this family is the Bartholomew index, which is widely used in the empirical literature.

Strategy-proofness with single-peaked and single-dipped preferences

We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result characterizes all strategy-proof rules and shows that they can be decomposed into two steps. In the first step, the agents with single-peaked preferences are asked about their peaks and, for each profile of reported peaks, at most two alternatives are preselected. In the second step, the agents with single-dipped preferences are asked to reveal their dips to complete the decision between the preselected alternatives. Our result generalizes the findings of Moulin (1980) and Barber\`a and Jackson (1994) for single-peaked and of Manjunath (2014) for single-dipped preferences. Finally, we show that all strategy-proof rules are also group strategy-proof and analyze the implications of Pareto efficiency

Measuring the cohesiveness of preferences: an axiomatic analysis

The final publication is available at Springer via http://dx.doi.org/10.1007/s00355-012-0716-9In this paper, we axiomatically study how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness. First, we provide axioms that characterize a family of linear and additive measures whose intersection is a partial ordinal criterion similar to first order stochastic dominance. The introduction of some additional properties isolates a one-parameter subfamily. This parameter evaluates the effect on the cohesiveness if one individual changes his ranking on a single pair of objects, as a function of how many of the remaining individuals in the group rank the first object over the second and vice versa. Finally, we characterize the focal measures of this subfamily separately showing that they coincide with measures constructed using two, at first sight, totally different approaches suggested in the literature.The author Jorge Alcalde-Unzu gratefully acknowledges financial support from the Spanish Ministry of Education and Science, through the projects ECO2009-11213 and ECO2009-12836. The author Marc Vorsatz gratefully acknowledges financial support from the Spanish Ministry of Education and Science (through the project ECO2009-07530) and from the Spanish Ministry of Economy and Competitiveness (through the project ECO2012-31985)

Size approval voting

We propose a new class of voting rules, called Size Approval Voting. According to this rule, the effective weight of a vote from a given individual depends on how many other alternatives the very same individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved alternatives. Then, for a given profile of individual votes, all those alternatives with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting is characterized by a set of natural properties

Non-anonymous ballot aggregation: an axiomatic generalization of Approval Voting

We study axiomatically situations in which the society agrees to treat voters with different characteristics distinctly. In this setting, we propose a set of intuitive axioms and show that they jointly characterize a new class of voting procedures, called Type-weighted Approval Voting. According to this family, each voter has a strictly positive and finite weight (the weight is necessarily the same for all voters with the same characteristics) and the alternative with the highest number of weighted votes is elected. The implemented voting procedure reduces to Approval Voting in case all voters are identical or the procedure assigns the same weight to all types. Using this idea, we also obtain a new characterization of Approval Voting.The first author’s financial support from the Spanish Ministry of Education and Science, through the project ECO2012–34202, and Fundación Ramón Areces is gratefully acknowledged. The second author’s financial support from the Spanish Ministry of Education and Science, through the project ECO2012–31985, and Fundación Ramón Areces is gratefully acknowledged

Uncertainty with ordinal likelihood information

This paper proposes a new framework of choice under uncertainty, where the only information available to the decision maker is about the the ordinal likelihood of the different outcomes each action generates. This contrasts both with the classical models where the potential outcomes of each action have an associated probability distribution, and with the more recent complete uncertainty models, where the agent has no information whatever about the probability of the outcomes, even of an ordinal nature. We present an impossibility result in our framework, and some ways to circumvent it that result in different ranking rules.The authors acknowledge financial support by the Spanish Ministerio de Educación y Ciencia (Project SEC2003-08105 and SEJ2006-11510) and by Junta de Castilla y León (Project VA040A05)