Open Access
Strategy-proof location of public facilities
(Elsevier, 2018) Alcalde Unzu, Jorge; Vorsatz, Marc; Economía; Ekonomia
Consider the problem of locating a public facility taking into account the agents' preferences. To construct strategy-proof social choice rules, we propose a new preference domain that allows agents to have any single-peaked or any single-dipped preference on the location of the facility such that the peak/dip of the preference is in her own location. We characterize all strategy-proof rules in this general framework and study the conditions under which this family of strategy-proof rules includes non-dictatorial rules that have more than two alternatives in the range or that are Pareto efficient. Finally, we characterize for some focal cases all strategy-proof and Pareto efficient rules.
Open Access
Size approval voting
(2007) Alcalde Unzu, Jorge; Vorsatz, Marc; Economía; Ekonomia
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.
Open Access
Allocating the costs of cleaning a river: expected responsibility versus median responsibility
(Springer, 2020) Alcalde Unzu, Jorge; Gómez Rúa, María; Molis Bañales, Elena; Economía; Ekonomia
We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.
Open Access
Sharing the costs of cleaning a river: the Upstream Responsibility rule
(Elsevier, 2015) Alcalde Unzu, Jorge; Gómez Rúa, María; Molis Bañales, Elena; Economía; Ekonomia
The cleaning up of waste present in transboundary rivers, which requires the cooperation of different authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang (2007) we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs “fairly” and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.
Open Access
Non anonymous ballot aggregation: an axiomatic generalization of Approval Voting
(2011) Alcalde Unzu, Jorge; Vorsatz, Marc; Economía; Ekonomia
We study axiomatically situations in which the society agrees to treat voters with different characteristics distinctly. In this setting, we propose a set of six intuitive axioms and show that they jointly characterize a new class of voting procedures, called Personalized 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. Hence, the implemented voting procedure reduces to Approval Voting in case all voters are identical or the procedure assigns the same weight to all types.
Open Access
Measuring the cohesiveness of preferences: an axiomatic analysis
(Springer Berlin Heidelberg, 2013) Alcalde Unzu, Jorge; Vorsatz, Marc; Economía; Ekonomia
In 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.
Open Access
Sharing the costs of cleaning a river: the upstream responsibility rule
(2013) Alcalde Unzu, Jorge; Gómez Rúa, María; Molis Bañales, Elena; Economía; Ekonomia
The cleaning up of waste present in transboundary rivers, which requires the cooperation of different authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang [12] we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of ach region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs 'fairly' and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.
Open Access
Ranking opportunity profiles through dependent evaluation of policies
(Springer US, 2012) Alcalde Unzu, Jorge; Ballester Oyarzun, Miguel Ángel; Economía; Ekonomia
Rankings to evaluate opportunity distributions present in most of the literature judge a policy (change from one distribution of opportunities to another) on the basis of the changes created and, thus, independently of the original situation. This paper proposes a group of axioms capturing the idea that rankings of equality of opportunities might consider not only the changes promoted, but also the initial situation in society. The combination of this group of axioms with other well-established properties enables us to characterize two families of new opportunity distribution rankings. The first family weighs each individual’s percentage share in the total number of opportunities, while the second weighs opportunities depending on how many agents have them available.
Open Access
Freedom of choice: John Stuart Mill and the tree of life
(Springer-Verlag, 2012) Alcalde Unzu, Jorge; Ballester Oyarzun, Miguel Ángel; Nieto Vázquez, Jorge; Economía; Ekonomia
This essay deals with the notion and content of freedom of choice proposing a new set up and a new family of measures for this concept which is, indeed, an ethical value of paramount importance in a well ordered and open society. Following some ideas of John StuartMill, we propose that freedom of choice has to be understood not in a single stage of choice, but in the ordered collection of choices that a person can make in her life.We then suggest to represent a life in a tree structure, where each node represents a state of life and the edges between nodes will represent possible decisions in life. In this new framework, we propose a set of axioms that imply the following family of measures of lifetime’s freedom of choice: the lifetime’s freedom of choice has to be evaluated by a weighted sum of all possible states of life an individual might visit, with weights representing the number of decisions the individual took to reach that state.
Open Access
Uncertainty with ordinal likelihood information
(2007) Alcalde Unzu, Jorge; Arlegi Pérez, Ricardo; Economía; Ekonomia
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.