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
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.
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
Strategy-proof location of public facilities
(2015) Alcalde Unzu, Jorge; Vorsatz, Marc; Economía; Ekonomia
Agents frequently have different opinions on where to locate a public facility. While some agents consider the facility a good and prefer to have it nearby, others dislike it and would like to see it built far away from their own locations. To aggregate agents' preferences in these situations, we propose a new preference domain according to which each agent is allowed to have single-peaked or single-dipped preferences on the location of the facility, but in such a way that the peak or dip is situated in her own location. We characterize all strategy-proof rules in this general framework and show that they are also group strategy-proof. Finally, we characterize for some focal cases the rules that additionally satisfy Pareto efficiency.
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
Strategy-proofness with single-peaked and single-dipped preferences
(Elsevier, 2024-07-01) Alcalde Unzu, Jorge; Gallo, Oihane; Vorsatz, Marc; Economía; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE
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 Barberà 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.
Open Access
Uncertainty with ordinal likelihood information
(Springer-Verlag, 2013) Alcalde Unzu, Jorge; Arlegi Pérez, Ricardo; Ballester Oyarzun, Miguel Ángel; Economía; Ekonomia
We present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain difficulties arising from the state space-based approach. Kelsey (Int Econ Rev 34:297–308, 1993) incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus filling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey’s approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability.
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
The measurement of the value of a language
(Elsevier, 2022) Alcalde Unzu, Jorge; Moreno Ternero, Juan D.; Weber, Shlomo; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We address the problem of assessing the value of a language. We consider a stylized model of multilingual societies in which we introduce axioms formalizing the principles of impartiality, monotonicity, invariance and consistency. We show that the combination of these axioms characterizes a family of communicative benefit functions which assign a value to each language in the society. The functions within the family involve a two-step procedure. First, they identify the groups of agents that can communicate in each language. Second, each group is assigned an aggregate (size-dependent) value, which is evenly divided among the languages in which the group can communicate. Our novel approach could be useful in a wide range of empirical applications and policy decisions.
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.