Red Española de Elección Social

 

 

XI Encuentro de la REES 21 y 22 de Noviembre en Madrid

Formulario de inscripción (hasta el 31 de Octubre)

Programa definitivo (15 de Noviembre)

Participantes (15 de Noviembre)

Hoteles

Acomodación

Lugar: en la Facultad de Economía y Empresa de la Universidad de Carlos III.

Sede: Facultad de CC. Jurídicas y Sociales. Campus de Getafe.

 
 

Colaboran:

Universidad Carlos III de Madrid.
Facultad de CC. Sociales y Juridicas de la Universidad Carlos III de Madrid.
Universidad Nacional de Educación a Distancia.
Departamento de Economía de la Universidad Carlos III de Madrid.
Instituto de Economía de la Universidad Carlos III de Madrid.

   
 
XI Encuentro de la Red Española de Elección Social (REES)
Universidad Carlos III de Madrid
Getafe, 21 y 22 de noviembre de 2014
Sede: Facultad de CC. Jurídicas y Sociales. Campus de Getafe.

 
Viernes 21 Noviembre: 14.0.11 Sala Buero Vallejo
10:00 -11:30
Chair:
José Carlos Rodríguez
Alcantud
Riste Gjorgjev (UdG)
“Impartial Social Rankings”.
  We model a situation where a set of selfish agents must rank themselves on the basis of the opinions that they hold regarding the merits of each candidate. Each agent submits an ordered list of the population representing his opinion about how should the final ranking be. We call the collection of such lists a profile and it is the input for a social ranking function that determines the final ranking. We are interested in impartial social ranking functions, that is those where the contribution of a single agent to the social outcome can have no consequence on his own position the final ranking.

We show that the only impartial social ranking functions that are anonymous are the constant ones. Furthermore, we show impossibility whenever individual full rank is combined with impartiality. We also provide several characterizations of impartial social ranking functions adding some properties like neutrality, monotonicity and partial unanimity.
   
  Carmen Herrero (UA)
“An Endogeneous Scoring Rule”.
  This paper presents a way of ranking alternatives on the basis of their relative support. This is measured by the eigenvector of a positive matrix whose entries are the Condorcet dominations (off-diagonal) and the Borda counts (diagonal). A characterization is also presented.
   
  11:30-12:00 Coffee Break. Room 14.0.09
   
12:00-13:30
Chair:
Omar de la Cruz
Vicente
Joaquín Pérez Navarro (UAH)
“No show paradox and the golden number in
generalized Condorcet voting methods”
  This paper extends the analysis of the No Show Paradox to the context of generalized q-Condorcet voting correspondences, in which the q-Condorcet winner is defined as the candidate who wins to any other by a qualified majority q higher than half the number of voters. We try to progress, for the case of general voting correspondences, in the resolution of an open problem proposed in Holzman (1988/89), asking for the range of q quota values for which all q-Condorcet voting rules are subjected to the paradox. This also means to extend a known general result of Moulin (1988) stating that all conventional Condorcet voting rules suffer the paradox. Interestingly, the well-known mathematical constant f, called the golden number, appears in the main theorem of the paper.
   
  Nora ibarzábal Laka (UPV-EHU)
“Making Blank Votes Count: The Basque Parliament
Cas
  In elections voters have generally four options: to abstain from participating, to go and vote for a candidate, to go and cast a blank vote or to go and cast a null vote. Voting for a candidate is a positive expression of support towards one candidate. The other three options may reflect lack of interest, dissatisfaction with the parties or the political system, or a vote of protest. However the number of seats allocated remains constant and even if the number of the voters who choose one of these three options is very large. The recently created political party “Blank Seats” proposes to make the number of blank votes count by leaving empty the seats that by numbers would correspond to the blank votes. Using the data of the elections held in the Basque Autonomous Community we try to quantify the effect of this proposition. We recalculate the distribution of seats if this proposition were implemented, and measure the power distribution among the parties with the new distribution of seats.
   
  13:30-15:00 Lunch. Club de Profesores
   
15:00- 16:30
Chair:
Bernardo Moreno
Juan Francisco Sánchez (UPCT)
“Distributive justice in conflicting claims problem: a
questionnaire study” (con JM Giménez-Gómez y Carmen Marco)
  A conflicting claims problem is a particular case of distribution problem, in which the amount to be distributed, the endowment E, is not enough to cover the agents' claims on it. This model describes the situation faced by a court that has to distribute the net worth of a bankrupt firm among its creditors. But, it also corresponds with cost-sharing, taxation, or rationing problems.

Following the line initiated by Bosmans and Schokkaert (2009), we analyze the choice made by 575 people who are involved in a conflicting claims situations. We introduce in our sample heterogeneity and diversity, that is, it is not restricted to a particular population, since we are trying to identifying how society distributes justice and selects its choice when there is not enough to honor all the claims. That is, we analyze the behavior of students, self-employed, retired people and workers. Doing so, we can analyze if there is some significative difference in people's choices in terms of age, education, and laboral or wealth situation, among others. We also analyze the questions of with- in context consistency and of between-context uniformity. Concretely, we design two types of questionnaires: an advertising department (firm) and a mutual benefit society (pensions). Note that we study the between-context uniformity by presenting two different stories. But also, we face the with-in context question, since in each story we propose three different situations where the agents involved in the conflicting claims problem have different personal characteristics: (i) all the agents have no any extra funds different from the obtained by the firm (pension); (ii) all the agents have extra funds different from the obtained by the firm (pension); (iii) all the agents have no any extra funds different from the obtained by the firm (pension) and have worked the same number of hours; (iv) all the agents have extra funds different from the obtained by the firm (pension) and have worked the same number of hours. The respondents act like an external arbitrator and they have to dictate how to distribute the available resources in terms of the three agents' personal characteristics. Note that it allows us to discriminate if there is some psychological patterns or fairness principle affect or not when a distribution among agents should be done. Even more, we analyze if the arbitrator's (respondents) personal situation determines the recommended allocation.
   
  Pedro Calleja Cortés (UB)
“Core selection, aggregate monotonicity and
consistency for single-valued solutions in cooperative
games”
  This paper studies the compatibility of properties for single-valued solutions of cooperative games. In particular, we focus on the possibility to combine properties of rationality (as core selection or individual rationality), with aggregate monotonicity properties and consistency properties (with respect to different reduced games). We introduce regular and strong regular aggregate monotonicity, and in our main result we show that core selection, regular aggregate monotonicity and max- consistency are incompatible. Finally, we analyze the compatibility of rationality properties with regular aggregate monotonicity and properties that concerns the features of the players in a game, like symmetry and the dummy player property.
   
  16:30-17:00 Coffee Break. Room 14.0.09
   
17:00-17:45
Chair:
Carmen Marco
Josep María Izquierdo Aznar (UB)
“Rationing problems with payoff tresholds”
  An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims over some amount of a scarce resource, but also by some payoff thresholds. These thresholds introduce exogenous differences among agents (full or partial priority, past allocations, pending debts, . . .) that may influence the final
distribution. Within this framework we provide generalizations of the constrained equal awards rule and the constrained equal losses rule. We show that these generalized rules are dual from each other. We characterize the generalization of the equal awards rule by using the properties of consistency, path-independence and compensated exemption. Finally, we use the duality between rules to characterize the generalization of the equal losses solution.
   
  18:30 Meeting Miembros de la REES
  21:30 Social Dinner
   
  Sábado 22 Noviembre Room 14.0.10
10:10 -11:40
Chair:
Ricardo Martínez
Jorge Alcalde-Unzu (UPNA)
“Strategy-proof location of public facilities” (con M
Vorsatz)
  There are many examples of public facilities that are considered public goods by some agents and public bads by others: cell towers, military bases, dog parks, music festivals, maritime ports, etc... The question that we are trying to answer in this paper is how we can aggregate the preferences of agents in this type of situations when we have to choose a location of a public facility and agents differ in considering it a public good or a public bad.

To study these situations, we propose a new domain of preferences and characterize strategy-proof rules. In particular, we show that, in this domain, we can escape from the Gibbard--Satterthwaite impossibility result.
   
  Elena Molís (UGr)
“A new solution for roommate problems: The Q-Stable
matchings
  In this paper we propose a new family of matchings as solution for the
roommate problem with strict preferences, when stable matchings may not exist. To define these matchings we proceed as follows: We introduce the solution of maximum irreversibility, a strong notion of stability, and consider two other existing solutions that deal with unsolvable roommate problems: the almost stable matchings (Abraham et al. (2006)) and the maximum stable matchings (Tan (1990), (1991)). Although each of these core consistent solutions is a good candidate for solving roommate problems, we find that it is not possible to reconcile almost stability with any of the other two. Hence we select the family of matchings, the Q-stable family, that lie in the intersection of the maximum irreversible matchings and maximum stable matchings. Then we offer an efficient algorithm to compute a member of this family.
   
  11:40-12:00 Coffee Break. Room 14.0.09
   
12:00-13:30
Chair: Juan Vidal -
Puga
María Teresa González Arteaga (UVall)
“A proposal of ranking codifications compatible with
Mahalanobis disconsensus measures” (con Rocío de
Andrés Calle y JC Rodríguez-Alcantud)
  We introduce the use of the Mahalanobis distance (\cite{Mahalanobis}) for the analysis of the cohesiveness of a group of linear orders or complete preorders. By the recourse to the standard distance-based construction, we define a Mahalanobis disconsensus measure in that setting, which requires to codify complete preorders.

The Mahalanobis distance is a powerful tool in Statistics and its applications. It allows
to introduce corrections due to correlations among the variables. In our case, this
permits to adjust the basic Euclidean approach to account for the effect of correlated
rankings.

The axiomatic analysis of the measurement of the coherence in a profile of preferences
has received growing attention since the seminal contribution by Bosch \cite{Bosch}. Some earlier analysis of that concept can be acknowledged, e.g., Hays \cite{Hays} or Day and McMorris \cite{DMc}. In most cases ([4], [7], or the recent Alcalde-Unzu and Vorsatz \cite{AUV}) agents are
presumed to linearly order the alternatives. There are proposals for extending those
approaches to the case when ties are allowed, that is, when agents have complete
preorders on the alternatives: see, e.g., Garc\'\i a-Lapresta and P\'erez-Rom\'an \cite{GLPR}. In a
related line, Alcantud et al. \cite{AAC} show that the case when agents have dichotomous
opinions (e.g. because they cast votes using Approval voting mechanism) on the
alternatives is both conceptually rich and technically favorable for the purpose of
providing axiomatic support to the consensus indexes (as in\cite{AUV} or \cite{Bosch}). Another way to analyze the coherence of a voting profile is through a referenced consensus measure as it is found in \cite{AAC2} for the Borda and the Copeland rules. In that work it is proved that this model contains the standard one.

As is usual in the distance-based approaches, a codification of the preferences in order
to transform profiles into matrices is needed for the purpose of building our Maha-
lanobis disconsensus measure. We study to what extent the choice of the codification
preserves the verdict as to which profiles are more `coherent' than others according to
our proposal, which seems to be a novel question in this realm. We refer to compati
bility of a class of codifications with respect to our disconsensus measure. Specifically,
we show that our ranking of preorders is unique up to affine transformations of a given
codification. Although we prove this for a benchmark codification, which in the case of
linear orders coincides with the Borda scores of the alternatives, the development for
the general case is completely analogous. We show by example that the choice among
a number of existing alternative codifications affects the comparison between two profiles in terms of a common consensus measure (namely, our Mahalanobis disconsensus
measure).

Finally, our proposal is illustrated with a real empirical example about different profiles
of rankings provided for a reduced set of top universities taking from the 'Academic
Ranking of World Universities' (ARWU) published every year since 2003 by the Insti-
tute of Higher Education of the Jiao Tong University in Shanghai and more commonly
known as the Shanghai ranking. Each of the fictitious agents (fields, subjects) emits
votes about the five alternatives according to the Borda count. Then, we study the
coherence of the emitted votes.

References
[1] J. Alcalde-Unzu, M. Vorsatz: Measuring the cohesiveness of preferences: an axiomatic
analysis. Social Choice and Welfare 41, 965{988, 2013.
[2] J. C. R. Alcantud, R. de Andrés Calle, and J. M. Cascón: Consensus and the act of voting.
Studies in Microeconomics 1, 1{22, 2013.
[3] J. C. R. Alcantud, R. de Andrés Calle, and J. M. Cascón: On measures of cohesiveness
under dichotomous opinions: some characterizations of Approval Consensus Measures. In-
formation Sciences 240, 45{55, 2013.
[4] R. Bosch: Characterizations of Voting Rules and Consensus Measures, Ph. D. Dissertation,
Tilburg University, 2005.
[5] W. H. E. Day, F. R. McMorris: A formalization of consensus index methods. Bulletin of
Mathematical Biology 47, 215{229, 1985.
[6] J. L. Garcíaa-Lapresta, D. Pérez-Román: Measuring consensus in weak orders. In: E.
Herrera-Viedma, J. L. García-Lapresta, J. Kacprzyk, H. Nurmi, M. Fedrizzi, S. Zadrozny
(Eds.) Consensual Processes, Springer-Verlag, 2011.
[7] W. Hays: A note on average Tau as a measure of concordance. Journal of the American
Statistical Association 55, 331{341, 1960.
[8] P. C. Mahalanobis: On the generalised distance in statistics. Proceedings of the National
Institute of Science of India 12, 49{55, 1936.
   
  Juan D Moreno-Ternero (UPO)
“Taxation and Poverty”
  We explore the implications of four natural axioms in taxation: \textit{continuity} (small changes in the data of a taxation problem should not lead to large changes in the tax allocation), \textit{equal treatment of equals} (agents with the same pre-tax incomes pay equal taxes), \textit{consistency} (the way in which a group allocates a tax burden only depends on their own after-tax incomes) and \textit{composition down} (an increase in the tax burden is handled according to agents' current post-tax incomes). The combination of the four axioms characterizes a large family of rules, which we call \textit{generalized equal-sacrifice} rules, encompassing the so-called \textit{equal-sacrifice} rules (such as the \textit{flat tax}), as well as \textit{constrained equal-sacrifice} rules (such as the \textit{head tax}), and \textit{exogenous poverty-line} rules (such as the \textit{leveling tax}, and some of its possible compromises with the previous ones)
   
   

 

©2013