La tesis de doctorado "Understanding, Evaluating and Selecting Voting Rules Through Games and Axioms" de Danilo Santa Cruz Coelho está compuesta de cuatro capítulos. La introducción es el primero y describe brevemente el contenido de los capítulos siguientes. En el Capítulo 2, en el contexto de un modelo de votación probabilística propuesto por Rae (1969), el autor investiga las consecuencias de elegir reglas de votación según el criterio de maximin. En el modelo, una regla de votación es el número mínimo de votantes favorables necesarios a una propuesta para que esta sea aceptada. El autor demuestra que la regla de votación que satisface el criterio de maximin puede ser distinta de la mayoría simple que es la que maximiza la suma de las utilidades esperadas de los votantes. El autor proporciona una caracterización de las reglas de votación que satisfacen el criterio de maximin. En el Capítulo 3, dos juegos que pueden ser inducidos por la regla de los k nombres son propuestos y analizados. El autor proporciona para cada uno de los juegos una caracterización del conjunto de los resultados del equilibrio fuerte de Nash. Estas caracterizaciones permiten al autor discutir las preferencias de los jugadores sobre diferentes variantes de la regla de los k nombres. Una parte importante de la regla de los k nombres es el procedimiento utilizado para seleccionar los k nombres que son propuestos al individuo que toma la decisión final. Seis reglas diferentes de selección que son utilizadas en la realidad por diferentes cuerpos decisorios alrededor del mundo son documentadas. En el Capítulo 4, el autor estudia si estas reglas satisfacen la propiedad de estabilidad. Una regla cumple esta propiedad si esta siempre selecciona un conjunto Weak Condorcet y cuando exista un conjunto con esta característica. El autor demuestra que todas estas seis reglas violan esta propiedad si los votantes no actúan estratégicamente. El autor entonces propone dos reglas estables. Finalmente, él proporciona dos justificaciones para el uso extensivo de las reglas inestables. / The dissertation entitled "Understanding, Evaluating and Selecting Voting Rules Through Games and Axioms" by Danilo Santa Cruz Coelho is composed of four chapters. The introduction is the first one and describes briefly the contents of the following chapters. In Chapter 2, in the context of a probabilistic voting model proposed by Rae (1969), the author investigates the consequences of choosing among threshold voting rules according to the maximin criterion. A threshold voting rule is given by the minimum number of votes needed to approve a proposal of change from the status quo. The author shows that the voting rules that satisfy the maximin criterion are different from the simple majority rule which is the one that maximizes the sum of voter's expected utilities. He provides a characterization of the threshold voting rules that satisfy this criterion as a function of the distribution of voters' probabilities to favour change from the status quo. In Chapter 3, two different game theoretical models that can be induced by the rule of k names are proposed and analysed. A characterization of the set of strong Nash Equilibrium outcomes of each of the games is provided. These characterizations enable the author to discuss the preferences of the players over different variants of the rule of k names. An important part of the rule of k names is the procedure used to screen out the k names to be proposed to the individual who takes the final decision. Six different screening rules which are used in reality by different decision bodies around the world are documented. In Chapter 4, he studies whether these screening rules satisfy stability. A screening rule is stable if it always selects a weak Condorcet set whenever such set exists. He shows that all of the six screening rules violate stability if the voters act not strategically. He then proposes two screening rules which satisfy stability. Finally, he provides two possible justifications for the widespread use of unstable screening rules.

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O presente trabalho tem por objetivos (i) apresentar a teoria do poder de votação a priori e (ii) analisar a justiça das regras de votação do Plenário do Conselho Federal de Economia (COFECON) com base nesta teoria. Utilizando como referencial teórico a teoria da escolha pública, os principais índices de poder de votação e a noção de justa distribuição de poder são apresentados. Para a análise da justiça das regras de votação do Plenário do COFECON, utilizamos os índices de poder de Banzhaf absoluto e relativo. Verificou-se que a recente mudança nas regras de tomada de decisão do Plenário do COFECON foi prejudicial do ponto de vista da justiça da distribuição do poder entre os Conselhos Regionais de Economia (CORECONs) que compõem o COFECON. CORECONs representantes de um grande número de economistas como Minas Gerais e Rio Grande do Sul passaram a ter o mesmo poder para influenciar decisões do que Conselhos pequenos como Amapá e Tocantins. Conseqüentemente, um economista membro do CORECON do Amapá tem um poder de alterar o resultado de uma decisão tomada no Plenário do COFECON muito maior do que um economista membro do CORECON do Rio Grande do Sul. / The goals of the present work are (i) present the theory of a priori voting power and (ii) analyze the justice of the voting rules in the Assembly of the Brazilian Federal Council of Economics (COFECON) based on this theory. Having as theoretical basis the public choice theory, the most important voting power indices and the notion of fair power distribution are presented. In the analysis of the fairness of the COFECON’s assembly voting rules, the Banzhaf absolute power index and the Banzhaf relative power index were employed. The analysis verified that the recent change in the rules of decision making in the COFECON’s assembly was harmful to the fairness of the voting power distribution between the Regional Councils of Economics (CORECONs). After the change, the power of CORECONs representing a great number of economists as Minas Gerais and Rio Grande do Sul equals the power of minor jurisdictions as Amapá and Tocantins. Hence, an economist member of Amapá’s CORECON has a power to change a decision of the Assembly of COFECON much larger than that of an economist member of the Rio Grande do Sul’s CORECON.

Στην εργασία αυτή ασχολούμαστε με θέματα κοινωνικής επιλογής και πιο συγκεκριμένα με συμβιβαστικές ψηφοφορίες στις οποίες κάθε ψηφοφόρος ψηφίζει ένα (πιθανόν κενό) σύνολο υποψηφίων και το αποτέλεσμα είναι ένα σύνολο υποψηφίων πλήθους k, για δεδομένο k (π.χ. εκλογή επιτροπής). Εξετάζουμε τον κανόνα minimax σε συμβιβαστικές ψηφοφορίες, στις οποίες το αποτέλεσμα αντιπροσωπεύει ένα συμβιβασμό μεταξύ των προτιμήσεων των ψηφοφόρων, με την έννοια ότι η μέγιστη απόσταση μεταξύ των προτιμήσεων οποιουδήποτε ψηφοφόρου και του αποτελέσματος είναι όσο το δυνατό μικρότερη. Αυτός ο κανόνας έχει δύο μειονεκτήματα. Πρώτον, ο υπολογισμός του αποτελέσματος που ελαχιστοποιεί τη μέγιστη απόσταση από κάθε ψηφοφόρο είναι ένα υπολογιστικά δύσκολο πρόβλημα και δεύτερον, οποιοσδήποτε αλγόριθμος που πάντα επιστρέφει ένα τέτοιο αποτέλεσμα, δίνει στους ψηφοφόρους κίνητρο να πουν ψέματα για την πραγματική τους προτίμηση, με σκοπό να βελτιώσουν την απόσταση τους από το τελικό αποτέλεσμα. Για να ξεπεράσουμε αυτά τα μειονεκτήματα χρησιμοποιούμε προσεγγιστικούς αλγορίθμους, δηλαδή αλγορίθμους που παράγουν αποτέλεσμα που αποδεδειγμένα προσεγγίζει την minimax απόσταση για κάθε δοσμένο στιγμιότυπο. Τέτοιοι αλγόριθμοι μπορούν να χρησιμοποιηθούν σαν εναλλακτικοί κανόνες ψηφοφορίας. Παρουσιάζουμε ένα 2-προσεγγιστικό αλγόριθμο πολυωνυμικού χρόνου, ο οποίος υπολογίζει το αποτέλεσμα στρογγυλοποιώντας ντετερμινιστικά τη λύση του χαλαρωμένου γραμμικού προγράμματος μέσω του οποίου εκφράζουμε το πρόβλημά μας. Ο καλύτερος προηγούμενος προσεγγιστικός αλγόριθμος επιτύγχανε λόγο απόδοσης 3 και συνεπώς το παραπάνω αποτέλεσμα αποτελεί σημαντική βελτίωση. Επιπλέον ασχολούμαστε με προσεγγιστικούς αλγορίθμους που είναι ανθεκτικοί σε χειραγώγηση είτε από μεμονωμένους ψηφοφόρους είτε από ομάδες ψηφοφόρων. Τέτοιοι αλγόριθμοι δεν προσφέρουν κίνητρο στους ψηφοφόρους να δηλώσουν ψευδώς τις προτιμήσεις τους με σκοπό να βελτιώσουν την απόστασή τους από το τελικό αποτέλεσμα. Μια τέτοια μελέτη εντάσσεται στα πλαίσια της έρευνας που γίνεται τα τελευταία χρόνια πάνω στο σχεδιασμό προσεγγιστικών αλγοριθμικών μηχανισμών χωρίς χρήματα. Συμπληρώνουμε προηγούμενα αποτελέσματα με νέα πάνω και κάτω φράγματα για strategyproof και group-strategyproof αλγορίθμους. / We consider approval voting elections in which each voter votes for a (possibly empty) set of candidates and the outcome consists of a set of k candidates for some fixed k, e.g., committee elections. We are interested in the minimax approval voting rule in which the outcome represents a compromise among the preferences of the voters, in the sense that the maximum distance between the preference of any voter and the outcome is as small as possible. This voting rule has two main drawbacks. First, computing an outcome that minimizes the maximum distance is computationally hard. Furthermore, any algorithm that always returns such an outcome provides incentives to voters to misreport their true preferences. In order to circumvent these drawbacks, we consider approximation algorithms, i.e., algorithms that produce an outcome that approximates the minimax distance for any given instance. Such algorithms can be considered as alternative voting rules. We present a polynomial-time 2-approximation algorithm that uses a natural linear programming relaxation for the underlying optimization problem and deterministically rounds the fractional solution in order to compute the outcome; this result improves upon the previously best known algorithm that has an approximation ratio of 3. We are furthermore interested in approximation algorithms that are resistant to manipulation by (coalitions of) voters, i.e., algorithms that do not motivate voters to misreport their true preferences in order to improve their distance from the outcome. This study falls within the recently initiated line of research on approximate mechanism design without money. We complement previous results in the literature with new upper and lower bounds on strategyproof and group-strategyproof algorithms.

O presente trabalho tem por objetivos (i) apresentar a teoria do poder de votação a priori e (ii) analisar a justiça das regras de votação do Plenário do Conselho Federal de Economia (COFECON) com base nesta teoria. Utilizando como referencial teórico a teoria da escolha pública, os principais índices de poder de votação e a noção de justa distribuição de poder são apresentados. Para a análise da justiça das regras de votação do Plenário do COFECON, utilizamos os índices de poder de Banzhaf absoluto e relativo. Verificou-se que a recente mudança nas regras de tomada de decisão do Plenário do COFECON foi prejudicial do ponto de vista da justiça da distribuição do poder entre os Conselhos Regionais de Economia (CORECONs) que compõem o COFECON. CORECONs representantes de um grande número de economistas como Minas Gerais e Rio Grande do Sul passaram a ter o mesmo poder para influenciar decisões do que Conselhos pequenos como Amapá e Tocantins. Conseqüentemente, um economista membro do CORECON do Amapá tem um poder de alterar o resultado de uma decisão tomada no Plenário do COFECON muito maior do que um economista membro do CORECON do Rio Grande do Sul. / The goals of the present work are (i) present the theory of a priori voting power and (ii) analyze the justice of the voting rules in the Assembly of the Brazilian Federal Council of Economics (COFECON) based on this theory. Having as theoretical basis the public choice theory, the most important voting power indices and the notion of fair power distribution are presented. In the analysis of the fairness of the COFECON’s assembly voting rules, the Banzhaf absolute power index and the Banzhaf relative power index were employed. The analysis verified that the recent change in the rules of decision making in the COFECON’s assembly was harmful to the fairness of the voting power distribution between the Regional Councils of Economics (CORECONs). After the change, the power of CORECONs representing a great number of economists as Minas Gerais and Rio Grande do Sul equals the power of minor jurisdictions as Amapá and Tocantins. Hence, an economist member of Amapá’s CORECON has a power to change a decision of the Assembly of COFECON much larger than that of an economist member of the Rio Grande do Sul’s CORECON.

O presente trabalho tem por objetivos (i) apresentar a teoria do poder de votação a priori e (ii) analisar a justiça das regras de votação do Plenário do Conselho Federal de Economia (COFECON) com base nesta teoria. Utilizando como referencial teórico a teoria da escolha pública, os principais índices de poder de votação e a noção de justa distribuição de poder são apresentados. Para a análise da justiça das regras de votação do Plenário do COFECON, utilizamos os índices de poder de Banzhaf absoluto e relativo. Verificou-se que a recente mudança nas regras de tomada de decisão do Plenário do COFECON foi prejudicial do ponto de vista da justiça da distribuição do poder entre os Conselhos Regionais de Economia (CORECONs) que compõem o COFECON. CORECONs representantes de um grande número de economistas como Minas Gerais e Rio Grande do Sul passaram a ter o mesmo poder para influenciar decisões do que Conselhos pequenos como Amapá e Tocantins. Conseqüentemente, um economista membro do CORECON do Amapá tem um poder de alterar o resultado de uma decisão tomada no Plenário do COFECON muito maior do que um economista membro do CORECON do Rio Grande do Sul. / The goals of the present work are (i) present the theory of a priori voting power and (ii) analyze the justice of the voting rules in the Assembly of the Brazilian Federal Council of Economics (COFECON) based on this theory. Having as theoretical basis the public choice theory, the most important voting power indices and the notion of fair power distribution are presented. In the analysis of the fairness of the COFECON’s assembly voting rules, the Banzhaf absolute power index and the Banzhaf relative power index were employed. The analysis verified that the recent change in the rules of decision making in the COFECON’s assembly was harmful to the fairness of the voting power distribution between the Regional Councils of Economics (CORECONs). After the change, the power of CORECONs representing a great number of economists as Minas Gerais and Rio Grande do Sul equals the power of minor jurisdictions as Amapá and Tocantins. Hence, an economist member of Amapá’s CORECON has a power to change a decision of the Assembly of COFECON much larger than that of an economist member of the Rio Grande do Sul’s CORECON.