One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φE value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φE value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

Les jeux stochastiques à somme nulle possèdent une structure récursive qui s'exprime dans leur opérateur de programmation dynamique, appelé opérateur de Shapley. Ce dernier permet d'étudier le comportement asymptotique de la moyenne des paiements par unité de temps. En particulier, le paiement moyen existe et ne dépend pas de l'état initial si l'équation ergodique - une équation non-linéaire aux valeurs propres faisant intervenir l'opérateur de Shapley - admet une solution. Comprendre sous quelles conditions cette équation admet une solution est un problème central de la théorie de Perron-Frobenius non-linéaire, et constitue le principal thème d'étude de cette thèse. Diverses classes connues d'opérateur de Shapley peuvent être caractérisées par des propriétés basées entièrement sur la relation d'ordre ou la structure métrique de l'espace. Nous étendons tout d'abord cette caractérisation aux opérateurs de Shapley "sans paiements", qui proviennent de jeux sans paiements instantanés. Pour cela, nous établissons une expression sous forme minimax des fonctions homogènes de degré un et non-expansives par rapport à une norme faible de Minkowski. Nous nous intéressons ensuite au problème de savoir si l'équation ergodique a une solution pour toute perturbation additive des paiements, problème qui étend la notion d'ergodicité des chaînes de Markov. Quand les paiements sont bornés, cette propriété d'"ergodicité" est caractérisée par l'unicité, à une constante additive près, du point fixe d'un opérateur de Shapley sans paiement. Nous donnons une solution combinatoire s'exprimant au moyen d'hypergraphes à ce problème, ainsi qu'à des problèmes voisins d'existence de points fixes. Puis, nous en déduisons des résultats de complexité. En utilisant la théorie des opérateurs accrétifs, nous généralisons ensuite la condition d'hypergraphes à tous types d'opérateurs de Shapley, y compris ceux provenant de jeux dont les paiements ne sont pas bornés. Dans un troisième temps, nous considérons le problème de l'unicité, à une constante additive près, du vecteur propre. Nous montrons d'abord que l'unicité a lieu pour une perturbation générique des paiements. Puis, dans le cadre des jeux à information parfaite avec un nombre fini d'actions, nous précisons la nature géométrique de l'ensemble des perturbations où se produit l'unicité. Nous en déduisons un schéma de perturbations qui permet de résoudre les instances dégénérées pour l'itération sur les politiques. / Zero-sum stochastic games have a recursive structure encompassed in their dynamic programming operator, so-called Shapley operator. The latter is a useful tool to study the asymptotic behavior of the average payoff per time unit. Particularly, the mean payoff exists and is independent of the initial state as soon as the ergodic equation - a nonlinear eigenvalue equation involving the Shapley operator - has a solution. The solvability of the latter equation in finite dimension is a central question in nonlinear Perron-Frobenius theory, and the main focus of the present thesis. Several known classes of Shapley operators can be characterized by properties based entirely on the order structure or the metric structure of the space. We first extend this characterization to "payment-free" Shapley operators, that is, operators arising from games without stage payments. This is derived from a general minimax formula for functions homogeneous of degree one and nonexpansive with respect to a given weak Minkowski norm. Next, we address the problem of the solvability of the ergodic equation for all additive perturbations of the payment function. This problem extends the notion of ergodicity for finite Markov chains. With bounded payment function, this "ergodicity" property is characterized by the uniqueness, up to the addition by a constant, of the fixed point of a payment-free Shapley operator. We give a combinatorial solution in terms of hypergraphs to this problem, as well as other related problems of fixed-point existence, and we infer complexity results. Then, we use the theory of accretive operators to generalize the hypergraph condition to all Shapley operators, including ones for which the payment function is not bounded. Finally, we consider the problem of uniqueness, up to the addition by a constant, of the nonlinear eigenvector. We first show that uniqueness holds for a generic additive perturbation of the payments. Then, in the framework of perfect information and finite action spaces, we provide an additional geometric description of the perturbations for which uniqueness occurs. As an application, we obtain a perturbation scheme allowing one to solve degenerate instances of stochastic games by policy iteration.

Machine learning-based systems are rapidly becoming popular because it has been realized that machines are more efficient and effective than humans at performing certain tasks. Although machine learning algorithms are extremely popular, they are also very literal and undeviating. This has led to a huge research surge in the field of interpretability in machine learning to ensure that machine learning models are reliable, fair, and can be held liable for their decision-making process. Moreover, in most real-world problems just making predictions using machine learning algorithms only solves the problem partially. Time series is one of the most popular and important data types because of its dominant presence in the fields of business, economics, and engineering. Despite this, interpretability in time series is still relatively unexplored as compared to tabular, text, and image data. With the growing research in the field of interpretability in machine learning, there is also a pressing need to be able to quantify the quality of explanations produced after interpreting machine learning models. Due to this reason, evaluation of interpretability is extremely important. The evaluation of interpretability for models built on time series seems completely unexplored in research circles. This thesis work focused on achieving and evaluating model agnostic interpretability in a time series forecasting problem.  The use case discussed in this thesis work focused on finding a solution to a problem faced by a digital consultancy company. The digital consultancy wants to take a data-driven approach to understand the effect of various sales related activities in the company on the sales deals closed by the company. The solution involved framing the problem as a time series forecasting problem to predict the sales deals and interpreting the underlying forecasting model. The interpretability was achieved using two novel model agnostic interpretability techniques, Local interpretable model- agnostic explanations (LIME) and Shapley additive explanations (SHAP). The explanations produced after achieving interpretability were evaluated using human evaluation of interpretability. The results of the human evaluation studies clearly indicate that the explanations produced by LIME and SHAP greatly helped lay humans in understanding the predictions made by the machine learning model. The human evaluation study results also indicated that LIME and SHAP explanations were almost equally understandable with LIME performing better but with a very small margin. The work done during this project can easily be extended to any time series forecasting or classification scenario for achieving and evaluating interpretability. Furthermore, this work can offer a very good framework for achieving and evaluating interpretability in any machine learning-based regression or classification problem. / Maskininlärningsbaserade system blir snabbt populära eftersom man har insett att maskiner är effektivare än människor när det gäller att utföra vissa uppgifter. Även om maskininlärningsalgoritmer är extremt populära, är de också mycket bokstavliga. Detta har lett till en enorm forskningsökning inom området tolkbarhet i maskininlärning för att säkerställa att maskininlärningsmodeller är tillförlitliga, rättvisa och kan hållas ansvariga för deras beslutsprocess. Dessutom löser problemet i de flesta verkliga problem bara att göra förutsägelser med maskininlärningsalgoritmer bara delvis. Tidsserier är en av de mest populära och viktiga datatyperna på grund av dess dominerande närvaro inom affärsverksamhet, ekonomi och teknik. Trots detta är tolkningsförmågan i tidsserier fortfarande relativt outforskad jämfört med tabell-, text- och bilddata. Med den växande forskningen inom området tolkbarhet inom maskininlärning finns det också ett stort behov av att kunna kvantifiera kvaliteten på förklaringar som produceras efter tolkning av maskininlärningsmodeller. Av denna anledning är utvärdering av tolkbarhet extremt viktig. Utvärderingen av tolkbarhet för modeller som bygger på tidsserier verkar helt outforskad i forskarkretsar. Detta uppsatsarbete fokuserar på att uppnå och utvärdera agnostisk modelltolkbarhet i ett tidsserieprognosproblem.  Fokus ligger i att hitta lösningen på ett problem som ett digitalt konsultföretag står inför som användningsfall. Det digitala konsultföretaget vill använda en datadriven metod för att förstå effekten av olika försäljningsrelaterade aktiviteter i företaget på de försäljningsavtal som företaget stänger. Lösningen innebar att inrama problemet som ett tidsserieprognosproblem för att förutsäga försäljningsavtalen och tolka den underliggande prognosmodellen. Tolkningsförmågan uppnåddes med hjälp av två nya tekniker för agnostisk tolkbarhet, lokala tolkbara modellagnostiska förklaringar (LIME) och Shapley additiva förklaringar (SHAP). Förklaringarna som producerats efter att ha uppnått tolkbarhet utvärderades med hjälp av mänsklig utvärdering av tolkbarhet. Resultaten av de mänskliga utvärderingsstudierna visar tydligt att de förklaringar som produceras av LIME och SHAP starkt hjälpte människor att förstå förutsägelserna från maskininlärningsmodellen. De mänskliga utvärderingsstudieresultaten visade också att LIME- och SHAP-förklaringar var nästan lika förståeliga med LIME som presterade bättre men med en mycket liten marginal. Arbetet som utförts under detta projekt kan enkelt utvidgas till alla tidsserieprognoser eller klassificeringsscenarier för att uppnå och utvärdera tolkbarhet. Dessutom kan detta arbete erbjuda en mycket bra ram för att uppnå och utvärdera tolkbarhet i alla maskininlärningsbaserade regressions- eller klassificeringsproblem.

Poussé par la demande croissante de services à haut débit sans fil, Long Term Evolution (LTE) a émergé comme une solution prometteuse pour les communications mobiles. Dans plusieurs pays à travers le monde, la mise en oeuvre de LTE est en train de se développer. LTE offre une architecture tout-IP qui fournit des débits élevés et permet une prise en charge efficace des applications de type multimédia. LTE est spécifié par le 3GPP ; cette technologie fournit une architecture capable de mettre en place des mécanismes pour traiter des classes de trafic hétérogènes comme la voix, la vidéo, les transferts de fichier, les courriers électroniques, etc. Ces classes de flux hétérogènes peuvent être gérées en fonction de la qualité de service requise mais aussi de la qualité des canaux et des conditions environnementales qui peuvent varier considérablement sur une courte échelle de temps. Les standards du 3GPP ne spécifient pas l’algorithmique de l’allocation des ressources du réseau d’accès, dont l’importance est grande pour garantir performance et qualité de service (QoS). Dans cette thèse, nous nous focalisons plus spécifiquement sur la QoS de LTE sur la voie descendante. Nous nous concentrons alors sur la gestion des ressources et l’ordonnancement sur l’interface radio des réseaux d’accès. Dans une première partie, nous nous sommes intéressés à des contextes de macro-cellules. Le premier mécanisme proposé pour l’allocation des ressources combine une méthode de jetons virtuels et des ordonnanceurs opportunistes. Les performances obtenues sont très bonnes mais n’assurent pas une très bonne équité. Notre seconde proposition repose sur la théorie des jeux, et plus spécifiquement sur la valeur de Shapley, pour atteindre un haut niveau d’équité entre les différentes classes de services au détriment de la qualité de service. Cela nous a poussé, dans un troisième mécanisme, à combiner les deux schémas. La deuxième partie de la thèse est consacrée aux femto-cellules (ou femtocells) qui offrent des compléments de couverture appréciables. La difficulté consiste alors à étudier et à minimiser les interférences. Notre premier mécanisme d’atténuation des interférences est fondé sur le contrôle de la puissance de transmission. Il fonctionne en utilisant la théorie des jeux non coopératifs. On effectue une négociation constante entre le débit et les interférences pour trouver un niveau optimal de puissance d’émission. Le second mécanisme est centralisé et utilise une approche de division de la bande passante afin d’obliger les femtocells à ne pas utiliser les mêmes sous-bandes évitant ainsi les interférences. Le partage de bande passante et l’allocation sont effectués en utilisant sur la théorie des jeux (valeur de Shapley) et en tenant compte du type d’application. Ce schéma réduit les interférences considérablement. Tous les mécanismes proposés ont été testés et évalués dans un environnement de simulation en utilisant l’outil LTE-Sim au développement duquel nous avons contribué. / Driven by the growing demand for high-speed broadband wireless services, Long term Evolution (LTE) technology has emerged as a competitive alternative to mobile communications solution. In several countries around the world, the implementation of LTE has started. LTE offers an IP-based framework that provides high data rates for multimedia applications. Moreover, based on the 3GPP specifications, the technology provides a set of built in mechanisms to support heterogeneous classes of traffic including data, voice and video, etc. Supporting heterogeneous classes of services means that the traffic is highly diverse and has distinct QoS parameters, channel and environmental conditions may vary dramatically on a short time scale. The 3GPP specifications leave unstandardized the resource management and scheduling mechanisms which are crucial components to guarantee the QoS performance for the services. In this thesis, we evaluate the performance and QoS in LTE technology. Moreover, our research addresses the resource management and scheduling issues on the wireless interface. In fact, after surveying, classifying and comparing different scheduling mechanisms, we propose three QoS mechanisms for resource allocation in macrocell scenarios focused on real time services and two mechanisms for interference mitigation in femtocell scenarios taking into account the QoS of real time services. Our first proposed mechanism for resource allocation in macrocell scenarios combines the well known virtual token (or token buckets) method with opportunistic schedulers, our second scheme utilizes game theory, specifically the Shapley value in order to achieve a higher fairness level among classes of services and our third mechanism combines the first and the second proposed schemes. Our first mechanism for interference mitigation in femtocell scenarios is power control based and works by using non cooperative games. It performs a constant bargain between throughput and SINR to find out the optimal transmit power level. The second mechanism is centralised, it uses a bandwidth division approach in order to not use the same subbands to avoid interference. The bandwidth division and assignation is performed based on game theory (Shapley value) taking into account the application bitrate . This scheme reduces interference considerably and shows an improvement compared to other bandwidth division schemes. All proposed mechanism are performed in a LTE simulation environment. several constraints such as throughput, Packet Loss Ratio, delay, fairness index, SINR are used to evaluate the efficiency of our schemes

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.

abstract: Due to large data resources generated by online educational applications, Educational Data Mining (EDM) has improved learning effects in different ways: Students Visualization, Recommendations for students, Students Modeling, Grouping Students, etc. A lot of programming assignments have the features like automating submissions, examining the test cases to verify the correctness, but limited studies compared different statistical techniques with latest frameworks, and interpreted models in a unified approach. In this thesis, several data mining algorithms have been applied to analyze students’ code assignment submission data from a real classroom study. The goal of this work is to explore and predict students’ performances. Multiple machine learning models and the model accuracy were evaluated based on the Shapley Additive Explanation. The Cross-Validation shows the Gradient Boosting Decision Tree has the best precision 85.93% with average 82.90%. Features like Component grade, Due Date, Submission Times have higher impact than others. Baseline model received lower precision due to lack of non-linear fitting. / Dissertation/Thesis / Masters Thesis Computer Science 2019

This thesis addresses two issues which arise in the context of airline revenue management. In the first part of the thesis, we develop an incentive mechanism to prevent revenue leakage caused by customers buying down. In the second part of the thesis, we discuss the revenue sharing problem between alliance partners and develop a mechanism by which the combined revenue can be distributed fairly among them. Situations which give rise to impossibility and possibility results are established. The practice of revenue management, employs the principle of differential pricing of a product based on various product restrictions. These product restrictions segment the market in such a manner so as to maximize the revenue. Airline industry which pioneered the practice of revenue management generally prices low for those who book early and high for those who book late for essentially the same seat. The low-fare products are targeted towards the market segment comprising of those customers who have a low valuation (reservation price) for the product (who are typically leisure customers, also called as low-fare customers).The high-fare product, on the other hand is targeted at the market segment comprising of customers who have a high valuation (reservation price) for the product (business class customers, also called as high-fare customers). However, it may happen that customers with high valuation for the product may also buy the low-fare product if it is available. This behavior of high-fare customers buying a low-fare product due to its availability is called the customer buy-down behavior. Such a customer behavior causes revenue leakage to the airline industry. Revenue management literature that primarily focuses on pricing and seat inventory control does not account for the customer buy-down behavior. In Part I of the thesis we address this issue of customer buy-down behavior. We develop an incentive mechanism in the form of a new product bundle which would attract only the high-fare customer. High fare customers such as business class customers typically have repeated travel plans, while low fare customers such as leisure travelers typically do not travel repeatedly. The proposed incentive mechanism takes advantage of this characteristic of high fare customers that distinguishes them from the low fare customers. In general, high fare product permits cancellation and does not impose any travel restrictions, and a low fare product, on the other hand does not permit cancellation and has other travel restrictions associated with them. A high fare customer with potential future travel plan might associate uncertainties with respect to travel dates and his ability to procure a low fare ticket for future travel. This uncertainty is exploited in the proposed product bundle. The new product bundle permits the customer to cancel the ticket for the future journey and relaxes the restrictions associated with the requested day and the future travel day. Such incentives would attract only the high fare customer and the low-fare customer will not be enticed by this product bundle. This is because the low fare customer is a one-off traveler. Thus, the acceptance of the product bundle by the customer reveals that he is a high-fare customer and its denial reveals that he is truly a low-fare customer. We determine the optimal price to be charged for each of the days (requested day and the future travel day) and the refund value for the future travel day. We find that multiple optimal solutions exist, and its existence indicate a win-win situation for both the customer and the seller. The customer benefits through the incentives offered and the seller benefits in the form of additional revenue that is achieved in the process of preventing revenue leakage. In Part II of the thesis, we discuss the revenue sharing problem between alliance partners of a network. Airlines form alliances and coordinate through activities such as code sharing, scheduling of flight arrival and departure times, arrival and departure gates, frequent flyer programs, airport lounges and ground facilities among several others. Code sharing is a key feature among the coordinated activities of alliance partners. Parallel code sharing refers to code sharing between carriers operating on the same route to increase frequency of services and to strengthen market position. Complementary code sharing refers to carriers using each other’s flights to provide connecting services, where they do not offer a full service on their own. The main objective of the complementary code share flights is to increase scope of the partner’s network, allowing them to supply service on markets where they did not operate before. When complementary code shared flights aim at maximizing their combined revenue, it might lead to inequitable distribution of revenue and may cause an alliance partner to lose revenue. In Part II of the thesis, we address this issue of achieving a fair division of the combined revenue generated by the alliance network. The common assumption in revenue sharing methods that are generally practiced is that airline’s valuation of seats in the alliance network is common knowledge. However, in reality it is not true. We therefore consider the valuations of the carriers of their respective products as private information and the price of the product over the entire network to be common knowledge. Under such an information environment, we formulate the problem in the bargaining framework. We discuss the implementation of two solution concepts; namely the Shapley value and the Core of a cooperative game. For the two person cooperative game, the Shapley value equally distributes the surplus among the two parties, while the core allocations of two person cooperative game consists of all possible proportions of the distribution of the surplus. In a bargaining set up, the parties communicate their valuations through sealed bids and agree upon a transfer rule. We analyze two situations. In the first situation we assume that the two parties do not associate any cost towards failure to arrive at an agreement. We determine the optimal bids for the two parties and prove that these optimal bids do not implement any desired point on the core i.e., desired proportion of the distribution of the surplus (which includes the Shapley value).This impossibility result motived the analysis of the second situation, in which we assume that the two parties associate costs towards failure to arrive at an agreement. We once again determine the optimal bids and prove that for a certain structure of the bargaining costs, any desired point on the core, including the Shapley value can be implemented by enticing the players to reveal their true valuations.

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.