Measures of epistemic utility are used by formal epistemologists to make determinations of epistemic betterness among cognitive states. The Brier rule is the most popular choice (by far) among formal epistemologists for such a measure. In this paper, however, we show that the Brier rule is sometimes seriously wrong about whether one cognitive state is epistemically better than another. In particular, there are cases where an agent gets evidence that definitively eliminates a false hypothesis (and the probabilities assigned to the other hypotheses stay in the same ratios), but where the Brier rule says that things have become epistemically worse. Along the way to this 'elimination experiment' counter-example to the Brier rule as a measure of epistemic utility, we identify several useful monotonicity principles for epistemic betterness. We also reply to several potential objections to this counter-example.

Fair division is the problem of dividing one or several goods among a set of agents in a way that satisfies a suitable fairness criterion. Traditionally studied in economics, philosophy, and political science, fair division has drawn a lot of attention from the multiagent systems community, since this field is strongly concerned about how a surplus (or a cost) should be divided among a group of agents. Arguably, the Shapley value is the single most important contribution to the problem of fair division. It assigns to each agent a share of the resource equal to the expected marginal contribution of that agent. Thus, it is implicitly assumed that individual marginal contributions can be objectively computed. In this thesis, we propose a game-theoretic model for sharing a joint reward when the quality of individual contributions is subjective. In detail, we consider scenarios where a group has been formed and has accomplished a task for which it is granted a reward, which must be shared among the group members. After observing the contribution of the peers in accomplishing the task, each agent is asked to provide evaluations for the others. Mainly to facilitate the sharing process, agents can also be requested to provide predictions about how their peers are evaluated. These subjective opinions are elicited and aggregated by a central, trusted entity, called the mechanism, which is also responsible for sharing the reward based exclusively on the received opinions. Besides the formal game-theoretic model for sharing rewards based on subjective opinions, we propose three different mechanisms in this thesis. Our first mechanism, the peer-evaluation mechanism, divides the reward proportionally to the evaluations received by the agents. We show that this mechanism is fair, budget-balanced, individually rational, and strategy-proof, but that it can be collusion-prone. Our second mechanism, the peer-prediction mechanism, shares the reward by considering two aspects: the evaluations received by the agents and their truth-telling scores. To compute these scores, this mechanism uses a strictly proper scoring rule. Under the assumption that agents are Bayesian decision-makers, we show that this mechanism is weakly budget-balanced, individually rational, and incentive-compatible. Further, we present approaches that guarantee the mechanism to be collusion-resistant and fair. Our last mechanism, the BTS mechanism, is the only one to elicit both evaluations and predictions from the agents. It considers the evaluations received by the agents and their truth-telling scores when sharing the reward. For computing the scores, it uses the Bayesian truth serum method, a powerful scoring method based on the surprisingly common criterion. Under the assumptions that agents are Bayesian decision-makers, and that the population of agents is sufficiently large so that a single evaluation cannot significantly affect the empirical distribution of evaluations, we show that this mechanism is incentive-compatible, budget-balanced, individually rational, and fair.

<p> Probability forecasts play an important role in many decision and risk analysis applications. Research and practice over the years have shown that the shift towards distributional forecasts provides a more accurate and appropriate means of capturing risk in models for these applications. This means that mathematical tools for analyzing the quality of these forecasts, may it come from experts, models or data, become important to the decision maker. In this regard, strictly proper scoring rules have been widely studied because of their ability to encourage assessors to provide truthful reports. This dissertation contributes to the scoring rule literature in two main areas of assessment - probability forecasts and quantile assessments. </p><p>In the area of probability assessment, scoring rules typically studied in the literature, and commonly used in practice, evaluate probability assessments relative to a default uniform measure. In many applications, the uniform baseline used to represent some notion of ignorance is inappropriate. In this dissertation, we generalize the power and pseudospherical family of scoring rules, two large parametric families of commonly-used scoring rules, by incorporating the notion of a non-uniform baseline distribution for both the discrete and continuous cases. With an appropriate normalization and choice of parameters, we show that these new families of scoring rules relate to various well-known divergence measures from information theory and to well-founded decision models when framed in an expected utility maximization context. </p><p>In applications where the probability space considered has an ordinal ranking between states, an important property often considered is sensitivity to distance. Scoring rules with this property provide higher scores to assessments that allocate higher probability mass to events “closer” to that which occurs based on some notion of distance. In this setting, we provide an approach that allows us to generate new sensitive to distance strictly proper scoring rules from well-known strictly proper binary scoring rules. Through the use of the weighted scoring rules, we also show that these new scores can incorporate a specified baseline distribution, in addition to being strictly proper and sensitive to distance. </p><p>In the inverse problem of quantile assessment, scoring rules have not yet been well-studied and well-developed. We examine the differences between scoring rules for probability and quantile assessments, and demonstrate why the tools that have been developed for probability assessments no longer encourage truthful reporting when used for quantile assessments. In addition, we shed light on new properties and characterizations for some of these rules that could guide decision makers trying to choosing an appropriate scoring rule. </p> / Dissertation

In this thesis I offer new results on how we can acquire, reward, and use accurate predictions of future events. Some of these results are entirely theoretical, improving our understanding of strictly proper scoring rules (Chapter 3), and expanding strict properness to include cost functions (Chapter 4). Others are more practical, like developing a practical cost function for the [0, 1] interval (Chapter 5), exploring how to design simple and informative prediction markets (Chapter 6), and using predictions to make decisions (Chapter 7). / Engineering and Applied Sciences

Fair division is the problem of dividing one or several goods among a set of agents in a way that satisfies a suitable fairness criterion. Traditionally studied in economics, philosophy, and political science, fair division has drawn a lot of attention from the multiagent systems community, since this field is strongly concerned about how a surplus (or a cost) should be divided among a group of agents. Arguably, the Shapley value is the single most important contribution to the problem of fair division. It assigns to each agent a share of the resource equal to the expected marginal contribution of that agent. Thus, it is implicitly assumed that individual marginal contributions can be objectively computed. In this thesis, we propose a game-theoretic model for sharing a joint reward when the quality of individual contributions is subjective. In detail, we consider scenarios where a group has been formed and has accomplished a task for which it is granted a reward, which must be shared among the group members. After observing the contribution of the peers in accomplishing the task, each agent is asked to provide evaluations for the others. Mainly to facilitate the sharing process, agents can also be requested to provide predictions about how their peers are evaluated. These subjective opinions are elicited and aggregated by a central, trusted entity, called the mechanism, which is also responsible for sharing the reward based exclusively on the received opinions. Besides the formal game-theoretic model for sharing rewards based on subjective opinions, we propose three different mechanisms in this thesis. Our first mechanism, the peer-evaluation mechanism, divides the reward proportionally to the evaluations received by the agents. We show that this mechanism is fair, budget-balanced, individually rational, and strategy-proof, but that it can be collusion-prone. Our second mechanism, the peer-prediction mechanism, shares the reward by considering two aspects: the evaluations received by the agents and their truth-telling scores. To compute these scores, this mechanism uses a strictly proper scoring rule. Under the assumption that agents are Bayesian decision-makers, we show that this mechanism is weakly budget-balanced, individually rational, and incentive-compatible. Further, we present approaches that guarantee the mechanism to be collusion-resistant and fair. Our last mechanism, the BTS mechanism, is the only one to elicit both evaluations and predictions from the agents. It considers the evaluations received by the agents and their truth-telling scores when sharing the reward. For computing the scores, it uses the Bayesian truth serum method, a powerful scoring method based on the surprisingly common criterion. Under the assumptions that agents are Bayesian decision-makers, and that the population of agents is sufficiently large so that a single evaluation cannot significantly affect the empirical distribution of evaluations, we show that this mechanism is incentive-compatible, budget-balanced, individually rational, and fair.

This thesis deals with ranked advanced voting systems. The aim is to determine the overall winner and the ranking of candidates based on voters' preferences. The thesis utilises basic voting systems - plurality rules, lexicographical and Borda's method - as well as advanced voting systems with the application of DEA models, specifically DEA/AR model, DEA/AR exclusion model (including variations with penalties), and Llamazares-Peňa model. Compromise programming is used to obtain common vector of weights. The models and their use are demonstrated on Formula One Grand Prix results from season 2016. Formula One World Drivers' Championship and Formula One World Constructors' Championship are being investigated.

L’apport principal de cette thèse réside dans l’évaluation de la vulnérabilité d’un certain nombre de règles de voteà la violation de deux propriétés ; nous nous appuyons pour cela sur l’approche axiomatique de la théorie du choixsocial, qui permet d’étudier le comportement d’un mécanisme de choix social vis-à-vis d’un jugement de valeurémis par l’économiste. La symétrie inverse ("reversal symmetry") est la première propriété examinée. A la suite destravaux de Saari [150], nous évaluons deux catégories de règles de vote en prenant cette propriété comme critèrede décision : d’une part, les règles positionnelles simples et d’autre part les règles positionnelles à deux tours. Plusprécisément, nous calculons la probabilité d’occurrence de ce phénomène à la fois en domaine universel (c’est-à-direlorsque les individus peuvent exprimer n’importe quel ordre de préférence), et en domaine restreint (lorsque deshypothèses supplémentaires sont introduites sur la manière dont les votants classent les « candidats » à l’élection).Nous examinons le cas de trois candidats, de quatre candidats ainsi que le contexte d’élections à un très grandnombre de votants, en faisant tendre ce nombre vers l’infini.La seconde thématique est consacrée à l’examen du comportement de la règle de Dodgson face à la propriété d’homogénéité.Nous proposons une méthode de calcul simple et systématique du score de Dodgson. Nous distinguonsensuite différentes classes de profils pour lesquels cette règle est susceptible d’être vulnérable à cette propriété. Afinde compléter notre recherche, des fréquences de violation de cette propriété par la règle de Dodgson sont fournies. / The contribution of this thesis lies in the evaluation of the vulnerability of a number of voting rules to the violationof two properties of the theory of social choice. We rely on the axiomatic approach of social choice theory to examinethe behavior of a social choice procedure according to a value judgment (or axiom) emitted by the economist.Reversal symmetry is the first property studied. Following the works of Saari [150], we evaluate two families ofvoting by using this property as the decision criterion : the simple scoring rules on the one hand, and the scoringrules with runoff on the other hand. We do probability calculations to evaluate how frequent this phenomenon is,in the three-candidate case under universal domain as well as under a restricted domain, and we also tackle thefour-candidate case and the infinite number of voters case.The second topic is devoted to the study of the Dodgsonrule according to the homogeneity axiom. We introduce a simple and systematic method for the computation ofthe Dodgson score. We distinguish various classes of profiles at which that rule may be vulnerable to this property.Further, frequencies of violation of this property by the Dodgson rule are provided.

Over the past decade, the explosive growth of the Internet has led to a surge of interest to understand and predict aggregate behavior of large number of people or agents, particularly when they are connected through an underlying network structure. Numerous Internet-based applications have emerged that are as diverse as getting micro-tasks executed through online labor markets (also known as crowd sourcing) to acquiring new skills through massively open online courses (also known as MOOCs). However, there has been a major inadequacy in existing studies with respect to evaluating the impact of strategic behavior of the agents participating in such networks, crowds, and classrooms. The primary focus of this doctoral work is to understand the equilibrium behaviour emerging from these real-world, strategic environments by blending ideas from the areas of game theory, graph theory, and optimization, to derive novel solutions to these new-age economic models. In particular, we investigate the following three research challenges: (1) How do strategic agents form connections with one another? Will it ever happen that strategically stable networks are social welfare maximizing as well? (2) How do we design mechanisms for eliciting truthful feedback about an object (perhaps a new product or service or person) from a crowd of strategic raters? What can we tell about these mechanisms when the raters are connected through a social network? (3) How do we incentivize better participation of instructors and students in online edu-cation forums? Can we recommend optimal strategies to students and instructors to get the best out of these forums?