Belief as Willingness to Bet

We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\geq\frac 12$. Identifying knowledge with the former and belief with the latter, we may think of $c$ as the agent's betting threshold, which leads to the motto "belief is willingness to bet." The logic $\mathsf{KB.5}$ for $c=\frac 12$ has an $\mathsf{S5}$ $K$ modality along with a sub-normal $B$ modality that extends the minimal modal logic $\mathsf{EMND45}$ by way of four schemes relating $K$ and $B$, one of which is a complex scheme arising out of a theorem due to Scott. Lenzen was the first to use Scott's theorem to show that a version of this logic is sound and complete for the probability interpretation. We reformulate Lenzen's results and present them here in a modern and accessible form. In addition, we introduce a new epistemic neighborhood semantics that will be more familiar to modern modal logicians. Using Scott's theorem, we provide the Lenzen-derivative properties that must be imposed on finite epistemic neighborhood models so as to guarantee the existence of a probability measure respecting the neighborhood function in the appropriate way for threshold $c=\frac 12$. This yields a link between probabilistic and modal neighborhood semantics that we hope will be of use in future work on modal logics of qualitative probability. We leave open the question of which properties must be imposed on finite epistemic neighborhood models so as to guarantee existence of an appropriate probability measure for thresholds $c\neq\frac 12$.Comment: Removed date from v1 to avoid confusion on citation/reference, otherwise identical to v

Estimating Risk Preferences in the Field

We survey the literature on estimating risk preferences using field data. We concentrate our attention on studies in which risk preferences are the focal object and estimating their structure is the core enterprise. We review a number of models of risk preferences—including both expected utility (EU) theory and non-EU models—that have been estimated using field data, and we highlight issues related to identification and estimation of such models using field data. We then survey the literature, giving separate treatment to research that uses individual-level data (e.g., property insurance data) and research that uses aggregate data (e.g., betting market data). We conclude by discussing directions for future research

Is Justification Necessary for Knowledge?

Justification has long been considered a necessary condition for knowledge, and theories that deny the necessity of justification have been dismissed as nonstarters. In this chapter, we challenge this long-standing view by showing that many of the arguments offered in support of it fall short and by providing empirical evidence that individuals are often willing to attribute knowledge when epistemic justification is lacking

The Impact of Motivational Factors on Daily Fantasy Sports Participation

Since the passing of the Unlawful Internet Gambling Act (UIGEA) in 2006, the fantasy sports world has had a tumultuous decade. Shortly after the passing of UIGEA, daily fantasy sports became marketable, and saw several years of tremendous growth. However, recent legal issues have clouded the industry, and lawmakers have questioned whether daily fantasy sports indeed fall under the exception granted by UIGEA as a “game of skill”, or whether the games are illegal gambling. This study is meant to look at what motivates fantasy sports participants, especially through this time of turmoil in the industry. It specifically looks at how players’ competitive, knowledge-seeking, or social tendencies affect their participation habits. Additionally, this thesis explores the effect that marketing messaging that portrays a daily fantasy sports website as a perfect place to satisfy these individual traits has on player participation. Finally, this study investigates the role that a sense of fairness plays in shaping players’ perceptions of these websites. To study these things, we began by looking at previous studies that focus on competition, knowledge, and social factors, both in the fantasy sports field and elsewhere, and creating a literature review. Following the literature review, an experiment was created, which tested these three scales as well as the perception of fairness, using a fictitious fantasy sports site, Fantasyland. The results obtained from this experiment indicate that those with competitive or social dispositions are the most likely to try fantasy sports. Additionally, it was found that those who are socially motivated are more likely to recommend a fantasy sports site to friends or strangers. Lastly, the perception of fairness did not have a direct effect of participants, although in one case, it did positively impact an individual’s willingness to try a daily sports website. These results and their implications as well as future research directions are outlined in the concluding discussion section

Common Knowledge and Interactive Behaviors: A Survey

This paper surveys the notion of common knowledge taken from game theory and computer science. It studies and illustrates more generally the effects of interactive knowledge in economic and social problems. First of all, common knowledge is shown to be a central concept and often a necessary condition for coordination, equilibrium achievement, agreement, and consensus. We present how common knowledge can be practically generated, for example, by particular advertisements or leadership. Secondly, we prove that common knowledge can be harmful, essentially in various cooperation and negotiation problems, and more generally when there are con icts of interest. Finally, in some asymmetric relationships, common knowledge is shown to be preferable for some players, but not for all. The ambiguous welfare effects of higher-order knowledge on interactive behaviors leads us to analyze the role of decentralized communication in order to deal with dynamic or endogenous information structures.Interactive knowledge, common knowledge, information structure, communication.

Consumer optimism and price discrimination

In many principal-agent environments, the two parties hold different prior beliefs regarding the agent's future preferences. These differences may be due to inherent biases such as over-optimism or over-pessimism. We analyze the principal's optimal contract design under the assumption that the agent's prior is private information. In order to screen the agent's prior, the principal devises a menu of contingent contracts, some of which are 'speculative' as they involve betting on the agent's future action. We characterize the optimal menu and show that the characterization enables us to interpret real-life contract design in a variety of economic contexts

Risk, ambiguity and quantum decision theory

In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do not follow the classic laws of probability theory. In particular, we show that it is possible to use consistently the classic expected utility formula, where the probability associated to the events are computed with the equation of quantum interference. Thus we show that the correct utility of a lottery can be simply computed by adding to the classic expected utility a new corrective term, the uncertainty utility, directly connected with the quantum interference term.Comment: 1 figur

Making Conditional Speech Acts in the Material Way

The conventional wisdom about conditionals claims that (1) conditionals that have non-assertive acts in their consequents, such as commands and promises, cannot be plausibly interpreted as assertions of material implication; (2) the most promising hypothesis about those sentences is conditional-assertion theory, which explains a conditional as a conditional speech act, i.e., a performance of a speech act given the assumption of the antecedent. This hypothesis has far-reaching and revisionist consequences, because conditional speech acts are not synonymous with a proposition with truth conditions. This paper argues against this view in two steps. First, it presents a battery of objections against conditional-assertion theory. Second, it argues that those examples can be convincingly interpreted as assertions of material implication