Choquet utility depending on the state of nature

This article, which is part of the general framework of mathematics applied to economics, is a decision-making model in total ignorance. Such an environment is characterized by the absence of a law of distribution of the states of nature allowing having good forecasts or anticipations. Based primarily on the integral of Choquet, this model allows aggregating the different states of nature in order to make a better decision. This integral of Choquet imposes itself with respect to the complexity of the environment and also by its relevance of aggregation of the interactive or conflicting criteria. The present model is a combination of the Schmeidler model and the Brice Mayag algorithm for the determination of Choquet 2-additive capacity. It fits into the framework of subjective models and provides an appropriate response to the Ellsberg paradox. Cet article qui s'inscrit dans le cadre général des mathématiques appliquées à l'économie est un modèle de prise de décision dans l'ignorance totale. Un tel environnement est caractérisé par l'absence d'une loi de distribution des états de la nature permettant d'avoir des bonnes prévisions ou anticipations. Se basant principalement sur l'intégrale de Choquet, ce modèle permet d'agréger les différents états de la nature afin de prendre une meilleure décision. Cette intégrale de Choquet s'impose par rapport à la complexité de l'environnement et aussi par son caractère pertinent d'agrégation des critères interactifs ou conflictuels. Le présent modèle est une combinaison du modèle de Schmeidler et de l'algorithme de Brice Mayag pour la détermination de la capacité 2-additive de Choquet. Il s'inscrit dans le cadre des modèles subjectifs et apporte une réponse appropriée au paradoxe d'Ellsberg.

The State of Nature

The chapter assumes that the state of nature is the state of the world prior to the existence of social rules, and then goes on to argue for the following claims. (1) We have reasons for action in the state of nature. (2) In those state of nature worlds in which we all know what reasons for action we have and are motivated to act on them—for short, those worlds in which we are ideal—these reasons for action would support our exiting the state of nature, that is, our creating and maintaining certain social rules. (3) The social rules we have reasons to create would include social rules telling us what to do in both worlds in which we are ideal and nearby worlds in which we are non-ideal. (4) These need not be rules that we have any reason to abide by in the actual world in which we are non-ideal. (5) Thinking about the role of social rules in fixing what we have reason to do in those states of nature in which we are ideal and non-ideal suggests a complicated and novel story about what we have knowledge of, insofar as we have knowledge of what we have reason to do in the actual world in which social rules exist willy-nilly.

Optimizing voting order on sequential juries: a median voter theorem and beyond

We consider an odd-sized “jury”, which votes sequentially between two equiprobable states of Nature (say A and B, or Innocent and Guilty), with the majority opinion determining the verdict. Jurors have private information in the form of a signal in $$[-1,+1]$$ [ - 1 , + 1 ] , with higher signals indicating A more likely. Each juror has an ability in [0, 1], which is proportional to the probability of A given a positive signal, an analog of Condorcet’s p for binary signals. We assume that jurors vote honestly for the alternative they view more likely, given their signal and prior voting, because they are experts who want to enhance their reputation (after their vote and actual state of Nature is revealed). For a fixed set of jury abilities, the reliability of the verdict depends on the voting order. For a jury of size three, the optimal ordering is always as follows: middle ability first, then highest ability, then lowest. For sufficiently heterogeneous juries, sequential voting is more reliable than simultaneous voting and is in fact optimal (allowing for non-honest voting). When average ability is fixed, verdict reliability is increasing in heterogeneity. For medium-sized juries, we find through simulation that the median ability juror should still vote first and the remaining ones should have increasing and then decreasing abilities.

Summarized distributions of mass: a statistical approach to consumers’ consumption spaces

This paper focuses on logical aspects of choices being made by the consumer under conditions of uncertainty or certainty. Such logical aspects are found out to be the same. Choices being made by the consumer that should maximize her subjective utility are decisions studied by revealed preference theory. A finite number of possible alternatives is considered. They are mutually exclusive propositions identifying all quantitative states of nature of a consumption plan. Each proposition of it is expressed by a real number. This research work distinguishes it from its temporary truth value depending on the state of information and knowledge of the consumer. Since each point of the consumption space of the consumer belongs to a two-dimensional convex set, this article focuses on conjoint distributions of mass. Indeed, the consumption space of the consumer is generated by all coherent summaries of a conjoint distribution of mass. Each point of her consumption space is connected with a weighted average of states of nature of two consumption plans jointly studied. They give rise to a conjoint distribution of mass. The consumer chooses a point of a two-dimensional convex set representing that bundle of goods actually demanded by her inside of her consumption space. This paper innovatively shows that it is nothing but a bilinear and disaggregate measure. It is decomposed into two real numbers, where each real number is a linear measure. In this paper, different measures are obtained. They can be disaggregate or aggregate measures, where the latter are independent of the notion of ordered pair of consumption plans.

Entrepreneurial Beliefs and Agency under Knightian Uncertainty

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later.

Fuzzy sets theory and applications in engineering economy: A literature review

Engineering economics is an essential issue in investments and can be quietly difficult to make decisions especially in indefinite, vague and incomplete environments because of human thought. Usage of fuzzy sets gives better solutions in vagueness. Fuzzy sets could be an agreeable tool when no probabilities are accessible for states of nature and decisions are given under incompleteness. In this study, fuzzy engineering economics studies are summarized for showing fuzzy sets usage in engineering economics applications and finding gaps for future studies. The possible suggested are given in conclusion.

Role and relation in Confucian IR: Relating to strangers in the states of nature

The literature on International Relations theory has yet to align relational theory with role theory, despite the fact that these two theories share so much epistemological common ground. This article uses role theory to bridge the gap between the Confucian and Western conceptions of relationality, whose practitioners regard each other as strangers. With the support of role theory, the comparative analysis of relationality in this article has mainly focused on two different types of relations: prior rule-based relations and improvised relations. The differences in the cultural preparation for these two relations partially explain the plurality of the relational universe and the perception of stranger. Role theory is one way to reconnect the seemingly irreconcilable relational universes. To illustrate the value of a composite agenda of relational theory and role theory, the article will use Kim Jong-un of North Korea as its case. Confucian relations propose that, for all nations, the necessity of having a certain role relation is a more important agenda than insisting on exactly what role to take.

Path-Dependence

The intertemporal linkages that both constrain and enable an organization are central to its adaptive properties. The most narrow expression of path-dependence is the process of state-dependence—having a particular asset stock at one point in time impacts the distribution of asset stocks that can be reached at a subsequent period. Development, how an organizational form unfolds over time, can change those dynamics. A considerable literature has sprung up around the idea of “dynamic capabilities.” This broad idea is broken down into five distinct facets: accessibility of organizational states, robustness of organizations to changes in the state of nature, capacity to influence future states of “nature,” cost of accessing future sets of attributes, and capacity to value the set of organizational attributes. However, this discourse tends to treat “capabilities” as isolated attributes and not to view the organization as a complex adaptive system, a perspective developed here.

Default and determinacy under quantitative easing

We show that the path of inflation under quantitative easing policies that target interest rates, is determinate in the presence of default. We achieve this through different payoff profiles that a collateralised defaultable bond achieves in different states of nature with distinct default outcomes. In the model, heterogeneous households trade this bond and other shorter maturity risk-free bonds to maximize their intertemporal utility of consumption and labour. The differentiated payoffs of the collateralised bond, in an equilibrium with active default, span the full state space giving determinacy of prices and inflation as an outcome. This, implies that quantitative easing as implemented by the ECB in the recent years, can control the stochastic path of inflation.