Muth’s Rational Expectations Hypothesis, That “…The Subjective Probability Distributions Are Distributed Around an Objective Probability Distribution, for a given Information Set…” is an Oxymoron. It Can Be Corrected by Amending It to Read “…The Subjective Probability Distributions Are Distributed Around a Subjective Consensus Probability Distribution, for a given Information Set…”

George Box’s Realization, That All Models, Especially Statistical Models, Are Wrong Means That It Is Impossible for There to Be Any True Probabilities, True Models, True Theories, True Expectations or True (Accepted) Hypotheses: The Claims, Made By Rational Expectations Proponents About True Objective Probabilities, True Models, True Expectations, True Expected Values, etc., Have No Scientific Foundation

We introduce a new type of fuzzy set called Fuzzy Distribution Set (FDS). Fuzzy distribution sets are fuzzy sets defined on a finite domain subject to a sum of membership values equal to 1. Such fuzzy sets can serve as models of subjective probability distributions and subjective weight distributions. Considering these distributions as fuzzy sets gives a possibility to extend on such distributions the operations of fuzzy sets and, more generally, the calculus of fuzzy restrictions developed during the last decades. Recently Yager introduced the concept of negation of probability distributions. In our works, we studied several classes of such negations. Here we consider an involutive negation of probability distributions as a complement of FDS. We introduce the operations of union and intersection of fuzzy distribution sets. These basic operations on FDS can serve as a basis for the application of fuzzy logic methods to subjective probability and weight distributions. These operations can be used for the development of reasoning models with subjective probability distributions and subjective weighting functions. Weight distributions can be used in multi-criteria, multi-person, and multi-attribute decision-making models.

Overconfidence in Probability Distributions: People Know They Don’t Know but They Don’t Know What to Do About It

Professor Smith's article “Ranking Procedures and Subjective Probability Distribution” (Smith, L. H. 1967. Ranking procedures and subjective probability distributions. Management Sci. 14 (4, December) B-236–B-249.) is a worthwhile attempt at making the Bayesian decision theory concepts more operational; however, he has fallen far short of this objective. The example he chose (obtaining a subjective probability distribution on market share) is in many ways inappropriate for Smith's technique, and although his procedure is more “mathematical” than some existing methods, it is not as relevant. There are some relatively minor points in Smith's article on which one might quibble, but there are also enough major, substantive matters that we will direct our critique to these issues.

Expert elicitation of directional metocean parameters

In Ch. 8, I distinguished epistemic probability from objective probability and then pointed out some debilitating problems with the three main accounts of epistemic probability. In this chapter, I propose my own account of epistemic probability. I first distinguish between two sides to epistemic probability, which I call the objective component and the normative component. In typical cases where we assert that some proposition is epistemically probable, two things get asserted: that the proposition is objectively probable with respect to the evidence (the objective component), and that it is rational (or reasonable) to place a high degree of confidence in the proposition, given the circumstances of having as evidence what in fact we do have as evidence (the normative component). Attempting to unpack these two components (especially the second), I sketch the view that (roughly) the normative component of the epistemic conditional probability of A on B is the interval containing the degrees of belief a rational person could have in A, provided she believed B and was aware that she believed B, considered the evidential bearing of B on A, had no other source of warrant for B or its denial, and had no defeater for the warrant, if any, accruing to A or its denial by virtue of being thus believed on the basis of B.

In Service-Oriented Computing (SOC) environments, the trustworthiness of each service provider is critical for a service client when selecting one from a large pool of service providers. The trust value of a service provider is usually in the range of [0, 1] and is evaluated from the ratings given by service clients, which represent the subjective belief of service clients on the satisfaction of delivered services. So a trust value can be taken as a subjective probability, by which one party believes that another party can perform an action in a certain situation. Hence, subjective probability theory should be adopted in trust evaluation. In addition, in SOC environments, a service provider usually can invoke the services from other service providers forming a composite service. Thus, the global trust of a composite service should be evaluated based on both the subjective probability property of trust and complex invocation structures. In this paper, we first interpret the trust dependency caused by direct service invocations as conditional probability. Then, on the basis of trust dependency, we propose a Subjective probability based deductive (SELECTIVE) approach to evaluate the subjective global trustworthiness of a composite service. All these processes follow subjective probability theory and keep the subjective probability property of trust in evaluations. Our experimental results demonstrate that when compared with existing approaches our proposed SELECTIVE approach can yield more reasonable results.

In the concept of Nash equilibrium and its refinements, players are assumed to be informed about the opponents’ subjective probability distributions about the other players’ strategy choices. In this chapter we investigate the implications of dropping this assumption, while maintaining the assumption that players are informed about the opponents’ utility functions at the terminal nodes. The key concept in this chapter is rationalizability, as each of the other concepts discussed subsequently is based upon it.KeywordsNash EquilibriumExtensive FormCommon BeliefStrategy ChoiceStrategy ProfileThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Capital Asset Pricing Model as Modern Austrian Business Cycle Theory

predicting sea surface temperature (SST) and atmospheric pressure anomalies in the eastern Pacific, culminating in the early, widely publicized forecast of the 1997-98 ENSO event. Now ENSOmania has swept the globe. Agricultural and resource economists have a special interest in ICF because these sectors are especially affected by climatic fluctuations. In commenting on the three papers in this session, I make five interrelated points about the economics of climate forecasting. First, El Nifio is heavily overhyped because forecast skill with respect to ENSO phase is not the same as the ability to forecast ENSO's impacts on variables of direct interest to decision makers. The papers by Mjelde, Hill, and Griffiths (MHG) and by Podbury, Sheales, Hussain, and Fisher (PSHF) explore different dimensions of this point. Forecasts have value only if they alter decision makers' subjective probability distributions over stochastic variables that influence choice. Few people care directly about SSTs or atmospheric pressure over the eastern equatorial Pacific (i.e., ENSO events). Even among Peruvian fishermen, interest in ENSO is indirect in its imperfectly understood effects on the spatial and temporal distribution of fish populations. For most people, ENSO forecasts are mediated by predicted climate teleconnections, the relationship between local climate and distant ocean temperature and pressure anomalies. Such links are statistically strong in relatively few places and only at coarse spatial and temporal resolution. Moreover, few choices are based directly on climate. Rather, climate has indirect effects on decisions through its relation to crop yields, livestock productivity, food prices, stream flow, and so on. Because ENSO forecast information is only of indirect interest to decision makers, its value is conditioned by the robustness of the mediating inferences, with forecast errors compounding in a complex fashion to the point where they might not change subjective probability distributions.

Probability estimation and information principles

This paper reports survey evidence on long-term care (LTC) risk misperceptions and demand for long-term care insurance (LTCI) in Canada. We study three LTC risks: needing help with at least one activity of daily living, needing access to a nursing home, and living to the age of 85. We contrast subjective (stated) probabilities with objective (predicted) probabilities for these three dimensions, and define misperceptions as the differences between them. We first provide descriptive statistics about objective and subjective probabilities. We then analyse how risk misperceptions correlate with individual characteristics and how they affect intentions and actual purchase of LTCI. We find that although misperceptions significantly affect both intention to buy LTCI and actual purchase of LTCI, they cannot explain the low take-up rate of LTCI in our sample. Correcting simultaneously the perceptions of LTC risks on the three dimensions would increase LTCI take-up by at most one percentage point.

Evaluating the relationship between health at old age and income is crucial for the design of equitable public policies targeted toward the elderly. Using 2016 Canadian survey data on adults aged between 50 and 70, we estimate the relationships between individual income, longevity and dependency at the old age. We use both subjective and objective measures of the probability to survive to age 85, of the probability to have activities of daily living (ADL) limitations, and of the probability of entering a nursing home. We find that income and the (objective and subjective) probability to live to age 85 and over are positively related while income and the (objective and subjective) probability to suffer from ADL limitations are negatively related. We also find that while the objective probability to enter a nursing home is negatively correlated with income, the subjective probability is positively correlated with income. Most of our results are driven by individuals in the highest tercile of the income distribution. Our results are robust to different sensitivity checks.

Journal Article Why Probabilities Are Not Assigned to Propositions Get access A. A. DERKSEN A. A. DERKSEN UNIVERSITY OF NIJMEGEN Search for other works by this author on: Oxford Academic Google Scholar Mind, Volume LXXXVII, Issue 2, 1978, Pages 250–255, https://doi.org/10.1093/mind/LXXXVII.2.250 Published: 01 January 1978

The paper takes the Abstract Principal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of both classical an non-classical (quantum) probability measure spaces. It is proved that the Abstract Principal Principle is weakly and strongly consistent both in the classical and non-classical cases. It is argued that it is desirable to strengthen the Abstract Principal Principle by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined, and the strong consistency of the Abstract Principal Principle is interpreted as necessary for a non-omniscient Bayesian agent to be able to have rational degrees of belief in all epistemic situations. We give a proof of weak consistency of the Stable Abstract Principal Principle in the framework of classical probability theory, a proof which is different from the proof in Bana (Philos Sci, 2016, forthcoming). Formulation and investigation of the status of a Stable Abstract Principal Principle in quantum probability spaces remains for further study.