Subjective probabilities and values of socio-economic events at different degrees of uncertainty

Abstract.— The relationship between values (negative] positive) and subjective probabilities was studied. Stimuli consisted of unique socio-economic events represented in the political discussion in Finland. Uncertainty was measured as hesitation in estimating probabilities, The results indicated different relationships between values and probability estimates at different degrees of uncertainty. At certainty the relation was u-shaped, at some uncertainty the variables were nearly uncorrelated, and at uncertainty an linear relationship between values and subjective probabilities was found.     

Decision by sampling: The role of the decision environment in risky choice

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts.     

A Logic For Inductive Probabilistic Reasoning

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone.     

Decision by sampling

We present a theory of decision by sampling (DbS) in which, in contrast with traditional models, there are no underlying psychoeconomic scales. Instead, we assume that an attribute's subjective value is constructed from a series of binary, ordinal comparisons to a sample of attribute values drawn from memory and is its rank within the sample. We assume that the sample reflects both the immediate distribution of attribute values from the current decision's context and also the background, real-world distribution of attribute values. DbS accounts for concave utility functions; losses looming larger than gains; hyperbolic temporal discounting; and the overestimation of small probabilities and the underestimation of large probabilities.     

Hierarchical Bayesian parameter estimation for cumulative prospect theory

Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and subjective probabilities. In practical applications of CPT, the model’s parameters are usually estimated using a single-participant maximum likelihood approach. The present study shows the advantages of an alternative, hierarchical Bayesian parameter estimation procedure. Performance of the procedure is illustrated with a parameter recovery study and application to a real data set. The work reveals that without particular constraints on the parameter space, CPT can produce loss aversion without the parameter that has traditionally been associated with loss aversion. In general, the results illustrate that inferences about people’s decision processes can crucially depend on the method used to estimate model parameters.     

SUBJECTIVISM,UTILITY, AND AUTONOMY

Taking as a starting point a thesis of David Gauthier's about the status of Rational Choice Theory. I discuss the relation between a subjectivist theory of value and an account of rational agency that leaves room for autonomy. I argue that if autonomy presupposes an activity of practical reason, the maximization of subjective expected utility (as prescribed by Rational Choice Theory) cannot serve as the principle of practical reason.     

Bolzano's deducibility and tarski's logical consequence

In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logical consequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logical consequence presupposes an ontic approach.     

Eliciting Subjective Probabilities through Pair‐wise Comparisons

We propose and test a novel approach for eliciting subjective joint probabilities. In the proposed approach, judges compare pairs of possible outcomes and identify which of the two is more likely and by how much. These pair‐wise comparative judgments create a matrix of ratio judgments from which the target probabilities are extracted using the rows' (or columns') geometric means. In Study 1, subjects provided direct assessments of the likelihood of joint events (e.g., sunny days and stock market gains) and also made pair‐wise comparisons of the same joint events. Subjects in Study 2 learnt the distribution of hypothetical events pairs and provided direct and ratio estimates. In both studies, the ratio estimates were significantly more accurate than the direct estimates. The results suggest that it is possible to elicit probabilistic estimates without explictly asking for probabilities and that the pair‐wise approach is a candidate for complementing or replacing traditional elicitation approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian decision theory,subjective and objective probabilities,and acceptance of empirical hypotheses

It is argued that we need a richer version of Bayesian decision theory, admitting both subjective and objective probabilities and providing rational criteria for choice of our prior probabilities. We also need a theory of tentative acceptance of empirical hypotheses. There is a discussion of subjective and of objective probabilities and of the relationship between them, as well as a discussion of the criteria used in choosing our prior probabilities, such as the principles of indifference and of maximum entropy, and the simplicity ranking of alternative hypotheses.     

How to use probabilities in reasoning

Conclusions Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated.     

Deterministic probability: neither chance nor credence

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability.     

Modeling behavior in a clinically diagnostic sequential risk-taking task

This article models the cognitive processes underlying learning and sequential choice in a risk-taking task for the purposes of understanding how they occur in this moderately complex environment and how behavior in it relates to self-reported real-world risk taking. The best stochastic model assumes that participants incorrectly treat outcome probabilities as stationary, update probabilities in a Bayesian fashion, evaluate choice policies prior to rather than during responding, and maintain constant response sensitivity. The model parameter associated with subjective value of gains correlates well with external risk taking. Both the overall approach, which can be expanded as the basic paradigm is varied, and the specific results provide direction for theories of risky choice and for understanding risk taking as a public health problem.     

Conceptualizations of valence and instrumentality: A fourfold model

Within the framework of valence-instrumentality (VI) theory, a fourfold model is developed to predict the contribution which is made by one outcome of an alternative to the valence of that alternative. The proposed model uses four subjective conditional probabilities which are based on the presence and absence of an alternative, and on the occurrence and nonoccurrence of an outcome. Valence is defined as the difference between the attractiveness values of the occurrence of an alternative (or an outcome) and the nonoccurrence of an alternative (or an outcome). Also, differences between subjective probabilities replace instrumentalities. Alternative valence-instrumentality formulations are analyzed in relation to the proposed fourfold model. The proposed model can be understood as a consistent application of Vroom's model (1964, Work and motivation, New York: Wiley), while other models are judged to be relatively deficient. The fourfold model, in combination with a matrix formulation of expectancy concepts, addresses a number of criticisms of VI theory and makes possible a test of the theory within the limits of its own assumptions.     

Autonomy and the Authority of Personal Commitments: From Internal Coherence to Social Normativity

Abstract

It has been argued – most prominently in Harry Frankfurt's recent work – that the normative authority of personal commitments derives not from their intrinsic worth but from the way in which one's will is invested in what one cares about. In this essay, I argue that even if this approach is construed broadly and supplemented in various ways, its intrasubjective character leaves it ill-prepared to explain the normative grip of commitments in cases of purported self-betrayal. As an alternative, I sketch a view that focuses on intersubjective constraints of intelligibility built into social practices and on the pragmatics of how those norms are contested in an ongoing fashion.     

Development of the concept of comparative subjective probability

This study investigates which formal principles govern subjective probability, and whether the validity of these principles depends on age. Two types of tasks were administered to 144 subjects from 3;8 to 19 years: a gambling task (with objective probabilities) and a sporting task (without objective probabilities). Six formal principles of the mathematical concept of qualitative probability (a nonnumerical concept based on ordinal scale properties) were tested. Results indicate that these principles are valid as principles of subjective probability for all age groups. Only the youngest age group (4 years or younger) had a smaller degree of confirmation.     

Protecting Against Low‐Probability Disasters: The Role of Worry

We carry out a large monetary stakes insurance experiment with very small probabilities of losses and ambiguous as well as exact probabilities. Many individuals do not want to pay anything for insurance whether the probabilities are given exactly or are ambiguous. Many others, however, are willing to pay surprisingly large amounts. With ambiguity, the percentage of those paying nothing is smaller and the willingness to pay (WTP) of the other individuals larger than with exact probabilities. Comparing elasticities with ambiguity, we find that worry is much more important than subjective probability in determining WTP for insurance. Furthermore, when the ambiguous loss probability is increased by a factor of 1000, it has almost no effect on WTP. Copyright © 2011 John Wiley & Sons, Ltd.     

An analysis of the structure of justification of ethical decisions in medical intervention

The most important distinction in value theory is the subjective-objective distinction which determines the epistemological status of value judgments about medical intervention. Ethical decisions in medical intervention presuppose one of three structures of justification — namely, an inductive approach, a deductive approach which can be either consequentialist or non-consequentialist, and a uniquely ethical approach. Inductivism and deductivism have been discussed extensively in the literature and are only briefly described here. The uniquely ethical approach which presupposes value objectivism is analyzed in detail. This method involves a purely ethical inference which moves from facts to values directly with an emphasis on reason which involves a non-logical justification (as opposed to illogical). It involves the use of natural practical arguments which have an imperative conclusion but no imperative premise and exhibit a value-requiredness between two states of affairs.     

Using Ordinal Data to Estimate Cardinal Values

We investigate methods developed in multiple criteria decision‐making that use ordinal information to estimate numerical values. Such methods can be used to estimate attribute weights, attribute values, or event probabilities given ranks or partial ranks. We first review related studies and then develop a generalized rank‐sum (GRS) approach in which we provide a derivation of the rank‐sum approach that had been previously proposed. The GRS approach allows for incorporating the concept of degree of importance (or, difference in likelihood with respect to probabilities and difference in value for attribute values), information that most other rank‐based formulas do not utilize. We then present simulation results comparing the GRS method with other rank‐based formulas such as the rank order centroid method and comparing the GRS methods using as many as three levels of importance (i.e., GRS‐3) with Simos' procedure (which can also incorporate degree of importance). To our surprise, our results show that the incorporation of additional information (i.e., the degree of the importance), both GRS‐3 and Simos' procedure, did not result in better performance than rank order centroid or GRS. Further research is needed to investigate the modelling of such extra information. We also explore the scenario when a decision‐maker has indifference judgments and cannot provide a complete rank order. Copyright © 2014 John Wiley & Sons, Ltd.     

Imitative learning from a third-party interaction: relations with self-recognition and perspective taking

Young children’s ability to learn something new from a third-party interaction may be related to the ability to imagine themselves in the third-party interaction. This imaginative ability presupposes an understanding of self-other equivalence, which is manifested in an objective understanding of the self and an understanding of others’ subjective perspectives. The current study measured imitative learning of a novel action seen only in a third-party interaction, mirror self-recognition, and perspective taking in a group of 48 18- to 20-month-olds. Patterns of performance suggest that understanding self-other equivalence is related to third-party learning.