Michael Smithson

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek’s Pasadena Game , and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both.

Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale (i.e., what levels of granularity) are useful for a rational agent? Where should these thresholds be placed given a rational agent’s preferences and risk-orientation? Do scale score assignments have any bearing on decision-making and if so, how should scores be assigned? Given two possible states of nature , an ordered collection of alternatives from which one is to be selected depending on the probability that A is the case, a simple expected utility condition stipulates when adjacent alternatives are distinguishable and determines the threshold odds separating them. Threshold odds and utilities are mapped onto scale scores via a simple distance model. The placement of the thresholds reflects relative concern over decisional consequences given A versus consequences given ∼ A. Likewise, it is shown that scale scores reflect risk-aversion or risk-seeking not only with respect to A versus ∼ A but also with respect to the rank of the R j . Connections are drawn between this framework and rank-dependent expected utility (RDEU) theory. Implications are adumbrated for both machine and human decision-making.

This paper focuses on one matter that poses a problem for both human judges and standard probability frameworks, namely the assumption of a unique (privileged) and complete partition of the state-space of possible events. This is tantamount to assuming that we know all possible outcomes or alternatives in advance of making a decision, but it is clear that there are many practical situations in prediction, diagnosis, and decision-making where such partitions are contestable and/or incomplete. The paper begins by surveying the impact of partitions on the choice of priors in formal probabilistic updating frameworks, and on human subjective probability judgements. That material is followed by an overview of strategies for dealing with partition dependence, including considerations of how a rational agent's preferences may determine the choice of a partition.

This paper attempts to establish that ignorance is a necessary condition for science to have a purpose, just as it is a precondition for any kind of intentional learning or discovety. The author argues that those who find intrinsic value in science must necessarily attribute positive value to ignorance, for the relationship between the two is symbiotic rather than combative. He presents a number of ways in which scientific ignorance may be positively valued by scientists and non-scientists and lays down a framework for discussing ignorance. He finds accumulating evidence of a shift in scientists' values towards more tolerance of ignorance. The paper concludes by saying that although some trends and currents suggest a swing towards an insistence on certainty, safety and security of political agendas, this does not indicate which way the rest of society is going. The author points out the possibility that at least some sectors of society may be moving towards a realization that many kinds of ignorance are irreducible, and with that, a recognition of the need for scientists to cultivate their particular type of purposive ignorance.

We examine how prior mental health predicts hopes and how hopes predict subsequent mental health, testing hypotheses in a longitudinal study with an Australian nation-wide adult sample regarding mental health consequences of the COVID-19 outbreak during its initial stage. Quota sampling was used to select a sample representative of the adult Australian population in terms of age groups, gender, and geographical location. Mental health measures were selected to include those with the best psychometric properties. Hypotheses were tested using generalized linear models with random intercepts, with the type of GLM determined by the nature of the dependent variable. Greater anxiety, depression, distress, and loneliness predict less hope, but impaired quality of life and stress positively predict hopes of gaining new skills. Distress and loneliness predict hopes for social connectedness and an improved society, suggesting that predictors of hope depend on what is hoped for. These findings suggest the need for more nuanced theories of hope. Greater hopes for societal improvement predict lower anxiety, depression, distress, and impaired quality of life, but greater hopes for skills and better mental health predict higher levels of these covariates. Moreover, when relevant prior psychological states are more intense, the impact of hope state declines. These findings indicate that the consequences of hope are heterogeneous, and suggest a possible explanation for the seemingly inconsistent therapeutic effectiveness of raising hope.