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We frequently engage in activities that impose a risk of serious harm on innocent others in order to realise trivial benefits for ourselves or third parties. Many moral theories tie the evidence-relative permissibility of engaging in such activities to the size of the risk that an individual agent imposes. I argue that we should move away from such a reliance on quantified individual risks when conceptualising morally permissible risk imposition. Under most circumstances of interest, a conscientious reasoner will identify a gap between the factors they deem potentially relevant to the riskiness of an agent’s behaviour, and the factors they are reasonably able to quantify. This then leads a conscientious reasoner to conclude that they cannot, in good faith, come up with a quantitative risk estimate that is genuinely tailored to the agent’s particular situation. Based on this, I argue that principles of morally permissible risk imposition fail to provide us with practical guidance if they ask us to take into account our agent-specific risks in a quantified manner. I also argue that principles of permissible risk imposition which appeal to quantified individual risks implausibly imply that it is frequently indeterminate whether engaging in some risky activity is morally permissible. For both of these reasons, I contend that principles of morally permissible risk imposition should make no reference to quantified individual risks. They should instead acknowledge that any quantitative estimates that an agent might usefully be able to consider will likely not be tailored to the agent’s idiosyncratic situation.

This article discusses the use of Bayes’ Theorem in medical diagnosis with a view to examining the epistemological problems of interpreting the concept of pre-test probability value. It is generally maintained that pre-test probability values are determined subjectively. Accordingly, this paper investigates three main philosophical interpretations of probability (the “classic” one, based on the principle of non-sufficient reason, the frequentist one, and the personalistic one). This study argues that using Bayes’ Theorem in medical diagnosis does not require accepting the radical personalistic interpretation. It will be shown that what distinguishes radical and moderate personalist interpretations is the criterion of conditional inter-subjectivity which applies only to the moderate account of personalist interpretation.

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik’s m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Eph √ 2 completeness estimator over the frequency estimator for the probability interval p ∈ (0.1, 0.9). The frequency estimator is better for p ∈ [0, 0.1] and p ∈ [0.9, 1].

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can be used in the studies of various applications of systems with dependent failures between their elements.