Special issue: Combining probability and logic

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.     

Learning from experience in nonlinear environments: Evidence from a competition scenario

We test people’s ability to learn to estimate a criterion (probability of success in a competition scenario) that requires aggregating information in a nonlinear manner. The learning environments faced by experimental participants are kind in that they are characterized by immediate, accurate feedback involving either naturalistic outcomes (information on winning and/or ranking) or the normatively correct probabilities. We find no evidence of learning from the former and modest learning from the latter, except that a group of participants endowed with a memory aid performed substantially better. However, when the task is restructured such that information should be aggregated in a linear fashion, participants learn to make more accurate assessments. Our experiments highlight the important role played by prior beliefs in learning tasks, the default status of linear aggregation in many inferential judgments, and the difficulty of learning in nonlinear environments even in the presence of veridical feedback.     

Concurrently examining unrealistic absolute and comparative optimism: Temporal shifts,individual‐difference and event‐specific correlates,and behavioural outcomes

Researchers have spent considerable effort examining unrealistic absolute optimism and unrealistic comparative optimism, yet there is a lack of research exploring them concurrently. This longitudinal study repeatedly assessed unrealistic absolute and comparative optimism within a performance context over several months to identify the degree to which they shift as a function of proximity to performance and performance feedback, their associations with global individual difference and event‐specific factors, and their link to subsequent behavioural outcomes. Results showed similar shifts in unrealistic absolute and comparative optimism based on proximity to performance and performance feedback. Moreover, increases in both types of unrealistic optimism were associated with better subsequent performance beyond the effect of prior performance. However, several differences were found between the two forms of unrealistic optimism in their associations with global individual difference factors and event‐specific factors, highlighting the distinctiveness of the two constructs.     

Manipulating the reported age in earliest memories

ABSTRACT

Previous work suggests that the estimated age in adults’ earliest autobiographical memories depends on age information implied by the experimental context [e.g., Kingo, O. S., Bohn, A., & Krøjgaard, P. (2013). Warm-up questions on early childhood memories affect the reported age of earliest memories in late adolescence. Memory, 21(2), 280–284. doi:10.1080/09658211.2012.729598] and that the age in decontextualised snippets of memory is younger than in more complete accounts (i.e., event memories [Bruce, D., Wilcox-O’Hearn, L. A., Robinson, J. A., Phillips-Grant, K., Francis, L., & Smith, M. C. (2005). Fragment memories mark the end of childhood amnesia. Memory & Cognition, 33(4), 567–576. doi:10.3758/BF03195324]). We examined the malleability of the estimated age in undergraduates’ earliest memories and its relation with memory quality. In Study 1 (n?=?141), vignettes referring to events happening at age 2 rendered earlier reported ages than examples referring to age 6. Exploratory analyses suggested that event memories were more sensitive to the age manipulation than memories representing a single, isolated scene (i.e., snapshots). In Study 2 (n?=?162), asking self-relevant and public-event knowledge questions about participants’ preschool years prior to retrieval yielded comparable average estimated ages. Both types of semantic knowledge questions rendered earlier memories than a no-age control task. Overall, the reported age in snapshots was younger than in event memories. However, age-differences between memory types across conditions were not statistically significant. Together, the results add to the growing literature indicating that the average age in earliest memories is not as fixed as previously thought.     

Corpus-based estimates of word association predict biases in judgment of word co-occurrence likelihood

This paper draws a connection between statistical word association measures used in linguistics and confirmation measures from epistemology. Having theoretically established the connection, we replicate, in the new context of the judgments of word co-occurrence, an intriguing finding from the psychology of reasoning, namely that confirmation values affect intuitions about likelihood. We show that the effect, despite being based in this case on very subtle statistical insights about thousands of words, is stable across three different experimental settings. Our theoretical and empirical results suggest that factors affecting traditional reasoning tasks are also at play when linguistic knowledge is probed, and they provide further evidence for the importance of confirmation in a new domain.     

Of matchers and maximizers: How competition shapes choice under risk and uncertainty

In a world of limited resources, scarcity and rivalry are central challenges for decision makers—animals foraging for food, corporations seeking maximal profits, and athletes training to win, all strive against others competing for the same goals. In this article, we establish the role of competitive pressures for the facilitation of optimal decision making in simple sequential binary choice tasks. In two experiments, competition was introduced with a computerized opponent whose choice behavior reinforced one of two strategies: If the opponent probabilistically imitated participant choices, probability matching was optimal; if the opponent was indifferent, probability maximizing was optimal. We observed accurate asymptotic strategy use in both conditions irrespective of the provision of outcome probabilities, suggesting that participants were sensitive to the differences in opponent behavior. An analysis of reinforcement learning models established that computational conceptualizations of opponent behavior are critical to account for the observed divergence in strategy adoption. Our results provide a novel appraisal of probability matching and show how this individually ‘irrational’ choice phenomenon can be socially adaptive under competition.     

A General Structure for Legal Arguments About Evidence Using Bayesian Networks

A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments, there is no systematic, repeatable method for modeling legal arguments as BNs. Hence, where BNs have been used in the legal context, they are presented as completed pieces of work, with no insights into the reasoning and working that must have gone into their construction. This means the process of building BNs for legal arguments is ad hoc, with little possibility for learning and process improvement. This article directly addresses this problem by describing a method for building useful legal arguments in a consistent and repeatable way. The method complements and extends recent work by Hepler, Dawid, and Leucari (2007) on object‐oriented BNs for complex legal arguments and is based on the recognition that such arguments can be built up from a small number of basic causal structures (referred to as idioms). We present a number of examples that demonstrate the practicality and usefulness of the method.     

Formalization of Reliability Block Diagrams in Higher-order Logic

Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability and maintainability analyses. Traditionally, these RBD-based analyses are done using paper-and-pencil proofs or computer simulations, which cannot ascertain absolute correctness due to their inaccuracy limitations. As a complementary approach, we propose to use the higher-order logic theorem prover HOL to conduct RBD-based analysis. For this purpose, we present a higher-order logic formalization of commonly used RBD configurations, such as series, parallel, parallel-series and series-parallel, and the formal verification of their equivalent mathematical expressions. A distinguishing feature of the proposed RBD formalization is the ability to model nested RBD configurations, which are RBDs having blocks that also represent RBD configurations. This generality allows us to formally analyze the reliability of many real-world systems. For illustration purposes, we formally analyze the reliability of a generic Virtual Data Center (VDC) in a cloud computing infrastructure exhibiting the nested series-parallel RBD configuration.     

Updating a progic

This paper presents a progic, or probabilistic logic, in the sense of Haenni et al. [8]. The progic presented here is based on Bayesianism, as the progic discussed by Williamson [15]. However, the underlying generalised Bayesianism differs from the objective Bayesianism used by Williamson, in the calibration norm, and the liberalisation and interpretation of the reference probability in the norm of equivocation. As a consequence, the updating dynamics of both Bayesianisms differ essentially. Whereas objective Bayesianism is based on a probabilistic re-evaluation, orthodox Bayesianism is based on a probabilistic revision. I formulate a generalised and iterable orthodox Bayesian revision dynamics. This allows to define an updating procedure for the generalised Bayesian progic. The paper compares the generalised Bayesian progic and Williamson's objective Bayesian progic in strength, update dynamics and with respect to language (in)sensitivity.