The influence of cognitive ability and instructional set on causal conditional inference

We report a large study in which participants are invited to draw inferences from causal conditional sentences with varying degrees of believability. General intelligence was measured, and participants were split into groups of high and low ability. Under strict deductive-reasoning instructions, it was observed that higher ability participants were significantly less influenced by prior belief than were those of lower ability. This effect disappeared, however, when pragmatic reasoning instructions were employed in a separate group. These findings are in accord with dual-process theories of reasoning. We also took detailed measures of beliefs in the conditional sentences used for the reasoning tasks. Statistical modelling showed that it is not belief in the conditional statement per se that is the causal factor, but rather correlates of it. Two different models of belief-based reasoning were found to fit the data according to the kind of instructions and the type of inference under consideration.     

A sampling approach to biases in conditional probability judgments: beyond base rate neglect and statistical format

Conditional probability judgments of rare events are often inflated. Early accounts assumed a general deficit in using statistical base rates. More recent approaches predict improvement when problems are presented in frequency format or refer to natural categories. The present theory focuses on sampling processes. Experiment 1 showed that a seeming advantage of frequency over probability formats is due to a confounded factor, the need to mentally transform stimulus samples. An information search paradigm was used in Experiment 2. When sampling by the predictor, the probability to be estimated, p(criterion/predictor), was conserved in the samples and judgments were quite accurate. However, when sampling by the criterion, the low base-rate event was strongly overrepresented, accounting for the entire bias. Judgments were quite sensitive to the sampled data, but failed to take sampling constraints into account, as shown in Experiments 3 and 4.     

Probabilities,causation, and logic programming in conditional reasoning: reply to Stenning and Van Lambalgen (2016)

Oaksford and Chater (2014 Oaksford, M., &; Chater, N. (2014). Probabilistic single function dual process theory and logic programming as approaches to non-monotonicity in human vs. artificial reasoning. Thinking and Reasoning, 20, 269–295. doi:10.1080/13546783.2013.877401[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Thinking and Reasoning, 20, 269–295) critiqued the logic programming (LP) approach to nonmonotonicity and proposed that a Bayesian probabilistic approach to conditional reasoning provided a more empirically adequate theory. The current paper is a reply to Stenning and van Lambalgen's rejoinder to this earlier paper entitled ‘Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater’ (2016) in Thinking and Reasoning. It is argued that causation is basic in human cognition and that explaining how abnormality lists are created in LP requires causal models. Each specific rejoinder to the original critique is then addressed. While many areas of agreement are identified, with respect to the key differences, it is concluded the current evidence favours the Bayesian approach, at least for the moment.     

Probabilities in implicit learning

The visual system possesses a remarkable ability in learning regularities from the environment. In the case of contextual cuing, predictive visual contexts such as spatial configurations are implicitly learned, retained, and used to facilitate visual search-all without one's subjective awareness and conscious effort. Here we investigated whether implicit learning and its facilitatory effects are sensitive to the statistical property of such implicit knowledge. In other words, are highly probable events learned better than less probable ones even when such learning is implicit? We systematically varied the frequencies of context repetition to alter the degrees of learning. Our results showed that search efficiency increased consistently as contextual probabilities increased. Thus, the visual contexts, along with their probability of occurrences, were both picked up by the visual system. Furthermore, even when the total number of exposures was held constant between each probability, the highest probability still enjoyed a greater cuing effect, suggesting that the temporal aspect of implicit learning is also an important factor to consider in addition to the effect of mere frequency. Together, these findings suggest that implicit learning, although bypassing observers' conscious encoding and retrieval effort, behaves much like explicit learning in the sense that its facilitatory effect also varies as a function of its associative strengths.     

Revising Probabilities and Full Beliefs

Journal of Philosophical Logic - A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a...     

Taurek, Numbers and Probabilities

In his paper, “Should the Numbers Count?" John Taurek imagines that we are in a position such that we can either save a group of five people, or we can save one individual, David. We cannot save David and the five. This is because they each require a life-saving drug. However, David needs all of the drug if he is to survive, while the other five need only a fifth each. Typically, people have argued as if there was a choice to be made: either numbers matter, in which case we should save the greater number, or numbers don't matter, but rather there is moral value in giving each person an equal chance of survival, and therefore we should toss a coin. My claim is that we do not have to make a choice in this way. Rather, numbers do matter, but it doesn't follow that we should always save the greater number. And likewise, there is moral value in giving each person an equal chance of survival, but it doesn't follow that we should always toss a coin. In addition, I argue that a similar approach can be applied to situations in which we can save one person or another, but the chances of success are different.     

Cognitive biases and depression

Compared symptomatically depressed, clinically remitted, and normal controls using cognitive measures designed to be traitlike and statelike in cross-sectional and longitudinal designs, respectively. Remitted depressives and normal subjects did not differ in their attributional biases, endorsement of dysfunctional attitudes, or interpretation of schema-relevant ambiguous events, but both groups differed from symptomatic depressives. Depressive episodes thus affect cognition, but cognitions measured by self-reports are more statelike than traitlike.     

Myopic biases in competitions

In three studies using both laboratory and field data, we show that the focal competitor’s strengths and weaknesses feature more prominently in predictions of the outcomes of future competitions than do the strengths and weaknesses of the opponents. People are more confident when their own side is strong, regardless of how strong the competition is. We show that this effect is driven by the fact that people have better information about their own side than the other side, in part because they preferentially seek out information about their own side. Implications for theories of decision making in competitive settings are discussed.     

Attentional and interpretative biases in appearance concern: An investigation of biases in appearance-related information processing

The present study examined associations between high levels of appearance concern and information processing biases in interpretation and attention. An opportunity sample (N = 79) categorised ambiguous stimuli as related or unrelated to appearance. Participants then responded to the same stimuli in a modified visual dot-probe task assessing attentional bias. Participant responses were assessed in relation to level of appearance concern. The results indicated a valence specific bias towards interpretation of ambiguous stimuli as negative and appearance-related in individuals with higher levels of concern. There was also evidence of attentional bias towards information perceived as appearance-related in participants with higher levels of appearance concern. The study findings suggest that association between appearance-orientated information processing biases and level of appearance concern; this association may lead to mutually reinforcing bias and concern.     

A comparison of attentional biases and memory biases in women with social phobia and major depression

Cognitive processes play an important role in the etiology and maintenance of anxiety and depression. Current theories differ, however, in their predictions regarding the occurrence of attentional biases and memory biases in depression and anxiety. To allow for a systematic comparison of disorders and cognitive processes, 117 women (35 with generalized social phobia, 27 with major depression, and 55 healthy controls) participated in a test of visual attention (visual search), an explicit memory test (free recall), and an implicit memory test (anagram solving). Both clinical groups exhibited attentional biases for disorder-related words, whereas only depressed participants showed clear evidence of explicit and implicit memory biases. The implications of these results for competing theories are discussed.     

Semantic Coherence and Inconsistency in Estimating Conditional Probabilities

Two studies examined semantic coherence and internal inconsistency fallacies in conditional probability estimation. Problems reflected five distinct relationships between two sets: identical sets, mutually exclusive sets, subsets, overlapping sets, and independent sets (a special case of overlapping sets). Participants estimated P(A), P(B), P(A|B), and P(B|A). Inconsistency occurs when this constellation of estimates does not conform to Bayes' theorem. Semantic coherence occurs when this constellation of estimates is consistent with the depicted relationship among sets. Fuzzy‐trace theory predicts that people have difficulty with overlapping sets and subsets because they require class‐inclusion reasoning. On these problems, people are vulnerable to denominator neglect, the tendency to ignore relevant denominators, making the gist more difficult to discern. Independent sets are simplified by the gist understanding that P(A) provides no information about P(B), and thus, P(A|B) = P(A). The gist for identical sets is that P(A|B) = 1.0, and the gist of mutually exclusive sets is that P(A|B) = 0. In Study 1, identical, mutually exclusive, and independent sets yielded superior performance (in internal inconsistency and semantic coherence) than subsets and overlapping sets. For subsets and overlapping sets, interventions clarifying appropriate denominators generally improved semantic coherence and inconsistency, including teaching people to use Euler diagrams, 2 × 2 tables, or relative frequencies. In Study 2, with problems about breast cancer and BRCA mutations, there was a strong correlation between inconsistency in conditional probability estimation and conjunction fallacies of joint probability estimation, suggesting that similar fallacious reasoning processes produce these errors. Copyright © 2012 John Wiley & Sons, Ltd.     

Interpretation biases in angry and anxious individuals

Although previous research has demonstrated many similarities between anxious and angry individuals, few studies have compared the degree and direction to which they exhibit cognitive biases in the presence of threat. The present study was a preliminary investigation of 28 angry participants, 30 anxious participants, and 26 non-angry/non-anxious participants who rated the likelihood of various explanations to account for ambiguous but potentially threatening events described in short prose passages. Angry participants rated the likelihood of positive explanations for ambiguous events lower than non-angry/non-anxious participants. Angry participants rated the likelihood of anger-related explanations higher than anxious and non-angry/non-anxious participants, and both angry and anxious participants rated anxiety-related explanations as being more likely than non-angry/non-anxious participants. Thus, both angry and anxious participants demonstrated a negative interpretation bias, although the bias was more pervasive in angry participants.     

Interpretation and judgmental biases in social phobia

Previous research demonstrated that social phobia is characterized by content-specific interpretation and judgmental biases. The present study investigated whether this interpretation bias occurs not only in ambiguous, but also in positive and negative social events, and whether social phobic patients (SPs) are more characterized by a judgmental bias in costs than in probability. Besides, we argued that the judgmental bias observed in former studies could also be attributed to accurate estimations of SPs (of, for example, stuttering). Therefore, we assessed judgmental bias by the ratings of probability and costs of a negative evaluation (e.g. ‘people dislike me’) and not, as in previous studies, of negative social events (e.g. ‘stuttering’). SPs (n=228) and normal controls (n=33) were presented social and non-social events ranging from positive to profoundly negative. They ranked four different interpretations on likelihood to assess interpretation bias, and rated the profoundly negative interpretation on probability and cost to assess judgmental bias. SPs demonstrated content-specific interpretation and judgmental biases that also occurred in positive and negative social events. In contrast with expectations, SPs were characterized by a judgmental bias in both costs and probability.     

Powers,Probabilities, and Tendencies

Philosophia - In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of...     

Cognitive biases and decision making in gambling

Heuristics and cognitive biases can occur in reasoning and decision making. Some of them are very common in gamblers (illusion of control, representativeness, availability, etc.). Structural characteristics and functioning of games of chance favor the appearance of these biases. Two experiments were conducted with nonpathological gamblers. The first experiment was a game of dice with wagers. In the second experiment, the participants played two bingo games. Specific rules of the games favored the appearance of cognitive bias (illusion of control) and heuristics (representativeness and availability) and influence on the bets. Results and implications for gambling are discussed.     

Probabilities of counterfactuals and counterfactual probabilities

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a counterfactual is true when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals.     

Imprecise Probabilities and Unstable Betting Behaviour

Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.