Alleviating inflation of conditional predictions

Previous studies indicated that conditional predictions—the assessed probability that a certain outcome will occur given a certain condition—tend to be markedly inflated. Five experiments tested the effects of manipulations that were expected to alleviate this inflation by inducing participants to engage in analytic processing. Rewarding participants for accurate predictions proved ineffective. A training procedure in which participants assessed the likelihood of each of several outcomes before assessing the probability of a target outcome was partly effective in reducing overestimation. Most effective was the requirement to work in dyads and to come to an agreement about the assessed likelihood. Working in dyads helped alleviate prediction inflation even after participants made their individual predictions alone, and its debiasing effect also transferred to the estimates that were made individually on a new set of stimuli. The results were discussed in terms of the factors that make prediction inflation resistant to change.     

Transfer of a conditional ordering response through conditional equivalence classes

Eight adult humans were taught conditional discriminations in a matching-to-sample format that led to the formation of two four-member equivalence classes. When subjects were taught to select one comparison stimulus from each class in a set order, they then ordered all other members of the equivalence classes without explicit training. When the ordering response itself was brought under conditional control, conditional sequencing also transferred to all other members of the two equivalence classes. When the conditional discriminations in the matching-to-sample task were brought under higher order conditional control, the eight stimulus members were arranged into four conditional equivalence classes. Both ordering and conditional ordering transferred to all members of the four conditional equivalence classes; for some subjects this occurred without a typical test for equivalence. One hundred twenty untrained sequences emerged from eight trained sequences for all subjects. Transfer of functions through equivalence classes may contribute to a behavior-analytic approach to semantics and generative grammar.     

Understanding conditional probabilities

In two experiments, subjects were asked to judge whether the probability of A given B was greater than, equal to, or less than the probability of B given A for various events A and B. In addition, in Experiment 2, subjects were asked to estimate the conditional probabilities and also to calculate conditional probabilities from contingency data. For problems in which one conditional probability was objectively larger than the other, performance ranged from about 25–80% correct, depending on the nature of A and B. Changes in the wording of problems also affected performance, although less dramatically. Patterns of responses consistent with the existence of a causal bias in judging probabilities were observed with one of the wordings used but not with the other. Several features of the data suggest that a major source of error was the confusion between conditional and joint probabilities.     

Contextual conditional discriminations

Three experiments used a discriminated operant procedure to study conditional discrimination learning in rats. The first experiment showed that rats were capable of learning a biconditional discrimination in which two contexts served as conditional cues signalling the reinforcement contingencies associated with two discriminative stimuli. The discrimination was learned equally well when one discriminative stimulus signalled food, the other its absence, and when one stimulus signalled food, the other extinction plus mild footshock.

In Experiment 2 it was shown that prior training on such a conditional discrimination enhanced the subsequent context specificity of simple conditioning relative to control groups of animals for whom the prior training had not been conditional. Experiment 3 showed that a reversal of the significance of one pair of discriminative stimuli produced no spontaneous reversal in performance to a second, target, pair.

The pattern of results is best accounted for by an analysis of contextual conditional discrimination learning in terms of stimulus configurations and offers no support for the notion that rats may learn a general conditional rule or set.     

A conditional theory of trying

What I shall do in this paper is to propose an analysis of ‘Agent P tries to A’ in terms of a subjunctive conditional, that avoids some of the problems that beset most alternative accounts of trying, which I call ‘referential views’. They are so-named because on these alternative accounts, ‘P tries to A’ entails that there is a trying to A by P, and therefore the expression ‘P’s trying to A’ can occur in the subject of a sentence and be used to refer to a particular, namely an act or event of trying. A conditional account such as mine avoids having to answer questions about those alleged particulars, for example their location and their causal relation to physical actions, or alternatively their identity to physical actions. In brief, the analysis I propose eschews any need to quantify over any sort of trying particulars. I both clarify the proposal and deal with five possible objections to it: (1) metaphysically impossible actions: (2) cases of finking and reverse-cycle finking; (3) the empirical emptiness of preventers and blockers; (4) proximate intentions and trying; and (5) alleged explanatory loss.     

Implicit learning of social predictions

Humans exchange a range of nonverbal social signals in every interaction. It is an open question whether people use these signals, consciously or unconsciously, to guide social behavior. This experiment directly tested whether participants could learn to predict another person’s behavior using nonverbal cues in a single interaction, and whether explicit knowledge of the cue-outcome relationship was necessary for successful prediction. Participants played a computerized game of rock-paper-scissors against an avatar they believed was another participant. Sometimes the avatar generated a predictive facial cue before the play. On these trials, participants’ win-frequency increased over time, even if they did not acquire explicit knowledge of the predictive cue. The degree to which participants could predict the avatar (wins on cued trials) related to their self-reported liking of the avatar. These findings demonstrate the importance of implicit associative learning mechanisms in guiding social behavior on a moment-to-moment basis during interaction.     

Repeated acquisition of conditional discriminations

A new technique was developed to study the repeated acquisition of conditional discriminations. Using a discrete trial procedure, pigeons were required to learn during each session a different two-member chain of conditional discriminations. Key color and geometric forms were used as stimuli. After the pigeons had reached a steady state of relearning (40 to 60 sessions), the technique was used to investigate variables that have previously been shown to affect the repeated acquisition of response sequences. Various (0 to 90 seconds) durations of timeout for errors were investigated in Experiment I. The stimulus change associated with a timeout, rather than its duration, was found to be the critical variable in acquisition of the discrimination. Extended training on a single chain was found to reduce total errors across sessions in Experiment II. Extended training (three sessions) did not, however, change the pattern of within-session error reduction. In some cases, extended training facilitated acquisition of a partially reversed discrimination. In Experiment III, color rather than chain position was found to control behavior, for three of the four birds, as the second stimulus dimension in the conditional situation. The results of these experiments replicate and extend previous findings concerning some of the variables that affect the repeated acquisition of response sequences.     

Shafer on conditional probability

Journal of Philosophical Logic -     

Conditionals and conditional probability

The authors report 3 experiments in which participants were invited to judge the probability of statements of the form if p then q given frequency information about the cases pq, p not q, not pq, and not p not q (where not = not). Three hypotheses were compared: (a) that people equate the probability with that of the material conditional, 1 - P(p not q); (b) that people assign the conditional probability, P(q/p); and (c) that people assign the conjunctive probability P(pq). The experimental evidence allowed rejection of the 1st hypothesis but provided some support for the 2nd and 3rd hypotheses. Individual difference analyses showed that half of the participants used conditional probability and that most of the remaining participants used conjunctive probability as the basis of their judgments.