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.     

People think about what is true for conditionals,not what is false: Only true possibilities prime the comprehension of “if”

We report the results of two priming experiments that examine the comprehension of conditionals—for example, “if there are apples then there are oranges”—and biconditionals—for example, “if and only if there are apples then there are oranges”. The first experiment showed that participants read a biconditional faster when it was primed by a true possibility, “there were apples and there were oranges” than when it was primed by a false possibility, “there were no apples and there were oranges”; a conditional was primed equally by both possibilities. The second experiment showed that participants read the negated-antecedent conjunction faster when it was primed by a conditional than when it was primed by a biconditional; the affirmative conjunction was primed equally by both connectives. The experiments show that (a) when people understand “if A then B”, they access the true possibilities, “A and B”, and “not-A and B”, and (b) when they understand “if and only if A then B” they access “A and B”, but they do not access “not-A and B”. We discuss their implications for current theories of reasoning.     

Prior probabilities and representational momentum

In many previous experiments on representational momentum (in which memory for the final location of a moving target is displaced in the direction of target motion), participants judged whether a probe presented after a target vanished was at the same location where that target vanished or at a different location. The experiments reported here manipulated the actual or expected prior probability a same response to such a probe would be correct. In Experiment 1, a same response was correct on 10%, 30%, 50%, 70%, or 90% of the trials, but observers were not instructed regarding these probabilities. In Experiment 2, a same response was correct on 11% of the trials, but different groups of participants were instructed that a same response would be correct on 10%, 30%, 50%, 70%, or 90% of the trials. Probabilities of a same response to different probe positions, weighted mean estimates of representational momentum, hit rates and false alarm rates, and d′ and ß are reported. Representational momentum occurred in all conditions but was not influenced by actual or expected prior probability a same response would be correct. The data suggest representational momentum does not result from changes in sensitivity, and a distinction between performance bias and competence bias is introduced.     

Indicative conditionals,conditional probabilities,and the “defective truth-table”: A request for more experiments

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ? entails conditional-free ψ, “if ? then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional.     

To what extent do we process the nondominant object in a morphed figure? Evidence from a picture–word interference task

Since the 1970s, the Heuristics and Biases Program in Cognitive Psychology has shown that people do not reason correctly about conditional probability problems. In the 1990s, however, evolutionary psychologists discovered that if the same problems are presented in a different way, people's performance greatly improves. Two explanations have been offered to account for this facilitation effect: the natural frequency hypothesis and the nested-set hypothesis. The empirical evidence on this debate is mixed. We review the literature pointing out some methodological issues that we take into account in our own present experiments. We interpret our results as suggesting that when the mentioned methodological problems are tackled, the evidence seems to favour the natural frequency hypothesis and to go against the nested-set hypothesis.     

Effects of guided reflexivity and team feedback on team performance improvement: The role of team regulatory processes and cognitive emergent states

The effectiveness of decision-making teams depends largely on the quality of information processing. Prior research has shown that guided team reflexivity and team feedback are important means of advancing team information processing and outcomes. However, the nature of the relationships, and how these relate to team regulatory processes, cognitive emergent states, and ultimately team performance, is currently poorly understood. Drawing on reflexivity and team information-processing theory, we proposed and found that teams that received guided team reflexivity or a combination of both guided reflexivity and feedback showed higher levels of actual reflection than teams that received neither a reflexivity intervention nor feedback. Conditional process analysis showed that the effects of team reflection on team performance improvement were mediated by a path from shared team mental models to shared task mental models and to adaptation. Finally, we also expected that team reflection would be lower in virtual teams than in face-to-face teams. These hypotheses were tested experimentally among 98 student teams that communicated either face-to-face or virtual (via chat) while completing a collective decision-making task. The information distribution among team members constituted a hidden profile. The results supported all our hypotheses, except for the one relating to virtuality.     

When good evidence goes bad: the weak evidence effect in judgment and decision-making

An indispensable principle of rational thought is that positive evidence should increase belief. In this paper, we demonstrate that people routinely violate this principle when predicting an outcome from a weak cause. In Experiment 1 participants given weak positive evidence judged outcomes of public policy initiatives to be less likely than participants given no evidence, even though the evidence was separately judged to be supportive. Experiment 2 ruled out a pragmatic explanation of the result, that the weak evidence implies the absence of stronger evidence. In Experiment 3, weak positive evidence made people less likely to gamble on the outcome of the 2010 United States mid-term Congressional election. Experiments 4 and 5 replicated these findings with everyday causal scenarios. We argue that this “weak evidence effect” arises because people focus disproportionately on the mentioned weak cause and fail to think about alternative causes.     

Effects of context on the rate of conjunctive responses in the probabilistic truth table task

The probabilistic truth table task involves assessing the probability of "If A then C" conditional sentences. Previous studies have shown that a majority of participants assess this probability as the conditional probability P(C│A) while a substantial minority responds with the probability of the conjunction A and C. In an experiment involving 96 participants, we investigated the impact on the rate of conjunctive responses of the context in which the task is framed. We show that a context intended to lead participants to consider all the possible cases (i.e. the throw of a die known to allow six possibilities) elicited more conjunctive responses than a context assumed not to have this effect (an unfamiliar deck of cards). These results suggest that the step of inferring the probability can distort our assessment of participants' interpretation of conditional sentences. This might compromise the validity of the probabilistic task in studying conditional reasoning.