A unified theory of counterfactual reasoning

<p>A successful theory of causal reasoning should be able to account for inferences about counterfactual scenarios. Pearl (2000) has developed a formal account of causal reasoning that has been highly influential but that suffers from at least two limitations as an account of counterfactual reasoning: it does not distinguish between counterfactual observations and counterfactual interventions, and it does not accommodate back- tracking counterfactuals. We present an extension of Pearl’s account that overcomes both limitations. Our model provides a unified treatment of counterfactual interventions and back- tracking counterfactuals, and we show that it accounts for data collected by Sloman and Lagnado (2005) and Rips (2010).</p

Discovering hidden causes using statistical evidence

<p>People frequently reason about causal relationships and variables that cannot be directly observed. This paper presents results from an experiment in which participants used statistical information to make judgments about the number and base rates of hidden causes, as well as the forms of causal relationships in which those causes participated. Our data allow us to evaluate several models of hidden cause discovery, and reveal that people have different expectations about the forms of causal relationships than recent theories predict</p

Superspace extrapolation reveals inductive biases in function learning

<p></p><p>We introduce a new approach for exploring how humans learn and represent functional relationships based on limited observations. We focus on a problem called superspace extrapolation , where learners observe training examples drawn from an n -dimensional space and must extrapolate to an n + 1 - dimensional superspace of the training examples. Many existing psychological models predict that superspace extrapolation should be fundamentally under-determined, but we show that humans are able to extrapolate both linear and non-linear functions under these conditions. We also show that a Bayesian model can account for our results given a hypothesis space that includes families of simple functional relationships</p><p></p

Model predictions for data in Experiment 1 of Fawcett and Markson [1].

<p>(A) Results for children who showed a preference for 4 interesting toys. (B) Results for children who only showed a preference for 3 of 4 toys. The first character for each pair of bars denotes whether the actors showed a positive (P) reaction to the hidden toys versus a negative (N) reaction. The second character reflects whether the hidden object was said to be in a similar (S) or different (D) category from those seen in training. is the probability of selecting Actor 1's novel object. Error bars represent 95 percent confidence intervals. Cases where children had fewer than 4 chances to play with the training objects are excluded. For (A), there were 17, 17, 11 and 11 participants in the PS, PD, NS, and ND groups, respectively. For (B), there were 26, 26, 32, and 32 participants in the PS, PD, NS, and ND groups, respectively.</p

Model predictions for Hu et al.'s experiment.

<p>Predicted probability that objects will be selected, plotted against observed proportions, where A was chosen over C 7 of 10 times, B was chosen over C 5 of 5 times, and D was a novel alternative.</p

Model predictions and data for Kushnir, Xu, and Wellman's study [2].

<p>(A) Predicted and observed proportions of children's offers under the default model. (B) Predicted and observed proportions of offers under the assumption that squirrel can decline to choose any object. Error bars represent 95% confidence intervals.</p

Results of simulations of the unmatched condition from Repacholi and Gopnik [3].

<p>Each line shows the mean across 15 simulations, with standard errors. In both plots, the upper dashed line marks the proportion of 14-month-olds who offered the actor goldfish over broccoli (7 of 8), while the lower dashed line marks the proportion of 18-month-olds who did so (8 of 26), with standard errors. Plot (a) assumes equal prior belief in each model, while (b) assumes that the simpler model has a prior probability of 0.9.</p