Dual frames for causal induction: the normative and the heuristic

ABSTRACT

Causal induction in the real world often has to be quick and efficient as well as accurate. We propose that people use two different frames to achieve these goals. The A-frame consists of heuristic processes that presuppose rarity and can detect causally relevant factors quickly. The B-frame consists of analytic processes that can be highly accurate in detecting actual causes. Our dual frame theory implies that several factors affect whether people use the A-frame or the B-frame in causal induction: among these are symmetrical negation, intervention and commitment. This theory is tested and sustained in two experiments. The results also provide broad support for dual process accounts of human thinking in general.

KEYWORDS:

• Causal induction
• dual frames
• negation
• intervention
• commitment

Acknowledgments

We thank Yutaka Nishida and Henrik Singmann for their valuable comments on data analyses, Masahiko Tamura for his coding computer programs for experiments, Ryo Orita for his assistance in conducting the experiments, and the members of CHORUS project for exciting discussions on our earlier study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ This relation is normative because it corresponds also to a Bayesian measure of confirmation. There are some other measures in the literature (Fitelson & Hitchcock, 2011).

² Although there are more recent rational models of causal induction other than ∆P, including Power PC (Cheng, 1997), Causal Support (Griffiths & Tenenbaum, 2005) and the SS power model (Lu et al., 2008), we do not address them. This is not only because ∆P is at the core of all the above rational models (e.g., ∆P is the numerator of the Power PC index), but also because our purpose is to contrast two frames, A and B, introduced later, of which, in our view, DFH and ∆P are representative, respectively.

³ The observed cell configurations of stimuli that each participant pair actually observed are available online.

⁴ There are two other possible mixed-effects models available: M0 and M3. M0 is the simplest model that has no fixed effect: Judgement ∼ 1 + (1 | Participant). This model assumes Judgment is predicted by neither DFH nor ∆P, and so we omit this model. M3 is the most complex model in which the slope and the intercept for the effect of DFH (or ∆P) are determined separately for each level of Participant as in the case of M2, while (unlike M2) allowing correlation between the intercept deviations and the effect of DFH (or ∆P) deviations within levels of Participant. Thus, M3 includes an additional parameter: the correlation between intercept deviations and DFH (or ∆P) deviations across levels of Participant. Although we prefer simpler models, we actually evaluated M3 against M1 and M2, and in most cases (seven out of all eight cases), M3 showed the worst fit to data according to BIC. Consequently, we decided to omit M3.

⁵ Barr, Levy, Scheepers, and Tily (2013) proposed the maximal model should be the “gold standard” in model selection although it seems to be still controversial. In this study, M3 mentioned in the footnote 4 is the maximal model, and the results of Experiments 1 and 2 do not alter even using this standard.

⁶ We selected these four stimuli because there should be multiple levels for ∆P, and there also should be a variation in other indices that have the same ∆P value. There was no stimulus that had high ∆P, since it was difficult for high ∆P to make variations in combination of P(E|C) and P(E|¬C). For example, to set ∆P 0.8, only a combination of 0.9 and 0.1 is available in a grid scale of 0.1, if an extreme probability of 1 or 0 is avoided. Moreover, such stimuli do not provide a significant difference between DFH and ∆P. Using a computer program, we exhaustively searched for a combination of stimuli that has a lesser internal correlation between ∆P and DFH. Under a constraint that the sample size is equal to or fewer than 20, a set of stimuli that have 3 (∆P: low/middle/high) × 3 (DFH: low/middle/high) levels was searched, but there was no such stimulus that had a high–low or low–high combination in ∆P and DFH. As a consequence, the levels of ∆P were set at approximately −.3, .0 and .5, and the levels of DFH were set at approximately .2, .5 and .8.

Additional information

Funding

JSPS–ANR CHORUS Program [grant number J12100148]; JSPS KAKENHI awarded to MH [grant number 22500247], [grant number 15H02717].