Simplicity as a Cue to Probability: Multiple Roles for Simplicity in Evaluating Explanations

Abstract

People often face the challenge of evaluating competing explanations. One approach is to assess the explanations’ relative probabilities–for example, applying Bayesian inference to compute their posterior probabilities. Another approach is to consider an explanation's qualities or “virtues,” such as its relative simplicity (i.e., the number of unexplained causes it invokes). The current work investigates how these two approaches are related. Study 1 found that simplicity is used to infer the inputs to Bayesian inference (explanations’ priors and likelihoods). Studies 1 and 2 found that simplicity is also used as a direct cue to the outputs of Bayesian inference (the posterior probability of an explanation), such that simplicity affects estimates of posterior probability even after controlling for elicited (Study 1) or provided (Study 2) priors and likelihoods, with simplicity having a larger effect in Study 1, where posteriors are more uncertain and difficult to compute. Comparing Studies 1 and 2 also suggested that simplicity plays additional roles unrelated to approximating probabilities, as reflected in simplicity's effect on how “satisfying” (vs. probable) an explanation is, which remained largely unaffected by the difficulty of computing posteriors. Together, these results suggest that the virtue of simplicity is used in multiple ways to approximate probabilities (i.e., serving as a cue to priors, likelihoods, and posteriors) when these probabilities are otherwise uncertain or difficult to compute, but that the influence of simplicity also goes beyond these roles.

Explanations and Causal Judgments Are Differentially Sensitive to Covariation and Mechanism Information

“…In addition to cautioning against characterizing one of these judgments in terms of another, our findings raise questions about the extent to which different kinds of explanatory and causal judgments could diverge. For instance, evaluating explanatory “goodness” could diverge from evaluations of explanation probability (see Vrantsidis and Lombrozo, in press ), just as evaluations of causal structure diverge from those of strength (e.g., Griffiths and Tenenbaum, 2005 ).…”

“…Finally, there is more general evidence that explanatory judgments may be “special” and differ in various ways from other related judgments (see Lombrozo, 2012 ; Lombrozo and Vasilyeva, 2017 , for reviews). When people evaluate explanatory claims, they take into account such properties of explanatory hypotheses as simplicity (preferring simpler explanations even when probabilistic evidence favors complex explanations; Lombrozo, 2007 ; Bonawitz and Lombrozo, 2012 ; Pacer and Lombrozo, 2017 ; Vrantsidis and Lombrozo, in press ), latent scope (preferring explanations that do not make unverified predictions; Khemlani et al, 2011 ), explanatory power [roughly tracking confirmation, ( Good, 1960 ) while deviating from the objective posterior probability of a hypothesis; Douven and Schupbach, 2015a , b ] and other explanatory “virtues” ( Lipton, 2004 ). This illustrates that explanation judgments are influenced by a variety of considerations beyond the covariation between cause and effect.…”

Revisiting the Narrow Latent Scope Bias in Explanatory Reasoning

“…By how much will a test question asking subjects to pick the most satisfying rather than the most probable explanation influence their explanatory choices? Two papers (Lombrozo, 2007;Vrantsidis & Lombrozo, 2022) have used and compared both types of test query formulations in experimental scenarios about diseases, where a satisfaction test query could be interpreted as a question asking for the more preferable outcome, e.g., having one rather than two diseases. These studies have found only small differences between the two kinds of test query formulations, which might mean that if there was this (mis-) interpretation of satisfaction test queries, it probably did not occur in many subjects (if many subjects did it, one would probability have observed very strong preferences for one disease over two in the satisfaction query conditions).…”

“…1. For example, in Vrantsidis and Lombrozo's (2022) experiments, subjects read a fictitious scenario about aliens from planet Zorg who can contract three different diseases: Tritchet's syndrome, which causes sore minttels and purple spots, Morad's disease, which causes only sore minttels, and a Humel infection, which causes only purple spots. The test case described an alien suffering from both sore minttels and purple spots.…”

“…Psychological research suggests that these explanatory virtues are shared by lay people (Lagnado, 1994;Lombrozo, 2007;Pacer & Lombrozo, 2017;Read & Marcus-Newhall, 1993;Shimojo, Miwa, & Terai, 2020;Vrantsidis & Lombrozo, 2022), even by children as young as five years old (see, e.g., Bonawitz & Lombrozo, 2012;Corriveau & Kurkul, 2014). A typical test situation revealing a preference for explanatory simplicity (Lombrozo, 2007) is abstractly summarized in Fig.…”