The diversity effect in inductive reasoning depends on sampling assumptions

Abstract

A key phenomenon in inductive reasoning is the diversity effect, whereby a novel property is more likely to be generalized when it is shared by an evidence sample composed of diverse instances than a sample composed of similar instances. We outline a Bayesian model and an experimental study that show that the diversity effect depends on the assumption that samples of evidence were selected by a helpful agent (strong sampling). Inductive arguments with premises containing either diverse or nondiverse evidence samples were presented under different sampling conditions, where instructions and filler items indicated that the samples were selected intentionally (strong sampling) or randomly (weak sampling). A robust diversity effect was found under strong sampling, but was attenuated under weak sampling. As predicted by our Bayesian model, the largest effect of sampling was on arguments with nondiverse evidence, where strong sampling led to more restricted generalization than weak sampling. These results show that the characteristics of evidence that are deemed relevant to an inductive reasoning problem depend on beliefs about how the evidence was generated. Electronic supplementary material The online version of this article (10.3758/s13423-018-1562-2) contains supplementary material, which is available to authorized users.

Sample size, number of categories and sampling assumptions: Exploring some differences between categorization and generalization

“…In contrast, the Twelve Helpful condition is designed to induce a strong sampling assumption by encouraging the belief that items are chosen from a specific category by a helpful teacher. Experimentally manipulating sampling assumptions has been applied fruitfully in a number of inductive generalization tasks including word learning (Xu & Tenenbaum, 2007a), property induction tasks (Ransom, Perfors, & Navarro, 2016;Hayes, Navarro, Stephens, Ransom, & Dilevski, 2019) and single category generalization tasks (Ransom, Hendrickson, Perfors, & Navarro, 2018;Ransom & Perfors, submitted). The consistent finding in these studies is that experimentally manipulating the sampling assumption does have an effect on generalization.…”

Evidential diversity increases generalisation in predictive learning

“…Our questionnaire data (see Supplementary Materials) support this idea that training with diverse category members increases the relative proportion of participants deriving categorical hypotheses rather than hypotheses about the specific training exemplars. This idea of hypothesis updating underlies formal Bayesian theories of induction (Heit, 1998; Kemp & Tenenbaum, 2009), which are also capable of predicting situations where the diversity effect will not occur (see Medin et al, 2003) or will be attenuated (Hayes, Navarro, Stephens, Ransom, & Dilevski, 2019). Clearly, further studies are needed to differentiate between these alternate accounts of diversity effects in the generalisation of predictive learning.…”

Adding Types, But Not Tokens, Affects Property Induction

“…The learner updates beliefs in these hypotheses as new evidence is observed, with certain hypotheses becoming stronger and others becoming weaker. As well as changes in generalization due to additional types, Bayesian models can account for a range of inductive phenomena such as the effects of premise diversity (Hayes, Navarro, Stephens, Ransom, & Dilevski, 2019), the impact of samples containing both positive and negative evidence (Lee, Lovibond, Hayes, & Navarro, 2019;Voorspoels, Navarro, Perfors, Ransom, & Storms, 2015), and generalization based on causal rather than categorical relations (Kemp & Tenenbaum, 2009).…”