Categorical induction from uncertain premises: Jeffrey's doesn't completely rule

Abstract

Studies of categorical induction typically examine how belief in a premise (e.g., Falcons have an ulnar artery) projects on to a conclusion (e.g., Robins have an ulnar artery). We study induction in cases in which the premise is uncertain (e.g., There is an 80% chance that falcons have an ulnar artery). Jeffrey's rule is a normative model for updating beliefs in the face of uncertain evidence. In three studies we tested the descriptive validity of Jeffrey's rule and a related probability theorem, the rule of total probability. Although these rules provided good approximations to mean judgments in some cases, the results from regression and correlation analyses suggest that participants focus on the parts of these rules that are associated with the highest overall probability. We relate our findings to rational models of judgment.

Keywords:

• Belief revision
• Categorical induction
• Jeffrey's rule
• Total probability theorem.

Notes

¹ A reviewer has pointed out to us that the English translation at this point is ambiguous, the left- and right-handed versions of a substance could be taken to be distributed equally either between animal species (as we intended) or within animal species. However, the original version in Italian is far less ambiguous in context, as has been confirmed for us by an Italian linguist who is also a native speaker. The linguist noted that although the ambiguity in the Italian text is present in 1. and in the first sentence of 2, the sentence, “This means that half of the animal species have the left handed version, whereas the other half have the right handed version”, clearly supports the between animal species interpretation.