Conjunction errors: Evidence for multiple judgment procedures, including "signed summation"

Abstract

A conjunction error is a judgment that a conjunctive event is more likely than one of the marginal events comprising the conjunction. Previous research has demonstrated conjunction errors in situations in which marginal events arose from a common generating process. In Studies 1-3, conjunction errors were reliably induced in cases where marginal events resulted from unrelated processes. This suggests that conjunction errors can be produced by "formalistic" judgment procedures, by which probability judgments for conjunctions are derived from probability judgments for marginal events according to some combination rule. Protocols from Studies 2 and 3 also indicated that subjects use multiple judgment procedures, several of which are capable of yielding conjunction errors. One new procedure suggested by the protocols is formalized in a "signed sum model." In this model, an event's likelihood is represented by a positive number, a negative number, or zero, depending on whether the event is considered likely, unlikely, or neither, respectively. The likelihood value for a conjunction is the sum of those for the constituent marginal events. In Study 4, this model successfully predicted when some subjects made zero, one, or two conjunction errors.