Two base rates, two weights: base-rate neglect has a second axis

Abstract

Base-rate neglect is usually treated as one mistake: giving the prior too little weight. Turning the co-occurrences you see into a useful judgment, though, means correcting for two base rates, not one. The first is the familiar prior, how common the outcome is. The second is how common the cue itself is. Those are two separate mistakes, and a learner can make either one alone. Under-correcting the prior is classical base-rate neglect; under-correcting the cue is the cue-density effect of contingency learning, long studied but not previously recognised as a kind of base-rate neglect. We write both corrections as two weights in one Bayesian equation. The task decides which weight it can measure: the cue-frequency weight appears only in graded ratings, because a two-choice test cancels it. At their extremes the two weights recover familiar quantities: base-rate neglect, the signal-detection criterion, the contiguity/sensitivity/validity triple, and the "lift" measure of causal strength. The same cue-frequency weight also sits inside six standard learning-and-memory models; they seem to agree, but only because the usual experiments squeeze the data into a form where they cannot disagree. Above all, the two neglects should be separately manipulable: an experimenter can move one without moving the other. That is a double dissociation, and a one-parameter account cannot produce it. That prediction is the framework's centre, and it has not yet been tested. This paper lays out the framework and the rating experiment that would settle it; a companion paper fits the two weights to an existing colour-flavour dataset.