Windschitl, P. D. (2000).  The binary additivity of subjective probability does not indicate the binary complementarity of perceived certainty.  Organizational Behavior and Human Decision Processes, 81, 195-225.

People’s numeric probability estimates for 2 mutually exclusive and exhaustive events commonly sum to 1.0, which seems to indicate the full complementarity of subjective certainty in the 2 events (i.e., increases in certainty for one event are accompanied by decreases in certainty for the other).  In this manuscript, however, a distinction is made between the additivity of probability estimates and the complementarity of internal perceptions of certainty.  In Experiment 1, responses on a verbal measure of certainty provide evidence of binary noncomplementarity in the perceived likelihoods of possible scenario outcomes, and a comparison of verbal and numeric certainty estimates suggests that numeric probabilities overestimated the complementarity of people’s certainty.  Experiment 2 used a choice task to detect binary noncomplementarity.  Soliciting numeric probability estimates prior to the choice task changed the participants’ choices in a direction consistent with complementarity.  Possible mechanisms yielding (non)complementarity are discussed.