Cognitive Bias

Call the random variable being forecasted X. If X is a discrete event, then it has the value zero or one. Forecasts of X depend on the information set available to the forecaster. Assume that there are two information sets Io and II, where Io is a subset of II. A forecaster with information set I, knows everything that the forecaster with in- formation set Io knows, and more.3 Denote the optimal forecast of X given the information set Io by E(X1IO). We are interested in forecasts of forecasts, which are useful when agents need to forecast behavior of other agents. An agent with information set I, who forecasts the forecast of an agent with information Io is estimating E[E(X1I0)1I11]

The law of iterated expectations states that if I, includes Io, then E[E(X1I0)1I1] must equal E(XIIo) (Chow and Teicher 1978, p. 204). Better-informed agents should ignore their additional information when forecasting the forecasts of less-informed agents. When the curse of knowledge occurs, the forecaster with information I, overesti- mates the scope of Io. Formally, the curse of knowledge means that E[E(X|Io)|I1 ] is not equal to E(X|IO), but is somewhere between E(X|Io) and E(X|II). A simple model we test in our experiments is

E[E(XI0)1I11] = wE(XIIi) (1 - w)E(XIIo).

If w = 0, an agent is applying the law of iterated expectations cor- rectly. If w = 1, agents who know II think that all other agents know II too. The parameter w thus measures the degree of curse of knowl- edge.

Break the chains of your prejudices and take up the torch of experience, and you will honour nature in the way she deserves, instead of drawing derogatory conclusions from the ignorance in which she has left you. Simply open your eyes and ignore what you cannot understand, and you will see that a labourer whose mind and knowledge extend no further than the edges of his furrow is no different essentially from the greatest genius, as would have been proved by dissecting the brains of Descartes and Newton; you will be convinced that the imbecile or the idiot are animals in human form, in the same way as the clever ape is a little man in another form; and that, since everything depends absolutely on differences in organisation, a well-constructed animal who has learnt astronomy can predict an eclipse, as he can predict recovery or death when his genius and good eyesight have benefited from some time at the school of Hippocrates and at patients' bedsides.

People tend to hold overly favorable views of their abilities in many social and intellectual domains. The authors suggest that this overestimation occurs, in part, because people who are unskilled in these domains suffer a dual burden: Not only do these people reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the metacognitive ability to realize it. Across 4 studies, the authors found that participants scoring in the bottom quartile on tests of humor, grammar, and logic grossly overestimated their test performance and ability. Although their test scores put them in the 12th percentile, they estimated themselves to be in the 62nd. Several analyses linked this miscalibration to deficits in metacognitive skill, or the capacity to distinguish accuracy from error. Paradoxically, improving the skills of participants, and thus increasing their metacognitive competence, helped them recognize the limitations of their abilities.