Importantly, the paradigm controls for a range of criticisms levelled against other positive judgment bias measures (e.g. contingency judgments; Haaga & Beck, 1995).
As noted in the Introduction, this result is predicted by many different theories of contingency judgments (see Blanco et al. 2011, 2012).
Thus, a variety of theories of contingency judgments, which are clearly different from each other (see Shanks, 2007; 2010 for comprehensive reviews of associative, inferential, and other theoretical accounts of contingency judgments), will nevertheless predict that any factor that contributes to a higher number cell a events, with respect to the other cells, should promote higher judgments.
Cause-outcome coincidences (i.e., cells a) are known to be the pieces of information that have the largest impact on contingency judgments (e.g., Anderson & Sheu, 1995; Kao & Wasserman, 1993, Matute et al., 2011, Smedslund, 1963; White, 2003).
However, there is evidence supporting the idea that the more the participants act, the greater their contingency judgments will be (e.g., Blanco, Matute, & Vadillo, 2009; Blanco et al., 2011; Matute, 1996).
Despite the many differences among the various theories of contingency judgments that attempt to explain the illusion of control and related effects (see Blanco, Matute, & Vadillo, 2011, 2012), they all agree that decades of research in this area have shown that people do not give the same weight to each cell in the contingency matrix (e.g., Kao & Wasserman, 1993).
In addition to the outcome-density bias there is the cue-density bias which refers to an overestimation of contingency judgments when the probability of the potential cause, p(C), is high (Allan & Jenkins, 1983; Hannah & Beneteau, 2009; Vadillo, Musca, Blanco, & Matute, 2011).
The analogy with scientific objectivity would reside in the fact that the way to arrive at such objective and universally valid truth would be to detect and correct for the biases and distortions introduced into one's practical judgment by contingencies of one's personal or parochial perspective.
Necessity and contingency are fundamental, and judgments of truth mean something different in each modal context, rather than truth being primary, and necessity and contingency providing a different valence to otherwise true propositions.
Therefore, and consistent with our hypothesis, participants' judgments of contingency were affected by p(C) and not by personal involvement.
