Explanation of Ellsberg's and Machina's Four-Color Paradoxes for Judgment under Uncertainty and Comparison

The Ellsberg's and Machina's paradoxes, involving colored balls - two, three, four, or more - continue to challenge canonical theory of decision making under uncertainty and comparison. Despite numerous models attempting to explain them, their joint explanation remains an open question, and they are often used as input filters to test models of decision making under uncertainty. The additive (with memorizing) and subtractive (with disregarding) models of cognition proposed in this paper provide the necessary means of explanation and open the prospect of unifying modeling of various biases. These models have already been applied to other cognitive biases, such as Ellsberg's two- and three-color paradoxes, as well as conjunction and disjunction fallacies. Uncertainty should be defined as probability in the context of the entire system and its set of possible states, perceived as real and imaginary images. These images depend on knowledge about them, on the randomness of their development, on the subjectivity of their assessment and are related to the structure of the human thought process. The cognitive context can be viewed and developed as possible dynamic constructions of symptoms (balls of a certain color) with varying degrees of significance. The paper presents a heuristic modeling and resolution of cognitive biases, the four-color paradoxes of Ellsberg and Machina, using the procedure for qualification and quantification of context with the performance evaluation of teamwork method. This human reliability assessment technique involves a symptom-based procedure for assessing the context probability and a step-by-step rational interpretation of cognitive and decision-making processes under conditions of uncertainty and comparison. The core idea behind overcoming cognitive biases is to exploit quantum principles and dual role of a symptom as a wave and a chunk of information in conscious processing, with delays, ambiguity, and violations.

Keywords: Bias, Context, Symptom, Judgment, Uncertainty, Risk, Ambiguity, Paradoxes of Ellsberg and Machina.