A Quantum Cognition Analysis of the Ellsberg Paradox

Abstract

The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the 'Allais' and 'Ellsberg paradoxes', in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a 'classical logical' and a 'quantum conceptual', in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.Comment: 11 page

Quantum structure of negation and conjunction in human thought

“…During the last decade there has been an increasing evidence of presence of quantum structures in processes that find their origin in human behaviour and cognition, more specifically, in situations of decision making and in the structure of language (see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,25,23,24,26,27]). The success of this quantum modeling is interpreted as due to 'descriptive effectiveness of the mathematical apparatus of quantum theory as formal instrument to model cognitive dynamics and structures in situations where classical set-based approaches are problematical', without a priori a direct or precise connection with the validity of quantum laws in the microscopic world, although also recently a reflection connecting the quantum modeling in the micro-world with these new quantum cognition approaches has been put forward [27].…”

A survey of quantum-like approaches to decision making and cognition

“…It can be inferred from these results that in both cases, the unambiguous bet is more preferred to the ambiguous one. It is interestingly pointed out by Alerts et al (Aerts et al, 2011c;Aerts and Sozzo, 2012a,d), that, ambiguity, due to its contextuality, structurally needs a nonclassical probability model.…”

“…Aerts et al, in a series of papers demonstrated the effectiveness of quantum-like modeling for the explanation of the irrationalities of human decision making in economics including the Ellsberg and Machina paradoxes (Aerts et al, 2011a(Aerts et al, , 2010(Aerts et al, , 2011cAerts and Sozzo, 2012a,d;.…”

“…Aerts et al argue that the two states p v ry and p v rb play a key role in the mind of the decision maker (Aerts et al, 2011c). In other words, in the mind of a decision maker a superposition will take form which is as follows:…”

Quantum Decision-making in Newcomb’s Problem: Effect of Reward Size

“…However, psychological and behavioral decision theoretical foundations of human decision making in the Newcomb's problem is still unknown. Recently, in order to model paradoxical human decisions in the situation such as the Prisoner's Dilemma (Rapoport and Chammah, 1965;Croson, 1999;Li et al, 2010), Ellsberg's urn problem (Ellsberg, 1961;Aerts et al, 2011) and two-stage gambling task , quantum decision theoretical models have been developed (Pothos and Busemeyer, 2009;Busemeyer et al, 2011). These quantum decisions theoretical studies revealed that human decision making is better accounted for by quantum probabilistic models in comparison to classical probabilistic models including Bayesian rational decision theory.…”