A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice

Seminal findings involving payoffs (Shafir and Tversky, 1992; Tversky and Shafir, 1992; Shafir, 1994) showed that individuals exhibit state-dependent behaviour in different informational contexts. In particular, in the condition of ambiguity as well as risk, individuals tend to exhibit ambiguity aversion. The core principle of rational (consequential) behaviour conceived by Savage (1954), that is the ‘Savage Sure Thing’ principle, has been shown to be violated. In mathematical language, this violation is equivalent to the violation of the “Law of total probability” (Kolmogorov, 1933). Given the importance of original findings in the call for a generalization of classical expected utility, we perform in this paper a set of experiments related to expressing investment preferences: (i) under objective risk, (ii) after a preceding gain, or loss. In accordance with previous findings we detected state dependence in human judgement (previous gain or loss changed the preference state of the participants) as well as violation of consequential reasoning under risk. We propose a quantum probabilistic model of agents’ preferences, where non-consequentialism and state dependence can be well explained via interference of complex probability amplitudes. A geometric depiction of the experimental findings with a state reconstruction procedure from statistical data via the inverse Born's rule (1926), allows for an accurate representation of agents’ preference formation in risky investment choice.