Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations\n and Applications

2019/07/10 by Sandro Sozzo, Sozzo, Sandro
Decision Sciences · Social Sciences · #Artificial Intelligence (cs.AI) #Decision-Making and Behavioral Economics #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Innovation, Sustainability, Human-Machine Systems #Neurons and Cognition (q-bio.NC) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1907.06314

openalex publication_date 2019/07/10 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We provide here a general mathematical framework to model attitudes towards\nambiguity which uses the formalism of quantum theory as a ``purely mathematical\nformalism, detached from any physical interpretation''. We show that the\nquantum-theoretic framework enables modelling of the "Ellsberg paradox", but it\nalso successfully applies to more concrete human decision-making (DM) tests\ninvolving financial, managerial and medical decisions. In particular, we\nelaborate a mathematical representation of various empirical studies which\nreveal that attitudes of managers towards uncertainty shift from "ambiguity\nseeking" to "ambiguity aversion", and viceversa, thus exhibiting "hope effects"\nand "fear effects". The present framework provides a promising direction\ntowards the development of a unified theory of decisions in the presence of\nuncertainty.\n

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