Testing quantum-like models of judgment for question order effect

TL;DR

This paper evaluates quantum-like models of judgment, specifically question order effects, deriving new empirical predictions and testing them against existing data, revealing limitations of non-degenerate models and suggesting further research on degenerate models.

Contribution

It introduces the Grand Reciprocity equations as empirical tests for quantum-like models and assesses their validity using existing data, highlighting the need for further exploration of degenerate models.

Findings

Non-degenerate quantum-like models often fail the Grand Reciprocity test

Degenerate models may be necessary for quantum-like models to be empirically adequate

Calls for more research on degenerate quantum-like models

Abstract

Lately, so-called "quantum" models, based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. We consider here some such quantum-like models that address question order effects, i.e. cases in which given answers depend on the order of presentation of the questions. Models of various dimensionalities could be used, can the simplest ones be empirically adequate? From the quantum law of reciprocity, we derive new empirical predictions that we call the Grand Reciprocity equations, that must be satisfied by several existing quantum-like models, in their non-degenerate versions. Using substantial existing data sets, we show that these non-degenerate versions fail the GR test in most cases, which means that, if quantum-like models of the kind considered here are to work, it can only be in their degenerate versions. However, we suggest that the route of degenerate models is not necessarily an easy one, and we argue for more research on the empirical adequacy of degenerate quantum-like models in general.