Classic-probability accounts of mirrored (quantum-like) order effects in human judgments.

Abstract

Using a large data corpus, Wang, Solloway, Shiffrin, and Busemeyer (2014) showed that order effects in the responses given to pairs of related agree/disagree questions presented in succession follow a specific pattern termed QQ-equality. The fact that QQ-equality corresponds to a parameter-free prediction of a proposed quantumprobability model, together with the failure of several alternative classic-probability accounts, led Wang et al. to conclude that it constitutes strong evidence for the quantum nature of human judgments and to issue a challenge for the development of suitable classic-probability accounts. We respond to Wang et al.'s challenge by discussing a class of repeat-choice models that is able to yield the QQ-equality as a parameter-free prediction (or a very-likely prediction a priori) and provide an overall account of the data that is comparable to the quantum model. The success of this class of models establishes a plausible benchmark against which quantum accounts of order effectslike the ones observed in this data corpus-can be compared. Finally, we argue that the assumption of respondent homogeneity implied in Wang et al.'s use of aggregated data is extremely problematic for some of the alternative models discussed here (but not necessarily for the quantum account), leading to spurious rejections at non-negligible rates. We also discuss how a move away from aggregated data could help resolve some theoretical challenges that the quantum account of QQ-equality currently faces.

Invariants in probabilistic reasoning

“…It is worth noting that we are not alone in presenting an alternative account of the QQ identity that does not depend on quantum probability effects: in a recent paper Kellen, Singmann, and Batchelder (2017) described a class of repeat-choice models that also predict the QQ identity. In the next section we test a specific prediction derived from our priming-based account of order effects in sequential question answering.…”

Modeling the Wason Selection Task: a Response to Ragni and Johnson-Laird (2020)

“…They rejected a total of nine theories out of twelve that predict independent selections. Kellen and Klauer (this issue) raised the well-documented point that one cannot infer dependencies at the individual-person level based on aggregate data (e.g., Davis-Stober & Regenwetter, 2019;Estes, 1956;Estes & Maddox, 2005;Kellen, Singmann, & Batchelder, 2018;Regenwetter & Robinson, 2017). Simply put, it is entirely possible to observe dependencies in the aggregate data even though each person selected cards independently.…”

Comparing Theories of Selection Tasks: A Critical Assessment of Boundaries and Benchmarks

“…Specifically, when discussing theory predictions, we need to determine whether these are preserved under aggregation, and if so, under which conditions/assumptions -one cannot merely take them for granted. To be clear, there are many instances in which predictions at the individual level are preserved under aggregation (e.g., Heck & Erdfelder, 2017;Kellen, Singmann, & Batchelder, 2018).…”