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Yes, Prime Minister, question order does matter -- and it's certainly not classical! But is it quantum?

Dorje C. Brody

Abstract

Response to a poll can be manipulated by means of a series of leading questions. We show that such phenomena cannot be explained by use of classical probability theory, whereas quantum probability theory admits a possibility of offering an explanation. Admissible transformation rules in quantum probability, however, do impose some constraints on the modelling of cognitive behaviour, which are highlighted here. Focusing on a recent poll conducted by Ipsos on a set of questions posed by Sir Humphrey Appleby in an episode of the British political satire \textit{Yes, Prime Minister}, we show that the resulting data cannot be explained quite so simply using quantum rules, although it seems not impossible.

Yes, Prime Minister, question order does matter -- and it's certainly not classical! But is it quantum?

Abstract

Response to a poll can be manipulated by means of a series of leading questions. We show that such phenomena cannot be explained by use of classical probability theory, whereas quantum probability theory admits a possibility of offering an explanation. Admissible transformation rules in quantum probability, however, do impose some constraints on the modelling of cognitive behaviour, which are highlighted here. Focusing on a recent poll conducted by Ipsos on a set of questions posed by Sir Humphrey Appleby in an episode of the British political satire \textit{Yes, Prime Minister}, we show that the resulting data cannot be explained quite so simply using quantum rules, although it seems not impossible.
Paper Structure (7 sections, 19 equations, 1 figure, 2 tables)

This paper contains 7 sections, 19 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Conjunction fallacy revisited
  3. Appleby's leading questions
  4. Classical vs quantum probabilities
  5. Can entanglement explain leading question effect?
  6. Ipsos data on Appleby's questions can be modelled by isolating the first question
  7. Discussion

Figures (1)

  • Figure 1: Probability comparison. The probability ${\mathbb P}^F(B)$ that Linda is a bank teller, after one has assessed whether she might be a feminist, is compared here with the probability ${\mathbb P}(B)=q$ that she is thought to be a bank teller, and the probability ${\mathbb P}(F)=p$ that she is thought to be a feminist. In the triangular region $0<q<p<1$, we have ${\mathbb P}^F(B)>{\mathbb P}(B)$, indicating that the feminist question can be used as a leading question to enhance the assessment that Linda might be a bank teller.