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Reinhard Blutner 1 Linear Algebra and Geometric Approches to Meaning 4a. Question Order Effects Reinhard Blutner Universiteit van Amsterdam ESSLLI Summer School 2011, Ljubljana August 1 – August 7, 2011

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Reinhard Blutner 2 1 1.Factual questions & attitude questions 2.Four types of question ordering effects 3.Modelling ordering effects 4.One-qubit realization

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Reinhard Blutner 3 Factual questions and attitude questions 1.a.What is your name? b.Where do you live? c.In what year did you first have an episode of back pain lasting a week or more? 2.a.Do you think the use of marijuana should be made legal, or not? b.Would you be for or against sex education in the public schools? c.On the average, (Blacks/African-Americans) have worse jobs, income, and housing than white people. Do you think these differences are mainly due to discrimination?

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Reinhard Blutner 4 Importance of attitude questions Survey reports –Schuman, H. & Presser, S. (1981). Questions and answers in attitude surveys: Experiments in question form, wording, and context. (New York: Academic Press) –Tourangeau, R., Rips, L. J. & Rasinski, K. (2000). The Psychology of Survey Response. (Cambridge: Cambridge University Press) –Moore, D. W. (2002). Measuring New Types of Question-Order Effects. Public Opinion Quarterly 66: 80-91. Personality theories –The Myers-Briggs type indicator (MBTI) –The big five personality test –Keirsey Temperament Sorter –The Singer-Loomis Inventory of Personality (SLIP)

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Reinhard Blutner 5 2 1.Factual questions & attitude questions 2.Four types of question ordering effects 3.Modelling ordering effects 4.One-qubit realization

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Reinhard Blutner 6 NORC 1948

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Reinhard Blutner 7 Schumann & Presser 1981

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Reinhard Blutner 8 Assimilation assimilation

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Reinhard Blutner 9 Contrast contrast

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Reinhard Blutner 10 Additive additive

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Reinhard Blutner 11 Subtractive subtractive

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Reinhard Blutner 12 3 1.Factual questions & attitude questions 2.Four types of question ordering effects 3.Modelling ordering effects 4.One-qubit realization

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Reinhard Blutner 13 Conditional probabilities Classical definition for propositions a and b : – (b/a) = (ab)/ (a) Gerd Niestegge´s generalisation: – (b/a) = (aba)/ (a) Sequence of two yes/no-questions – (a;b) = (a) (b/a) = (aba)

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Reinhard Blutner 14 Two-dimensional example (A) =.3 (B; A) =.6 (B) =.9 (A; B) =.2 A (A; B) B s (B; A) assimilation

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Reinhard Blutner 15 Question order effects (yes/no-questions) Definition: a (b) = (a;b) + (a´;b) (b) (*) Fact: a (b) = 2 (a; b) 2( (a) (b)) ½ cos, when con- sidering a pure state ; is a phase shift parameter Proof: (a;b) + (a´;b) (b) = ba ba + ba ba (ba + ba ) (ba + ba ) = ba ba ba ba = 2 Re(ba ba ) = 2 Re(ba (b ba) ) = 2 ba ba 2 Re(a b )= 2 (a; b) 2( (a) (b)) ½ cos. (*) Note: we write a´ instead of a

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Reinhard Blutner 16 Explaining order effects Wang & Busemeyer (2010): Quantum Model of Question Order Effects. Submitted for publication

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Reinhard Blutner 17 Niestegges theorem (a; b) (b; a) = (a; b) (b; a) Proof: Using the fact that (a;b) = (a) (b/a) = (aba), the proof reduces to showing that aba+aba = bab+bab. Using a=1-a and b=1-b this equality can be shown by elementary algebraic manipulations.

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Reinhard Blutner 18 Empirical test Wang & Busemeyer (2010) found empirical evidence that the constraint expressed by Niestegges theorem is satisfied in 3 of 4 cases: a(b) = -.0031assimilation -.0031 contrast -.0189additive 0.1514subtractive (sign. different of 0) T he prediction for the quantum model was based on the assumption that only the question order influences the question context. This assumption is violated in the Rose/Jackson data set. Respondents lacked sufficient knowledge about the baseball players. Thus, additional information was given. Hence, the context for the second question was changed not only by answering the first question, but also by the additional background information on the player in the second question.

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Reinhard Blutner 19 4 1.Factual questions & attitude questions 2.Four types of question ordering effects 3.Modelling ordering effects 4.One-qubit realization

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Reinhard Blutner 20 Qubit states A bit is the basic unit of information in classical computation referring to a choice between two discrete states, say {0, 1}. A qubit is the basic of information in quantum computing referring to a choice between the unit- vectors in a two-dimensional Hilbert space. The orthogonal states and can be taken to represent true and false, the vectors in between are appropriate for modeling vagueness.

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Reinhard Blutner 21 Bloch spheres Real Hilbert Space: Complex Hilbert Space

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Reinhard Blutner 22 3 dimensions –Introverted vs. Extraverted –Thinking vs. Feeling –Sensation vs. iNtuition 8 basic types C.G. Jungs theory of personality

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Reinhard Blutner 23 Introverted iNtuitive Thinker Sherlock Holmes Shadow

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Reinhard Blutner 24 Diagnostic Questions When the phone rings, do you hasten to get to it first, or do you hope someone else will answer? (E/I) In order to follow other people do you need reason, or do you need trust? (T/F) c.Are you more attracted to sensible people or imaginative people? (S/N)

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Reinhard Blutner 25 Predictions of the model Real Hilbert space: Complex Hilbert space

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Reinhard Blutner 26 Predictions of question order effects The qubit model forbids subtraction and contrast effects Assimilation and addition effects are possible. cos( )=0 cos( )=1 T S

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Reinhard Blutner 27 Conclusions Descriptive framework for describing all four types of question order effects Restrictive framework: there are general constraints on order effects which can be empirically tested Explanatory framework? Why do we find certain ordering effects for certain pairs of questions? What does the phase parameter mean?

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