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Updating Context in the Equation: An Experimental Argument with Eye Tracking

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

The Bayesian model was recently proposed as a normative reference for psychology studies in deductive reasoning. This new paradigm supports that individuals evaluate the probability of an indicative conditional if A then C in the natural language as the conditional probability \(P(\textit{C given A})\) (P(C|A) according to Bayes’ rule). In this paper, we show applying an eye-tracking methodology that if the cognitive process for both probability assessments (\(P(\textit{if A then C})\) and P(C|A)) is really identical, it actually doesn’t match the traditional focusing situation of revision corresponding to Bayes’ rule (change of reference class in a static universe). Individuals appear to revise their probability as if the universe was evolving. They use a minimal rule in mentally removing the elements of the worlds that are not A. This situation, called updating, actually seems to be the natural frame for individuals to evaluate the probability of indicative conditional and the conditional probability.

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Notes

  1. 1.

    In this paper we refer to de Finetti’s subjective Bayesian probability theory [16] that provides a unified perspective to study reasoning and probability judgment [10].

  2. 2.

    The two usual forms of Bayes’ rule are the conditional probability:

    $$\begin{aligned} P(H|D) = \frac{P(H \wedge D)}{P(D)}=\frac{P(H \wedge D)}{P(H \wedge D)+P(\lnot H \wedge D)} \nonumber \end{aligned}$$

    and the Bayes’ identity:

    $$\begin{aligned} P(H|D) = \frac{P(H)P(D|H)}{P(D)}=\frac{P(H)P(D|H)}{P(H)P(D|H)+P(\lnot H)P(D|\lnot H)} \nonumber \end{aligned}$$

    with P(H) the prior probability of hypothesis H, P(H|D) the posterior probability after the knowledge of data D, P(D|H) the likelihood and P(D) the probability of D.

  3. 3.

    The other main change, not covered in this paper, is the analyzis of deductive arguments in the light of de Finetti’s Bayesian coherence interval [12, 41, 45]. Some studies show a relative coherence in Human deduction under uncertainty [14, 41–43, 46, 48].

  4. 4.

    Recent studies show that a majority of individuals have a trivalent interpretation of the conditional event [47] and that de Finetti’s three-valued tables [18] are the best approximation for participants’ truth tables [5, 6, 11].

  5. 5.

    With \(\wedge _{k}\) for the Kleene-Łukasiewicz-Heiting conjunction.

  6. 6.

    This minimal rule is actually the intuitive local rule proposed in [30, 31] to estimate the probability of a conditional in a problem of type 2. It recently ignated a philosophical debate [19, 33, 34]. In this updating context, this rule is axiomatically justified [29, 49].

  7. 7.

    The minimal rule is isomorphic to redistributing the weights of removed world(s) proportionally to the remaining world(s). For the type 1 problem, it mathematically corresponds to Bayes’ rule:

  8. 8.

    These colors were better discriminated.

  9. 9.

    The viewing angle of the stimuli was 9.6 on a \(1920 \times 1080\) resolution computer screen.

  10. 10.

    To avoid a possible order effect, the participants were randomly allocated to six groups which all answered five questions (two controls and the three conditionals in different orders).

  11. 11.

    The gaze behavior were also recorded for scan path and visual strategy (VS) investigation.

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Authors and Affiliations

  1. Laboratoire CHArt, Université Paris 8 & EPHE, Site Paris-EPHE, 4-14 Rue Ferrus, 75014, Paris, France

    Jean Baratgin, Brian Ocak, Hamid Bessaa & Jean-Louis Stilgenbauer

  2. Institut Jean Nicod (École Normale Supérieure), Paris, France

    Jean Baratgin

  3. Université de Franche-Comté, Besançon, France

    Brian Ocak

Authors
  1. Jean Baratgin
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  2. Brian Ocak
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  4. Jean-Louis Stilgenbauer
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Correspondence to Jean Baratgin .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Baratgin, J., Ocak, B., Bessaa, H., Stilgenbauer, JL. (2017). Updating Context in the Equation: An Experimental Argument with Eye Tracking. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_4

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