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Theoretical Note: On the Practical Uses of Mathematical Theory for Attitude Research

Mark G. Orr, Emily S. Teti, Andrei Bura, Henning Mortveit

Abstract

In attitude theory, formal theoretical predictions come largely from the simulation of computational models. We argue that to push attitude theory further, we should employ mathematical analysis/analytic methods alongside of computational simulation, something that other sciences and engineering consider standard practice. Our work first attempts to portray the complementary nature of mathematical analysis along side of computational simulation using as an example the Causal Attitude Network model of attitudes (Dalege et al., 2016). We then introduce a mathematical theory, Graph Dynamical Systems (GDS), as a broad theoretical framework for network models of attitudes. We illustrate the use of GDS, in the context of the Attitudes as Constraint Satistfaction (ACS) theory of attitude dynamics (Monroe & Read, 2008), as a generator of precise, quantitative theoretical predictions. We conclude by pointing out the value of improved attitude theory for the so-called replication crisis in psychology. KEYWORDS: attitudes, neural networks, dynamical systems, psychological networks

Theoretical Note: On the Practical Uses of Mathematical Theory for Attitude Research

Abstract

In attitude theory, formal theoretical predictions come largely from the simulation of computational models. We argue that to push attitude theory further, we should employ mathematical analysis/analytic methods alongside of computational simulation, something that other sciences and engineering consider standard practice. Our work first attempts to portray the complementary nature of mathematical analysis along side of computational simulation using as an example the Causal Attitude Network model of attitudes (Dalege et al., 2016). We then introduce a mathematical theory, Graph Dynamical Systems (GDS), as a broad theoretical framework for network models of attitudes. We illustrate the use of GDS, in the context of the Attitudes as Constraint Satistfaction (ACS) theory of attitude dynamics (Monroe & Read, 2008), as a generator of precise, quantitative theoretical predictions. We conclude by pointing out the value of improved attitude theory for the so-called replication crisis in psychology. KEYWORDS: attitudes, neural networks, dynamical systems, psychological networks

Paper Structure

This paper contains 12 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Computational Theories of Attitudes
  3. Mathematical Analysis and Simulation are Complements
  4. The CANEA System
  5. An Illustrative Theoretical Claim
  6. Complementarity In Action
  7. A Mathematical Attitude Theory
  8. Graph Dynamical Systems
  9. Attitudes as Constraint Satisfaction
  10. From Mathematical Analysis to Experimental Predictions
  11. Conclusions
  12. Author Note

Figures (2)

  • Figure 1: Left: the network of the basic example. Right: dynamics evolving over the network for state $(x_o = 1, x_p = 1, x_c, x_e)$ and assessing whether parameter choices cause compliant or non-compliant behaviors with the persuasion attempt ($x_e < 0$ or $x_e > 0$).
  • Figure 2: A simple, textbook-like example of experimental predictions via mathematical analysis for the Attitudes as Constraint Satisfaction (ACS) model MonroeRead2008. We have introduce the two parameter relation $\alpha'=f-\delta^2$ and assert that $\alpha + \delta = 1$. Under this particular choice, we obtain the boundary curve $\gamma = \delta^2$ separating the non persuadable (light; $x_e < 0$)) and the persuadable regions (dark gray; $x_e > 0$) as a function of manipulations of persuasive influence $delta$ and automatic associative bias $gamma$. See text for details.

Theorems & Definitions (1)

  • Definition 1