Abstract
We propose a dynamical systems model for approximating the certainty as a function of communication. Uncertainty is measured during a small group decision-making process, in which participants aim to reach consensus. Assuming that the communication is a one-dimensional continuum variable, both first- and second-order differential models of certainty are analyzed, and then, the general model is obtained by superposition. An experiment was organized, and the data have been used to test the model. A detailed discussion on the assumptions of this approach from the decision theory point of view is also included.
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Notes
We say that a function of time oscillates if, for a significant period of time, it increases and decreases consecutively for a significant number of times.
The constant solution of a linear differential equation with constant coefficients and constant forcing function is called the equilibrium solution; given another solution, we say that it has an evolution to equilibrium if, as time goes, it becomes closer and closer to the equilibrium solution (asymptotically converges to the equilibrium value) (Medio and Lines 2001: 25).
The state space (phase space, configuration space) is the space of the dependent variables (the variables that specify the state of the system); in the context of the proposed model, it is \(\mathbb {R}\) (the real line) (Medio and Lines 2001:11).
In the context described at the beginning of Sect. 2 regarding the view of individual characteristics as comprising of both social and individual characteristics.
We thank Cătălin Zamfir for bringing this issue to our attention.
Beck and Katz (2007) show that least-squares approximations for time series in cross-section data are appropriate only if the errors are spherical. This means that the variance of the distribution of variances of residuals is relatively small (\(VVR\,=\,1.649589\)) and that the correlation matrix of the residuals is diagonal (has close to \(0\) correlations outside of the diagonal). The results of this analysis showed that the use of the ordinary least-squares approximation method employed is justified and appropriate.
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Acknowledgments
I would like to thank Cătălin Zamfir for the helpful discussions and for facilitating and encouraging the experimental process. I am also indebted to Cosmin Toth for encouraging this project in the first place and for participating in many helpful discussions. Also I am indebted to Adrian Duşa for helpful comments on earlier manuscripts of this paper. I would like to thank Aurelian Gheondea for his help with using MATLAB. Many thanks as well to Sorin Costiner for pointing me toward bootstrapping methodology. I am also grateful to the anonymous reviewers at GDN for the constructive feed-back that helped in considerably improving the presentation of this research.
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Appendix
See Table 5.
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Gheondea-Eladi, A. The Evolution of Certainty in a Small Decision-Making Group by Consensus. Group Decis Negot 25, 127–155 (2016). https://doi.org/10.1007/s10726-015-9436-8
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DOI: https://doi.org/10.1007/s10726-015-9436-8