On the Hegselmann-Krause conjecture in opinion dynamics. (English) Zbl 1216.91023
Summary: We give an elementary proof of a conjecture by Hegselmann and Krause in opinion dynamics, concerning a symmetric bounded confidence interval model: If there is a truth and all individuals take each other seriously by a positive amount bounded away from zero, then all truth seekers will converge to the truth. Here, truth seekers are the individuals who are attracted by the truth by a positive amount. In the absence of truth seekers, it was already shown by Hegselmann and Krause that the opinions of the individuals converge.
References:
| [1] | DOI: 10.1142/S0129183104006479 · Zbl 1058.81730 · doi:10.1142/S0129183104006479 |
| [2] | Hegselmann R., J. Artif. Soc. Soc. Simul. 5 pp 1– (2007) |
| [3] | Hegselmann R., J. Artif. Soc. Soc. Simul. 9 pp 1– (2006) |
| [4] | DOI: 10.3366/E1742360009000604 · doi:10.3366/E1742360009000604 |
| [5] | DOI: 10.1142/S0129183107011789 · Zbl 1151.91076 · doi:10.1142/S0129183107011789 |
| [6] | DOI: 10.1142/S0129183106009850 · doi:10.1142/S0129183106009850 |
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