Jan Lorenz (2006)
Consensus Strikes Back in the Hegselmann-Krause Model of Continuous Opinion Dynamics Under Bounded Confidence
Journal of Artificial Societies and Social Simulation
vol. 9, no. 1
<https://www.jasss.org/9/1/8.html>
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Received: 06-Jun-2005 Accepted: 28-Sep-2005 Published: 31-Jan-2006
Given an initial opinion profile x(0) we define the HK process of opinion dynamics as a sequence of opinion profiles (x(t))_{t} recursively defined through x(t+1) = A(x(t)) x(t).
With abbreviation M_{i} = M_{i}(p,k) we define the HK transition matrix B(p,k) as
Cluster | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|---|
t | k = 10 | 8 | 11 | 15 | 18 | 21 | 24 | 27 | 31 | 34 | 37 |
k = 100 | 8 | 12 | 15 | 18 | 21 | 25 | 28 | 31 | 34 | 37 | |
Δ | k = 10 | - | 24.41 | 23.74 | 23.45 | 23.38 | 23.29 | 23.21 | 23.16 | 23.16 | 23.08 |
k = 100 | - | 228.86 | 225.33 | 222.56 | 221.73 | 220.65 | 221.95 | 220.35 | 219.64 | 219.70 | |
# | k = 10 | 24.93 | 24.11 | 23.64 | 23.40 | 23.35 | 23.31 | 23.18 | 23.10 | 23.22 | 23.08 |
k = 100 | 238.84 | 227.48 | 224.91 | 222.57 | 220.90 | 220.50 | 223.13 | 220.75 | 216.69 | 220.87 |
We calculate the interactive Markov chains until stabilisation for the uniform initial distribution and all interesting discrete bounds of confidence. Figure 10 shows the results for n = 100 and k = 1, ..., 30 in an animation stabilising in a kind of bifurcation diagram.
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