Hegselmann-Krause bounded-confidence opinion dynamics

Field: sociology · Zoo name: hegselmann_krause · Module: modelly.zoo.hegselmann_krause.model

Every agent holds an opinion in [0, 1]. At each step, all at once, every agent moves to the mean opinion of the agents within epsilon of its own, itself included. Agents further apart never influence each other, so the population splits into clusters that stop moving after a finite number of steps; a wide bound ends in consensus.

How it is written

Opinions are a Column of the Voter agents. The confidence set of an agent is a contiguous range of the sorted opinions: two searchsorted calls find its ends and a running sum gives its mean, so a step costs O(n log n) instead of the O(n^2) of comparing every pair (confidence_means). The run stops, with running set to False, as soon as no opinion moves by more than tolerance.

from modelly.zoo.hegselmann_krause.model import HegselmannKrause, HKScenario

model = HegselmannKrause(HKScenario(rng=42, epsilon=0.1))
model.run()
model.n_clusters(), model.time  # clusters, and the step at which they froze

Parameter	Default	Meaning
n	300	number of agents
epsilon	0.15	confidence bound
tolerance	1e-9	the run stops when no opinion moves more than this
min_cluster_share	0.02	clusters smaller than this share are not counted
steps	100	maximum run length of run()

Validation

tests/zoo/test_hegselmann_krause.py checks, with three seeds, that epsilon = 0.3 settles into consensus, that epsilon = 0.05 and 0.1 leave more than two and at most 1 / (2 epsilon) clusters, and that the mean cluster count falls to one over the sweep 0.05, 0.1, 0.2, 0.3. The fast step is compared with the plain O(n^2) definition on 200 agents over five steps, to within rounding (1e-12). A zero bound stops the run after one step, and the same seed gives the same run.

References

• Hegselmann, R. and Krause, U. (2002). Opinion dynamics and bounded confidence: models, analysis and simulation. Journal of Artificial Societies and Social Simulation, 5(3).

Start a project from it with modelly zoo copy hegselmann_krause my_opinions.