  In the Hegselmann-Krause model, an agent updates its opinion by averaging
with others whose opinions differ by at most a given confidence threshold. With
agents' initial opinions uniformly distributed on the unit interval, we provide
a straightforward proof that establishes the critical value is up to one-half.
This implies that the probability of consensus approaches one as the number of
agents tends to infinity for confidence thresholds larger than or equal to
one-half.
