  We study a stochastic model of consensus formation, introduced in 2015 by
Grinfeld, Volkov and Wade, who called it a multidimensional randomized
Keynesian beauty contest. The model was generalized by Kennerberg and Volkov,
who called their generalization the Jante's law process. We consider a version
of the model where the space of possible opinions is a convex body
$\mathcal{B}$ in $\mathbb{R}^d$. $N$ individuals in a population each hold a
(multidimensional) opinion in $\mathcal{B}$. Repeatedly, the individual whose
opinion is furthest from the center of mass of the $N$ current opinions chooses
a new opinion, sampled uniformly at random from $\mathcal{B}$. Kennerberg and
Volkov showed that the set of opinions that are not furthest from the center of
mass converges to a random limit point. We show that the distribution of the
limit opinion is continuous, thus proving the conjecture made after Proposition
3.2 in Grinfeld et al.
