  We study the phenomenon of intransitivity in models of dice and voting.
  First, we follow a recent thread of research for $n$-sided dice with pairwise
ordering induced by the probability, relative to $1/2$, that a throw from one
die is higher than the other. We build on a recent result of Polymath showing
that three dice with i.i.d. faces drawn from the uniform distribution on
$\{1,\ldots,n\}$ and conditioned on the average of faces equal to $(n+1)/2$ are
intransitive with asymptotic probability $1/4$. We show that if dice faces are
drawn from a non-uniform continuous mean zero distribution conditioned on the
average of faces equal to $0$, then three dice are transitive with high
probability. We also extend our results to stationary Gaussian dice, whose
faces, for example, can be the fractional Brownian increments with Hurst index
$H\in(0,1)$.
  Second, we pose an analogous model in the context of Condorcet voting. We
consider $n$ voters who rank $k$ alternatives independently and uniformly at
random. The winner between each two alternatives is decided by a majority vote
based on the preferences. We show that in this model, if all pairwise elections
are close to tied, then the asymptotic probability of obtaining any tournament
on the $k$ alternatives is equal to $2^{-k(k-1)/2}$, which markedly differs
from known results in the model without conditioning. We also explore the
Condorcet voting model where methods other than simple majority are used for
pairwise elections. We investigate some natural definitions of "close to tied"
for general functions and exhibit an example where the distribution over
tournaments is not uniform under those definitions.
