Can Continuous Time Markov Chains be used as a reasonable voting system?

Note that a much simpler way to find the stationary distribution of a CTMC is to solve $\mathbf M \boldsymbol \pi = \mathbf 0$.

One of the problems with this system is a severe vulnerability to candidate cloning. Imagine two candidates $A, B$ with a 60% majority preferring $A$. As expected, $A$ wins.

$$ \begin{align*} 3 &: A > B \\ 2 &: B > A \\ \end{align*} \\ \mathbf M = \begin{bmatrix}-2 & 3 \\ 2 & -3\end{bmatrix}, \boldsymbol \pi = \begin{bmatrix}3 \\ 2 \end{bmatrix} $$

Now suppose we add a candidate $C$ that’s almost an exact copy of $B$ whose only purpose is to be slightly worse than $B$. Now $B$ wins!

$$ \begin{align*} 3 &: A > B > C \\ 2 &: B > C > A \\ \end{align*} \\ \mathbf M = \begin{bmatrix}-4 & 3 & 3 \\ 2 & -3 & 5 \\ 2 & 0 & -8\end{bmatrix}, \boldsymbol \pi = \begin{bmatrix}12 \\ 13 \\ 3 \end{bmatrix} $$