Monotonicity conjecture for final-state probabilities in the Offended Voter Model

Let $\mathcal{A}_N$ and $\mathcal{C}_N$ be the final states defined in the model's classification, and write $\mathbb{P}_q$ for probability under parameter $q$. Monotonicity conjecture. The final-state probabilities satisfy

$$q\mapsto\mathbb{P}_q(\mathcal{A}_N)\text{ is decreasing},\qquad q\mapsto\mathbb{P}_q(\mathcal{C}_N)\text{ is increasing}.$$

Thus increasing $q$ should decrease the probability of state $\mathcal{A}_N$ and increase the probability of consensus state $\mathcal{C}_N$. The paper states this as a suspected monotonicity and provides no proof in the supplied text.