Conjecture on decreasing marginal value of defectors in majority dynamics

Let $c1(k,n)$ be the probability that Red wins when Red's camp initially has size $n/2+k$, with $p=.5$, and define the value of the $i$th defector by

$$v(i,n)=\rho(i,n)-\rho(i-1,n),$$

with $c1(n,0)=1/2$. Values of defectors conjecture. For any fixed $i$ and sufficiently large $n$,

$$v(i,n)\geq v(i+1,n).$$

The claim formalizes the intuition that successive defectors provide diminishing advantages; the paper gives no proof or resolution, so the conjecture remains open.