Let's say there are L Labour members and C Conservative members, then p=L/(L+C) (probability of randomly choosing a Labour member) and 1-p=C/(L+C) (probability of choosing a Conservative member).
On the next vote rC/(L+C) Conservative members will change their minds while (1-r)C/(L+C) will vote the same as they did before. The respective probabilities are r(1-p) and (1-r)(1-p).
But on the next vote all Labour members (probability=1) will vote the same again. The combined probability is p.
So p+(1-r)(1-p)=p+1-p-r+pr=1-r+pr.
EXAMPLE
Let L=200, C=400, so L+C=600, p=⅓, 1-p=⅔.
Let r=⅗, so 1-r=⅖.
Since Labour members don't change their minds on a particular issue, 200 will vote the same on successive votes. ⅖ of the 400=160 Conservative members will also vote the same. Total voting the same=360. So 360/600=0.6, ⅗ or 60% is the proportion and the probability that a random member will vote the same on successive votes.
The formula also predicts 1-r-pr=1-⅗+⅕=⅗.