Pertaining a Short, Weird Dream Last Week. Or, a Simplistic Mathematical Hooey Against Lesser of Two Evil Fallacy

This is gonna be very short.

Some days ago, I had a not-so-usual dream. In my dream, I was discussing with a man, whom I never know in real life. We were discussing about the latest Indonesian presidential election. Perhaps - representing my inner conscience - he accused my decision to vote for a certain candidate as a fallacy. Specifically, a lesser of two evil fallacy. To make it short, the lesser of two evil fallacy (more or less) states that even if you choose "the lesser evil" of two evil options, your choice still constitute a bad choice, i.e. lesser or greater notwithstanding, it's still an evil. Not voting is thus considered a better option than choosing the less evil one.

What follows is a weird answer from me.

I replied that this is not actually the case. Suppose there are candidate 1 and 2, who have (let's say) "evil score" of non-negative value of A and B, respectively. And since this is a presidential election, you will still get a president, either 1 or 2 (which is both evil anyway), even if you don't vote.

Let's assume, arbitrarily, that the value of A (evil score of candidate 1) > B (candidate 2's score). Then, there is a probability  p between 0 and 1 of you getting candidate 1, and (1 - p) of getting candidate 2 as president. Not choosing either candidates will give you expected value of  "evil score" as: pA + (1 - p)B.

Since A > B, it follows that pA + (1 - p)B > B, by the dumb calculation that because p + (1 - p) = 1, B = pB + (1 - p)B. And since A > B, then pA > pB for any value of 0 < p < 1. Thus, it is easily seen that pA + (1 - p)B > pB + (1 - p)B, which is another way to say that not choosing any candidates bears an expected value of evil score more than simply choosing the lesser evil one.

This of course can only  be applied to personal choice and cannot be aggregated as a decision function of a whole society. After all, this is a super-duper-simplistic stuff coming from my sleeping brain. I'm putting this here because how funny it is for me, to be able to sleep and conjuring mathematical ramblings in a dream.