Is your question “what is the probability for one of my post to have 69% upvotes”? This should be answered by a binomial distribution!
According to this website, for p=0.5; n=100; and x=69 the probability should be ~0.005%.
This means that if 100 people vote your post perfectly randomly, the chance of getting 69% upvotes is ~0.005%. This number will also become smaller if more people start voting since given an infinite amount of votes, the ratio of upvotes should converge towards the chance that a person gives your post an upvote (aka. 50%) so we’d get even further from our 69% target.
Basically, if people vote perfectly randomly it’s unlikely to get to exactly 69%. Such is the fate of us mortals :(
Yup! In that case, this is not an answer that can be solved “mathematically” as you asked: convincing a large group of total strangers to do something for you is within the realm of crowd psychology.
If r/place showed us anything, it’s that you can get people to work hard together if you make them feel part of a community. Maybe creating a Lemmy community whose goal is to keep all posts within that community at 69% would work?
Not sure if that’s the answer you wanted but that’s how I’ve understood your question so don’t hesitate to correct me :)