Even if it was, which it isn't, why would it matter? The point remains that is just makes more logical sense to cater to the larger group then the smaller. Everywhere you look this is fact. If you had 4 friends and 3 apples, and 3 of the friends wanted 1 apple each and one friend wanted all 3 apples, what would you do? I doubt you would toss a coin or roll a die to decide to make 3 people happy or just one person.
Oh and btw, A Socialist would imply equality, in this case it would be most likely neither the majority vote OR the 80% and the 20%, it would be a pure even chance no matter how many people picked a champ.