I note your (accurate) critique of the 3 systems above. Overall, I find that FPTP is the least fair.

I would be intrigued as to how a weighted AV (known as Single Transferable Vote) fares in your analysis/ opinion - it gives more weight to a higher preference vote than to a lower one (1st over 3rd say). I imagine if there was only one position you could still find that less than 50% weighted of the vote share was for any one candidate, but i think the liklihood of that happening would be slim.