This seems like a more cardinal version of Distributed Score Voting. Also probably worth investigating whether this is a generalized form of Nanson and Baldwin's methods, since those operate by eliminating the last-place candidate based on points and redistributing support. BetterVotingAdvocacy (talk) 22:25, 20 February 2020 (UTC)
I don't think the bit about the optimum strategy is correct.
For p>1 it may be beneficial to distribute some weight to other choices due to the effective penalty on the highest rated candidate by pushing that rating a little higher, vs the lesser penalty by pushing some other candidate's rating higher. See e.g. the Wikipedia article on quadratic voting.
In addition, even if it were correct about optimum cumulative voting strategy, adding a runoff does not preserve the invariant: consider e.g. Plurality vs IRV. So I'll remove that part. Kristomun (talk) 17:38, 16 December 2021 (UTC)