It is not strategy proof. If it were, that would violate https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem [Edit: I think, for some version of the theorem. It might not literally violate it, but I also believe you can make a small example that demonstrates it is not strategy proof. This is because the equilibrium sometimes extracts all the value from a voter until they are indifferent, and if they lie about their preferences less value can be extracted.]
Further, it is not obviously well defined. Because of the discontinuities around ties, you cannot take advantage of the compactness of the space of distributions, so it is not clear that Nash equilibria exist. (It is also not clear that they don’t exist. My best guess is that they do.)
I proposed this same voting system here: https://www.lesswrong.com/s/gnAaZtdwjDBBRpDmw
It is not strategy proof. If it were, that would violate https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem [Edit: I think, for some version of the theorem. It might not literally violate it, but I also believe you can make a small example that demonstrates it is not strategy proof. This is because the equilibrium sometimes extracts all the value from a voter until they are indifferent, and if they lie about their preferences less value can be extracted.]
Further, it is not obviously well defined. Because of the discontinuities around ties, you cannot take advantage of the compactness of the space of distributions, so it is not clear that Nash equilibria exist. (It is also not clear that they don’t exist. My best guess is that they do.)