I still think that all the benefits you talk about end when the voters notice that the ratings are converted like this, before being added up:

{0,1,2,3,4,5} --> {-1, -0.6, -0.4, -0.25, -0.15, -0.1}

Note, that by converting them to negative metrics, the greater sum wins (equivalent to saying that, with positive metrics, the smaller sum wins).

**I donâ€™t want to talk about other voting systems, just about the idea used to avoid maximization.**

**FAIR-Max**

STAR uses the sum of the points in the first round (utilitarian) to get only 2 candidates, on which it then makes an automatic-runoff (majoritarian). The first round introduces the problem of min-maxing while the second round introduces the â€śproblemâ€ť of the majority.

FAIR-Max treats the votes as rankings as it eliminates the candidates (very majoritarian) and when only 2 candidates remain, it adds up the points (utilitarian). Overall itâ€™s very utilitarian but also resistant to maximization.

The method itself also has an actual mathematical property that effectively nullifies maximization as a tactic, leaving only minimization.

**Extended DV**

In Score Voting, to maximize a candidate itâ€™s sufficient to give him 5 points, while to minimize it is given 0 points.

By voting in one of the following two ways:

A [5] B [5] C [0] D [0]

A [5] B [0] C [0] D [0]

A is always maximized in the same way, that is, it always has 5 points of difference (maximum difference) from all those minimized.

This ensures that even minimized candidates are always minimized in the same way.

In DV, effective maximization and minimization is possible only in one case:

A [5] B [0] C [0] D [0] which then (with 100 points distributed) becomes

A [100] B [0] C [0] D [0]

If you vote like this instead:

A [5] B [5] C [0] D [0] which then (with 100 points distributed) becomes

A [50] B [50] C [0] D [0]

A is no longer maximized because it no longer has 100 points of difference with all other candidates. Likewise, all other candidates are no longer minimized to the maximum.

All this prompts voters to accumulate 100 points on their preferred candidate (similar to bullet voting, in single-winner case).

Extended DV (or Reversed DV), instead of assigning 100 â€śpositiveâ€ť points to approved candidates, assigns -100 â€śnegativeâ€ť points to disapproved candidates.

This means that, in Reversed DV, the only way to maximize-minimize is by voting like this:

A [5] B [5] C [5] D [5] E [5] F [0] invert the vote

A [0] B [0] C [0] D [0] E [0] F [-5] and distribute the -100 points

A [0] B [0] C [0] D [0] E [0] F [-100]

This means that the more candidates, the harder it becomes to maximize.

A vote like this (bullet vote):

A [5] B [0] C [0] D [0] E [0] F [0] inverted in

A [0] B [-5] C [-5] D [-5] E [-5] F [-5] and distribute the -100 points

A [0] B [-20] C [-20] D [-20] E [-20] F [-20]

as you see, this converted vote is much less maximized-minimized than this one (the previous one):

A [0] B [0] C [0] D [0] E [0] F [-100]

In practice, while DV favors bullet voting, Reversed DV favors the opposite of bullet voting (which is much less harmful).

**Again, these are just examples to expose anti-maximization ideas in ranged votes.**