**Problem to face**

In methods with range [0,5] there are almost always min-max strategies that force the voters to use only ratings 0 and 5, as in approval.

In the case of methods that eliminate and normalize (STAR, etc) 1 is also used.

- If the intermediate candidates are set to 0 it is to favor as much as possible the most appreciated candidates, who have 5.
- If intermediate candidates are put at 5 is to disadvantage hated candidates at most, who have 0.

**S-TM Procedure**

You vote in a range with these values: {worst,1,2,3,4,best}.

For each pair of candidates the best is found, by adding up the points (win the highest sum), with these rules:

- the candidate with [best] receives 5 points, and 0 points to the other.
- the candidate with [worst] receives 0 points, and 5 points to the other.
- if both have intermediate values, so they are added as they are.

(- a vote in which the two candidates have both [worst] or [best], is not added).

The candidate who wins in the most pairwise matches wins.

**Tie**

- Only the 2 candidates (among those in tie) with the highest number of ratings [best] are considered, among which the one who won in the pairwise match wins.

or
- Only the 2 candidates (among those in tie) with the lowest number of ratings [worst] are considered, among which the one who won in the pairwise match wins.

**Example (tie 1)**

Given an honest vote like this:

A [best] B [4] C [3] D [2] E [1] F [worst]

A's probability of winning does not change if the vote were like this:

A [best] BCDEF [worst] *(all at worst except A).*

while, the probability of victory of candidate F [worst] would increase.

There is no point in minimizing it in that way.

Respectively, if the vote were tactically like this:

ABCDE [best] F [worst]

the probability of victory for F would not decrease (apart from the rare cases of ties), while the probability of victory for A would decrease compared to honest vote.

Maximization is extremely disadvantaged (it can only serve in rare cases of tie, and it can disadvantage the victory of the true best candidate).

**Tie 2)** Maximization could be more disadvantaged (slightly favoring minimization) using procedure 2 in tie cases.

**Conclusion**

Limiting ourselves to the case of min-max strategies, the voter after assigning [best] to the candidates that he loves the most, and [worst] to those he hates most, will be able to feel free to assign intermediate scores to the other candidates.

Extreme case:

The intermediate ratings are maximized, making the honest starting vote become:

A [best] B [4] C [**4**] D [**1**] E [1] F [worst]

However, min-max intermediate candidates remains less favorable than min-max on the classic other systems with range.

P.S.

Due to the meaning of [worst] and [best] (not numeric values), it's not possible to uniquely convert a vote with range [0,5] into an S-TM vote.

**I think** that ratings with range [0,7] would probably be converted like this:

{7,6,5,4,3,2,1,0} --> {best, 4,3,2,2,1, worst, worst}