In an election, the voter often divides the candidates into two categories: approved (positive) and disapproved (negative) candidates, which can be more or less approved / disapproved.
In this case, the voter wants two contradictory things (this is the paradox):
R1) wants his vote to influence the victory of approved and disapproved candidates, based on how much he approves / disapproves them.
R2) wants its limited power to be used completely in favor of approved candidates, without going in any way wasted on disapproved ones.
Positive side of R1): generally offers a better representation of interests.
Downside of R1): it generally benefits unknown candidates (e.g. those only heard of by friends and relatives) who would be placed halfway between those approved and those disapproved. If on average the disapproved are more than those approved, the little-known candidates may also be winners.
Positive side of R2 ): in general, there is no risk of favoring unknown candidates.
Downside of R2 ): generally, it doesn’t offer a good representation of interests.
-] Methods like FPTP and AV, support R2).
-] Borda support the R1), classifying all candidates.
-] Score Voting and Distributed Voting use ranges [0,10] which although in theory they can fully satisfy R1), in practice they end up being used in mode R2), that is “the candidates disapproved at 0 points, and the others by 1 at 10 points.”
-] IRV somewhat supports R1 and R2 but is also subject to both downside.
Distributed 2-Voting is the only method that supports R1 and R2 simultaneously, with both positive sides.
This manages to do this by dividing each vote (which uses range [-9,+9]) into two votes: positive vote (which considers only approved candidates) and negative vote (which considers only disapproved candidates).
In the counting, only positive votes are used (satisfies R2) to find the worst candidate who is then eliminated, normalizing the votes.
If during the elimination of the candidates, a positive vote loses all the supported candidates, then it’s replaced in the count with the negative one (satisfies R1).
With this middle ground, monotony is given up a little (because it is like IRV with 2 ranking position), but without benefiting unknown candidates and in fact providing a total and unambiguous representation of interests (also regarding disapproved candidates, which is missing in other systems).