I was thinking about this in the shower and the big issue is that neither of the two suggestions are really ideal, as both have potential cases where the placing following the system doesn't really give a placing that makes sense.In post 2, Ellibereth wrote:- Best way to order teams after getting a n-ple with scum positions? We already have two possible methods just from this tiebreak thread.
The system used, while overall effective, places a very large weight towards placing scum in first or second. While this is something that does make a lot of sense to me (for obvious reasons of "you've got one of the scumteam right"), it would cause some issues with placings when one team has a scum in the top two and another right by the bottom, while the other team has middling places (i.e. 2-9 and 3-4 in the most extreme case - I think most would agree that the latter had a "better" overall placing).
However, the other system suggested by Kagami has almost the opposite issue, wherein so much weight is placed on the placing of the lower scum that the higher scum is all but irrelevant, which then causes issues in cases where one team has a scum at the top and one at the bottom, while the other team has low-middle places. The most extreme example here is 1-9 and 7-8, where the latter would win while, again, most would agree that the former has better placing.
I think the best kind of system would be a points-based system (with lower points for better placings, lowest points win) similar to either, but without the weighting being so extreme - a bonus lowering of points for scum placed in the top two, for example, or maybe a higher negative weight given to the lower scum but not by a factor of ten.
Of course, without literally making a poll ahead of time and then constructing a table with literally every combination and the agreed comparison of which is better, there will always be some middle grounds which will be highly contested, but by keeping a weighted system but without being so extreme it'll generally create a more agreeable result.