The first is the tournament scoring system that, while not originating from, I first encountered at The Boroughs Diplomacy Tournament. It’s a Sum of Squares scoring system with two easy rules
A) WTA. In the event of a solo, the winner receives 100

; all other players receive 0

B) In the event of a draw, each player will receive a percentage of 100

, proportionally to the number of centers they control as follows:
(I’m betting 1000:1 that webdip forum will fuck up formatting of sigma notation and sub/super scripts so forgive the crudeness)
Percentage to Player 1 = (SC owned by Player 1)^2 divided by [SUM FOR PLAYERS 1-7 (SC owned by player N)^2 ]
Where N of course is players 1-7
In descriptive rather than mathematical terms, what this means is that the portion of the 100

you get increases non-linearly with SC you own, AND ALSO increases the more fragmented the other players’ SCs are spread out.
Let’s take an example [country: SC; points]:
England: 8; 27.83
Russia: 8; 27.83
France: 7; 21.3
Turkey: 6; 15.65
Italy: 4; 6.96
Austria: 1; 0.43
Germany: 0; 0
How did England get 27.83? Well, it’s 100 * (8^2 / (8^2+8^2+7^2+6^2+4^2+1^2+0^2)).
It should be immediately obvious how more SC means more points. While the numerator rises quadratic ally, the denominator does not rise as much (although it still does) due to being diluted out by the other scores.
The denominator is what’s really interesting here. To easily illustrate this, a score of 16 SC against a 9 SC and 9 SC power would give you 100 * (16^2 / (16^2 + 9^2 + 9^2)), or 61.24. A score of 16 SC against the other 6 powers each having 3 SC would give you 100 * (16^2 / (16^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2) = 82.58.
So this scoring system (A) has a WTA mechanic (B) non-linear scaling (C) promotes not eliminating other players unless you’re the one eliminating them. It actually hurts your score to allow weaker players to be taken over by others and (C.2) disregards amount of players in a draw, only their SC amounts