The scoring system in use is called Fibonacci Scoring, developed by Alex Ronke and based off a very popular FtF tournament scoring system, Carnage.
Fibonacci is a rank-based scoring system, meaning that in a game that ends in a draw rather than a solo, everyone is scored according to their place within that draw relative to everyone else. So how many people are included in a draw is irrelevant--what matters is if you have the most SCs, the second most, etc.
For Vikings and Medieval, the scoring breakdown is:
8th—1200
7th—1200
6th—2400
5th—3600
4th—6000
3rd—9600
2nd—15600
1st—27600
With 80000 points awarded for a solo (everyone else gets zero). So, for example, a 14 center board topper will score the same no matter if there are 3 other players alive or 7.
For Baltic, the points are distributed as such:
4th—4800
3rd—4800
2nd—9600
1st—14400
With 40000 points awarded for a solo.
In addition, every SC counts for one point (so it's a tiebreaker only, basically). Ties in position will be averaged--so a tie for 5th in Vikings would result in each team being awarded 3000 points. The maximum number of points you can score without a solo is 69658 (three board tops with the most possible SC without soloing), which isn't enough to beat a solo in either Vikings or Medieval, but could defeat a solo in Baltic (depending on the soloists other results).
Note that only one round of Baltic will be counted towards a teams score, although they may play both--so if Team X scores 4800 in the first Baltic round, decides to play again and scores 9600, only the 9600 score will be counted towards their tournament score.
At the end of the tournament, the team with the highest cumulative score wins.
Clarification for Vikings: if two powers achieve 26+ centers in the same turn (or at the end of the time limit), either may call for the game to end. If that happens, each player with 26+ centers will split the first and second place scores (plus their centers), and everyone with fewer than 26 centers will receive a zero.
Clarification: in the event of a solo, no points for SCs will be awarded. The soloist will receive 80,000 or 40,000 points depending on game, everyone else will score zero. In Vikings, in the case of the special 26+ center draw, the players with 26+ centers will receive points for the amount of SCs they own, and everybody else will receive a zero, no matter how many SCs they own.