"Players who are part of a Brawl team can vote, however special rules apply for them. Each player who wants to vote gives out points as normal. However these points are not counted in the same way as non-team voints. For each team, all the points of its voting players are added, and whichever team gained the most points, will get 2 voints, while the second team will get 1 voint. Players can not give any voting points to their own team."
So team voting is not mandatory, and by voting you are harming your chances because you can't vote for yourselves.
This will only work if at least 1 player from each team must vote, and if all votes from each team are amalgamated into one vote for that team (this is ambiguous in the rules, do all player votes from all teams get added together, or each team's votes get amalgamated?).
The rule should read as this:
"Players who are part of a Brawl team can vote, however special rules apply for them. Each team must have at least one player vote. Each player who wants to vote gives out points as normal. However these points are not counted in the same way as non-team voints. For each team, all the points of its voting players are added, and whichever team gained the most points from that team's votes, will get 2 voints, while the second team will get 1 voint. Players can not give any voting points to their own team."
Example 1:
Team A votes team B as best and team D as 2nd best.
Team B votes team C as best and team D as 2nd best.
Team C votes team B as best and team D as 2nd best.
Team D doesn't vote. if they had, chances are they would have voted for team C for 1st or 2nd, and they would have come third, but because they didn't they come 2nd.
Example 2:
3 players from team A vote.
2 players from team B vote.
1 player from team C votes.
2 players from team D vote.
Only 5 players could have cast votes for team A.
6 players could have voted for teams B and D.
7 players could have voted for team C.