'taxed by a proportional voting system' means that the Swedish system of proportional voting imposes a burden on Swedish viewers (presumably of TV channels) because the TV stations interrupted their normal programming to show the eight-way debate that resulted from the voting system.

"Taxed by" means they suffer due to the proportional voting system. To be taxed by something means that thing holds you back. Ex. Her return to competitive running would forever be taxed by her bad knee. A "proportional voting system" is a little more complicated. I had to look this up, since we don't use it in America. Consider a district in a democratic state that can vote on 10 representatives to represent them in the government. If 50% of them vote for Party A, 30% vote for Party B, and 20% vote for Party C, then 5 of the district's representatives will be from Party A, 3 will be from Party B, and 2 will be from Party C. Therefore, the representation the district receives from each party is proportional to the votes they receive.