They are still responsible, as far as our laws are concerned. The government derives its power from the people, and one of those powers is the power to tax.
Not every tyrannical decision is made by the majority, and not every majority decision is tyrannical.
We make collective decisions, and we live with the consequences. Every election presents us with such a decision. Moreover, voting is not the limit. If you truly believe a particular candidate is bad, you are free to share your ideas, donate to his opponent, or perhaps even run against him yourself.
Correct, you can run opposition. However, a representative in the US is typically voted using first-past-the-post (modified for the US president). It doesn't matter whether the society accepts the winner with 99.9% or 50.0001%, the spoils remain the same.
It doesn't make sense to me that the losing bloc, which now does not have representation, is subject to the whims of the majority (that is the definition of the tyranny of the majority). A parliamentary system with proportionate representation makes more sense if "blame"for a representative is apportioned to the entire set of constituents and not the bloc that gained power.
When the taxpayers are citizens with voting rights they do bear responsibility for the actions of the state they voted in.