A principle you already hold
Hire someone to steal, and you are a thief. Hire someone to hurt a person, and you are complicit in the injury. Every legal system anyone takes seriously treats it this way, and so does ordinary moral intuition, without needing the legal system to explain it.
The intermediary does not absorb the responsibility. Responsibility travels through them and arrives back at whoever authorized the act. That is what an agent is: someone acting on your behalf, at your direction, in your place.
This is not a controversial position. It is close to the least controversial position available.
Follow the chain
Now take a policy — any policy you support that carries a penalty for noncompliance — and trace what actually happens to someone who declines to comply.
A notice. Then a demand. Then a fine. Then, if the fine goes unpaid, a lien, a seizure, or a summons. Then, if the summons is ignored, a warrant. Then people arrive at the door who are authorized to restrain a body and place it in a locked room.
Most policies never travel the full length of that chain, because most people stop somewhere along it. But the chain is what makes the earlier steps work. A notice with nothing behind it is a request. The reason people comply at step one is that everyone understands step seven.
Every law you support is a description of something you are willing to have done to a person who will not comply.
What the vote is
Voting for a policy that will be enforced through fines, seizure, or confinement is hiring an agent. The politician is the intermediary. The enforcement apparatus is the mechanism. You are the principal.
The chain is longer than in the burglary case, and the language is a great deal more polished. Nobody in it describes their job the way the chain describes it. But the structure is the same: one person authorizes the use of force against another person's body, property, or time, and someone else carries it out.
What the extra length buys is distance. Not moral distance, since the outcome at the far end is identical, but psychological distance. It becomes possible to hold a position without ever picturing the person it lands on.
Three ways out, and how far they go
"I did not design the system." True, and it matters. You were born into it, you did not consent to its founding, and there is no exit that does not cost more than most people can pay. Responsibility for a system you inherited is not the same as responsibility for one you built.
"I voted against it." Also true, and also relevant. Someone who argued and lost occupies a different position from someone who campaigned and won.
"Everyone participates, so nobody is responsible." This one does less work than it appears to. Diffusion changes how responsibility is distributed. It does not make it disappear, or the same reasoning would excuse every crowd that has ever done something no individual would have done alone.
What these defenses establish, taken together, is that moral responsibility here is a spectrum rather than a switch. But the spectrum runs from fully responsible to complicit by participation. It does not run from responsible to innocent. Living inside a coercive system and benefiting from it does not make you a bad person. It does not make you a bystander either.
The question this leaves
The philosophy does not ask you to stop voting, and it does not ask you to feel guilty about anything you have already done.
It asks for one question to be carried into every political decision from here on: am I willing to send someone to use force on a neighbor for this?
Sometimes the honest answer will be yes. Some things may be worth it, and there is no dishonesty in saying so — only in saying so without noticing what is being said.
When the answer is no, the useful thing is not guilt. It is to go looking for the version that does not require it.