Is there a fallacy in the argument, "Don't blame me; I voted for ..."? Or is a voter's entire responsibility for their contribution to whatever current state of political affairs they experience entirely waived because they voted for a candidate(s) other than the most recently elected official(s)?
Please note: This question is not tied to any one particular country, official, or point in history.
Your question seems simple, but is very complicated indeed!
Instead of giving a complicated answer ;) I want to bring to your attention the problematic nature of an assumption in it, which I will call Principle P. This assumption is important because if Principle P doesn't hold, then your question cannot even get off the ground.
Your questions seems to imply that
a person A who voted for the currently elected official X is responsible (and therefore to blame, culpable, etc.) for the state of political affairs brought on by X. (Principle P)
This seems a reasonable assumption, at first: The act of voting caused the election of X. If we take for granted that there is a link between causation and moral responsibility, then it would seem that A's voting makes him morally responsible for the election of X. Additionally, A is not just morally responsible for the act of voting, but also for the downstream consequences of this act.
There are, however, two problems which renders this assumption worthy of being questioned:
A is not just morally responsible for the act of voting, but also for the downstream consequences of this act. However, there seems to be a limit as to how far this chain of consequences can go: Voter A caused the election of X; X brought on a certain state of political affairs; did A bring on that state of political affairs? Causation may be seen as a transitive relation (if x causes y and y causes z, then x causes z), in which case the answer is yes. However, it is dubious under which conditions moral responsibility can be transitive in the same way: If A is morally responsible for the election of X; and if X is morally responsible for the current state of political affairs; is A morally responsible for the current state of political affairs?
An affirmative answer to this question becomes even more improbable if we take a very basic principle in ethics that A is morally responsible (and therefore potentially morally blameworthy) for an occurrence E only if E is a consequence of some culpable act on A's part. Since the act of voting is in no way a culpable act per se, A cannot be held responsible for any nefarious consequences of this act.
Therefore, Principle P fails.
In a setting such as mass elections, where group agency causes the election of X, what is the causal role of a single vote? Somewhere between very little and none. If we agree that moral responsibility diminish as the degree of causal contribution diminishes, then the moral responsibility is very little to none - even if it isn't easy to precisely quantify the causal contribution of each of the voters to the occurrence of the election's outcome.
Still, we could envision an electoral tie. In this context a vote can be "more" causally efficacious then others. This is called the vote's "pivotal" (i.e. effective) role in the election's result. However, it can be shown that the probability that A's vote is effective and affects the election's outcome is practically non-existent (e.g. minuscule wrt to A's probability of winning a lottery!). Again, A's moral responsibility for the election's outcome is almost non-existent.
Therefore, Principle P fails.
If Principle P doesn't hold, i.e. if even voter A who voted for X is not morally responsible for the state of political affairs brought on by X, then it is not really conceivable how a voter B, who didn't vote for X, might be morally responsible for the state of political affairs brought on by X.
Presuming I understand you correctly, if the only responsibility which a voter has a duty to perform is voting (in order to cause positive change, or prevent negative change), then it's not a bad argument. However, in the real world, voters ("citizens") have a duty to more than merely vote for an official, but to ensure existing officials actions are accounted for. This is through further voting (non-election ballots), activism/raising awareness to issues, being up-to-date on political issues, etc.
So simply saying, "Yes, X (economy, jobs, taxes, etc) is bad, but it's not my fault because I voted for the other guy" isn't a very compelling argument, because if the official was bad enough, that person should have done something about it.
It's just an excuse for apathy, in my mind.
Each individual must take responsibility for his/her own actions alone. If I vote for someone whose campaign slogan was "death to squirrels," I would bear some responsibility if that person won and promptly began executing all squirrels, even if I never lifted a finger against a squirrel directly. The brunt of squirrel genocide would obviously rest upon the actual decision maker and active participants, but I couldn't completely absolve myself because I knew what they intended to do and played a part in enabling them to do it.
If that same individual ran on a slogan of "save the furry forest animals," and then promptly began annihilating squirrels when in office, I would bear no responsibility for those actions. Maybe if I knew/suspected the slogan was a lie and voted for them anyway I would share some blame.
Usually when I hear "don't blame me..." it is put forward by an individual or group who "saw through" (or claims to have) the guise of an official before they were elected and wants to make a point about it to everyone else. Often it seems that they are asserting that everyone else should also have known what would happen if that individual was elected, thus implying that the other voters are at least partly responsible for whatever that official has done.
To the degree that an elected official sticks to the platform they campaigned on, those that funded and voted for that individual have some responsibility in those actions because they knowingly and willingly supported it. But 'support' comes in all shades and at the time of the election, a voter usually has very limited choices. They must choose what they perceive as the better of imperfect options or the the lesser of evils. A voter who tries to select the most reasonable candidate based on personal research and understanding has acknowledged and performed their responsibility. To the degree that politicians make poor decisions or enact bad policy, the politicians must then take responsibility.
The problem is the indirection of cause and effect. Person A tells Person B that Event E happened but accuses institution I for which A did not vote.
E.g., John tells Mike that he lost his job because of the policies of the Republicans for which he did not vote. (Now follow above chain of reasoning).
Assuming, from the talk of voting, that it is a functionally democratic system, we can make the further assumption that there is a congress/senate/parliamentary infrastructure, which is normally comprised of representatives of most/all of the available parties. This means that all but key decisions are processed through the hands of all parties, including the alignment of the hypothetical Voter in the question.
This means that his argument may be flawed at base... the situation he is deriding could possibly be as a result of the party he supports, regardless of the key power figure.
It's often said that "if you don't vote, you can't complain." I hold the opposite. If you voted, you ratified the system. And since it's the system that's fundamentally broken; the various parties being akin to the blue-suited guards and the red-suited guards at the prison camp; then I say:
If you voted ... you can't complain.
You got exactly what you voted for.
