The essence of the trolley problem is to ask whether choosing not to exercise the agency that you have is a moral choice. The fact that you may not have complete control over the outcome doesn’t make the analogy bad in and of itself.
Suppose everyone else except you had already voted and exit polls suggested Trump had won by one vote. Would you vote, then? I don’t care what your answer is would be; that is between you and your own conscience. But, is the situation really so different from the real world situation where for all you know your vote might actually count?
You can disagree that the trolley problem comparison is apt, but I think calling it “deceitful and self-serving” is a stretch.
FWIW I am from the UK and I don’t care whether you vote or not.
People have known that water fluoridation is an international communist plot to sap and impurity our precious bodily fluids since at least the 50s!