Rabbi Dessler in Michtav M'Eliyahu explains that "free will" is manifested by the "point of choice". Rabbi Isbee of Ner Yisrael has said that only two entities in this world exhibit free choice, Hashem and living humanity. In this case it does not matter that the results may appear to be independent of the choice being made but that the person has made the choice and has exhibited his hishtadlus by doing so.
My Rav also explained that by voting a person is showing his "citizenship" and that he is acting as a good and valid member of the society. In that case, it is his actions that matter, even though it appears that he can accomplish nothing.
Yes, the individual vote appears to be mathematically insignificant, but consider the analogy of the tenth person who did not stand up in S'dom to allow Avraham to save the cities or the one person who could have joined Noach to prevent the mabul. Note that Hashem delayed the mabul until after Mesushelach died even thogh he was only one person among however many millions there were in the world.
We see that we are told to act as if the entire world has been placed in exact balance and our actions will place the weight in on scale or the other. Rabbi Dessler explains that not only is a person to treat himself as if he is at the tipping point, but that the entire world will depend on the next action that the individual chooses to make.
One can never know how what appears to be an insignificant action can change the world. We can call it the butterfly effect.