The question is in what way I make a difference through my vote, given that my vote has 0 probability to make any difference in the outcome in the majoritarian or Westminster democracy (term a la Arend Lijphart). This is a question addressed by political scientists, not by political philosophers.
To understand the question, we first need to know the pivotal theory of voting, advanced from the economist front (mainly by social choice theorists). The theory begins with stating that my voting is meaningful if and only if my vote can make a difference. The reason, according to the theory, is that a rational and self-interested person will pursue a course of action only when her agency matters. Her agency is non-existent in a national election (i.e., 0 probability to make a difference). Thus follows from the theory is that it is irrational for her to vote, let alone study the agenda. A lemma of the theory thus is rational ignorance that voters purposefully choose to remain ignorant and not to learn about agenda for the reason of lacking agency in voting.
It has been political scientists who tried to refute the pivotal voting theory.
Professor Gerry Mackie at UCSD (my dissertation committee member) offers the contribution theory of voting, according to which voting is instrumental to locate public good, and citizens do aim to contribute to the advancement of the public good. Thus it is rational for citizens to vote. To Mackie, individuals vote not for the reason of pivotness, but for the reason of contribution toward the group effort. A similar contribution idea was also offered by Josiah Ober, Stanford University political scientist and classic literature theorist. Ober elaborates Aristotle's analogy of democracy as a potluck party to argue for the agency as well as epistemicness of democracy.
Political scientists' answer to the question then is contribution, which is involved with agency.
Aristotle's potluck analogy: When comparing democracy with aristocracy and oligarchy (both are characterized by rule by a few) in terms of wisdom, Aristotle questions which party has more food, a party prepared by money from a few rich individuals, or a party prepared by money from all. Aristotle says that the latter has more food. From this, Aristotle concludes that there is reason to think that the democratic decision is smarter than the others.