From p. 92 of Randall Holcombe’s 2018 book Political Capitalism: How Political Influence Is Made and Maintained:
Voting is the best way, from the elite’s standpoint, for the masses to participate, because each individual vote has essentially no impact on the outcome of an election, so voters are provided with the illusion that their participation determines the election outcome, which reinforces the perceived legitimacy of government.
Voting has practically no impact on policy outcomes. Even small local elections rarely have one-vote margins where a given person’s vote would be decisive. It’s so rare that it makes the news when it does happen. Voting’s instrumental value requires many decimal places to accurately express. But voting does have significant expressive value.
People genuinely feel good about participating in democracy, and get value from signaling their participation to others. Some people also get value from shaming people who do not vote. There is nothing wrong with most of that. But most people would benefit from a more accurate understanding of how much a person’s vote impacts election and policy outcomes. As Holcombe points out, this would make people less easily mollified by reform agendas that end at lip service.