Doubts about the integrity of an election, whether justified or not, have been found to undermine the legitimacy of democratic processes and decrease levels of turnout: voting becomes less attractive when citizens perceive the outcome of the election to be a foregone conclusion. Yet, this mechanism relies on the assumption that all citizens decide to vote in order to influence the outcome of the election. We put this purely instrumental assumption to the test by examining how public perceptions of election integrity relate to electoral participation. We aim to disentangle this association and suggest that it can be explained by a new variable meant to capture whether citizens find a meaning in voting or not, and the content of these meanings. We test this using original survey data collected in thirteen countries with different levels of election integrity, all of which held general elections between March 2022 and May 2023. The results show that high levels of perceived election integrity do not affect all voters in the same way. Perceptions of fairness are particularly relevant for individuals who are more skeptical about voting, whereas those who view voting as a civic duty remain largely unaffected. By showing that evaluations of procedural fairness are more relevant for certain groups, our findings challenge the assumed direct link between election integrity and turnout, contributing to ongoing discussions about democratic legitimacy.