Citizens of democracies are already forced to do things that they may not want to do but are in the public good, this includes allowing their children to be educated, paying tax, and serving on juries. All of these serve a greater societal good and reflect a broader social contract between the governors of society and the governed, which is a careful balance between a citizen’s rights and responsibilities. Voting is the responsibility of each citizen and making it compulsory would ensure that people see it as part of a broader social contract where full participation benefits society as a whole.
Despite modern democratic societies compelling citizens to participate in education, taxation, and the judicial system, many people still opt out of these supposedly 'compulsory' activities. It is common for people to opt out of jury duty, some people elect to home school their children with relatively little oversight from the Government, and many wealthy people avoid taxation by arranging their tax affairs offshore. If people are willing to avoid activities that society already considers compulsory and fundamental to a broader social contract, there is little to reason to suppose that they would not also find a way of avoiding voting as well.
[P1] It is not unusual for citizens to be compelled by law to do things that are in the public interest. [P2] Voting should be treated as one of these activities.
Rejecting the premises
[Rejecting P2] Making voting a compulsory activity does not mean people will actually vote.