Andrew Coyne thinks voting should be mandatory in Canada*; Dylan Matthews makes a similar argument for America.
The best argument for compulsory voting, Coyne's, is that it could shift politicians away from campaigns based on getting out the vote: if everyone has to vote, then GOTV matters less, as does playing to the party's base.
While that's one notch in favour of compulsory voting, there are a few considerations against it that might give us pause.
Blood donation is almost entirely a public good. Were we to implement a mandatory blood donation regime, we would have to couple it with a tick-box allowing "donors" to indicate that their blood probably shouldn't be used or at least should undergo heavier screening: a Hepatitis B patient's blood probably shouldn't enter into general circulation.
But nobody seems to worry much about the quality of a compelled vote. They should.
Jason Brennan makes a pretty convincing argument that while none of us have a positive duty to vote, those choosing to vote have a duty to vote well: to weigh seriously whether the policies offered up by the different parties would achieve the ends that the voter wishes and that the trade-offs are worthwhile, in the voter's estimation. While few voters meet that duty, things are even worse among current non-voters: non-voters, on average, aren't made up of rational calculators and conscientious objectors like me; most non-voters instead have little political knowledge and little intention of acquiring any. And forcing them to vote does not encourage them to acquire more information.
I'll offer instead a compromise position: make voting compulsory, but also implement a simple quiz at the ballot box. Voters would need to be able to match parties with their main supported policies. They'd also be quizzed on a few basics, like which parties formed the prior government, whether crime rates increased or decreased over the prior administration, whether income inequality has been increasing or decreasing, whether most climate scientists agree that the planet has been warming, and order-of-magnitude level quizzes on the composition of the budget. The quiz questions would vary election to election but would hit on the baseline matters necessary for understanding the policy issues at stake in that year's election. Everyone's vote counts for at least 1, but we could award bonus votes for voting well. Everyone would have the opportunity to vote well: Elections NZ would put up the 50-or-so quiz questions and their answers; each voter might get a random draw of 10 at the ballot box. Those compelled to vote but unable to vote well would have less opportunity to do harm to their own interests with their vote. I won't go all the way to nudge-based voting, but we could at least avoid some harm with this version.
Think of the incentive effects. GOTV campaigns would be focused on informing supporters about basic facts so that the party's supporters' votes might count for more.
I could support compulsory voting if it came with this kind of mechanism. Or we could keep things voluntary.
* And see his prior similar argument here.