For economists, the puzzle is not why voting participation rates are so low in voluntary systems, but why they’re so high. The so-called paradox of voting, highlighted in a 1957 book by the political scientist Anthony Downs, occurs because the probability that any individual voter can alter the outcome of an election is effectively zero. So if voting imposes any cost, in terms of time or hassle, a perfectly rational person would conclude it’s not worth doing. The problem is that if each person were to reach such a rational conclusion no one would vote, and the system would collapse.
Mandatory voting solves that collective action problem by requiring people to vote and punishing nonvoters with a fine.
Not an advocate of compulsory voting myself, I am willing to make note of the implications in the above quote and conclude that if our goal is simply to improve voter turnout, then it is the only way to do so effectively.