Nicholas Stephanopoulos laid out the numbers supporting compulsory voting in a 2015 piece for The Atlantic.
Start with some statistics: In years with presidential elections, voter turnout peaks at just above 60 percent. In off-year elections, turnout dips to 40 percent or less. In November 2014, only 36 percent of eligible voters went to the polls—the lowest share in more than 70 years. Participation this paltry calls into question the political system’s legitimacy. It also hints that election outcomes might be quite different if more people bothered to show up.
...Compulsory voting isn’t as draconian as it sounds. No one is dragged to the polls against his or her will, and no one is thrown in jail for refusing to cast a ballot. Instead, a modest fine (about $20 in Australia) is levied on people who fail to show up and have no good excuse for their absence. There also isn’t any danger of political speech being compelled—a no-no under the First Amendment. People are free to do what they like with their ballots, including turning them in blank.
The main argument, however, against compulsory voting, is that the average U.S. citizen is unschooled on political issues and is probably abstaining from voting due to a lack of knowledge. As Jason Brennan wrote in a 2011 op-ed for The New York Times:
The median voter is incompetent at politics. The citizens who abstain are, on average, even more incompetent. If we force everyone to vote, the electorate will become even more irrational and misinformed. The result: not only will the worse candidate on the ballot get a better shot at winning, but the candidates who make it on the ballot in the first place will be worse.
Most people believe that more voting causes better government. This is an article of faith, not fact. Social scientists have shown that higher quality government tends to cause higher turnout. But higher turnout does not cause higher quality government.
In a 2017 op-ed for The New York Times, writer Waleed Aly argues that compulsory voting would eliminate the hyper-partisanship the United States is currently facing. Since everyone, including typically unmotivated swing voters, are required to turn out to the polls, extreme politicians would no longer be able to coast to victory on the strength of their base alone.
[C]ompulsory voting changes more than the number of voters: It changes who runs for office and the policy proposals they support.
In a compulsory election, it does not pay to energize your base to the exclusion of all other voters. Since elections cannot be determined by turnout, they are decided by swing voters and won in the center. Australia has its share of xenophobic politicians, but they tend to dwell in minor parties that do not even pretend they can form a government.
That is one reason Australia’s version of the far right lacks anything like the power of its European or American counterparts. Australia has had some bad governments, but it hasn’t had any truly extreme ones and it isn’t nearly as vulnerable to demagogues.
...On balance, the overriding result of compulsory voting is a more complete democracy. One that includes the voices of those most easily discouraged from turning up: poorer people and minority communities, for instance. One that refuses to hand power to someone whose plan is to keep turnout low, hoping to appeal to an impassioned minority rather than a nation at large.
Washington Post columnist Ilya Somin disagreed in a 2015 piece, saying that mandatory voting would force uneducated voters to cast ill-informed votes.
Somin was responding to a speech by former President Barack Obama, in which he said mandatory voting would help dramatically reduce the effects of partisan spending in elections, saying "It would be transformative if everybody voted — that would counteract money more than anything.”
[M]andatory voting would exacerbate the already severe problem of voter ignorance. While the differences are not enormous, people who currently don’t vote are on average less interested in political issues and more ignorant than those who do.
In his speech, President Obama claimed that mandatory voting would diminish the significance of money in politics. The opposite effect is more likely. Most campaign spending represents expenditures on televised ads. For fairly obvious reasons, relatively ignorant voters are more likely to be influenced by simplistic 30 second ads than relatively well-informed ones (who, among other things, tend to have stronger preexisting views). Thus, a more ignorant electorate is likely to be one where campaign spending on television ads exercises more influence. I don’t think the influence of money on politics is either as great or as harmful as President Obama and many other liberals do. But if you disagree with me on that, you may have even more reason to oppose mandatory voting than I do.
In a November 2014 opinion piece for CNN, political commentator William Galston conjured up a hypothetical future after compulsory voting has been introduced in the United States:
As turnout rose from 60% to 90%, citizens with less intense partisan and ideological commitments flooded into the electorate. Campaigns could no longer prevail simply by mobilizing core supporters. Instead, they had to persuade swing voters to come their way. They soon discovered that these new voters preferred compromise to confrontation and civil discourse to scorched-earth rhetoric. Candidates who presented themselves as willing to reach across the aisle to get things done got a boost while zealots went down to defeat.
Both political parties soon realized that they had a stake in a nominating process that produced the kinds of candidates the expanded electorate preferred. They eliminated party caucuses dominated by intense minorities and opened up their primaries to independents. They discovered that maximizing participation in their primaries was the best way of preparing for the general election. Individual donors, who wanted to invest in winners, favored candidates who could command broad support.
There is a concern, though, that these uneducated voters could dramatically sway the country, voting for xenophobic policies. Per The Washington Post:
Mandatory voting would be less dangerous if it could be combined with an effective strategy for increasing political knowledge. But doing so through education and other traditional means has turned out to be extremely difficult. Unconventional strategies, such as paying voters to become better-informed, also have serious pitfalls.