You can see my contribution to the discussion here. I discuss the research of Jan Leighley, Jonathan Nagler, and others. Here’s my conclusion:

Whether or not mandatory voting is a good idea, I think it’s unlikely to happen at a national level. Even setting aside the practical difficulties of taking a now-voluntary action and making it compulsory, bringing in the other half of the potential electorate would change the political conversation so much that it’s hard for me to see current officeholders supporting such a plan.

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University. He has received the Outstanding Statistical Application award from the American Statistical Association, the award for best article published in the American Political Science Review, and the Council of Presidents of Statistical Societies award for outstanding contributions by a person under the age of 40.