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.