Jonothan Louth and Lisa Hill have posted this paper in the Australian Review of Public Affairs. Here is the abstract:

In this paper we address claims made by those supporting the abolition of compulsory voting about the relationship between turnout levels and compulsory voting. Via a critique of the methodology used, we query estimations of the effectiveness of compulsory voting laws and dispute common assertions about how high Australian turnout would be under a voluntary system. We then show that projected comparisons with places like Malta, New Zealand and The Netherlands are questionable. We also challenge other projections, that are based on data that has been insufficiently disaggregated. We conclude that when compulsory voting is properly administered in a congenial setting (such as Australia), it is the best means for guaranteeing high and socio-demographically equal rates of voting participation. Without it, Australian democracy would be experiencing the same citizenship crises currently being experienced in most other industrialised, voluntary voting settings.