In a piece forthcoming in the journal Politics, I suggest that if we want to increase voter turnout then, rather than making it compulsory, we should consider paying people an incentive to vote. Employing the carrot rather than the stick may be less effective (i.e. predictably the increase in turnout will be less), but I think it is less objectionable on grounds of coercion.
It's interesting to see that in the US they've trialled paying people to stop voting and it works. Since offers are generally perceived as less objectionable than threats, this suggests the potential for paying people to act as we desire in many other cases.