Simple; make a law that says everyone has to vote.
One big problem with this is what if - for example - a socialist ends up with 3 capitalist parties on his ballot?
Also simple; add a NOTA option. None Of The Above. If NOTA wins the election, the seat is vacant, and a by-election will need to be held later.
This can be coupled with some form of alternative vote, some form of proportional representation, some form of voting on different days (like a weekend) or simply keeping everything as it is, monday FPTP.
I feel that without a NOTA option, mandatory voting is unethical, so by adding it, we remove that ethical problem, and as such, I feel this is a great idea.