Everybody votes in Australia (not sure how rich, but in top 20 for sure). If you don't you have to show cause or pay a AUD$50 fine. I know some think this is anti-freedom, but it does prevent farces like the current USA. Historically there have been problems in the past (30 years ago) but these days the Australian Electoral Commission (Independent from government) revise electoral boundaries to ensure no more gerrymanders.
In Belgium attendance is mandatory as well. I think it's a positive as it means complacency ("my side has already won, no reason to go out and vote") is never a factor in the outcome.
In Brazil as well. I think a good side effect, or perhaps the main intended one, is that governments aren't allowed to supress voters and have to make sure everyone has easy access to the voting booths. Every election there are mandatory pieces on TV about how people are voting even in the most remote of places.