I've said previously on this group that non-deterministic elections can be a good way to simplify proportional representation. It doesn't have to be as crude as simple random ballot where you have one representative per constituency selected by the drawing of a single ballot. As I said here just earlier this month:
Proportional methods tend to just be more complex by their nature. But if you allow them to be non-deterministic then that goes away. E.g. COWPEA Lottery which uses approval ballots. Or if you have a region that elects, say, 6 candidates, voters just rank their top 6 candidates. Then you consecutively pick six ballots at random and elect the unelected candidate that is highest ranked on that ballot.
This type of method, while it doesn't guarantee a very proportional result in each region, would actually give better proportionality nationally than deterministic methods that use these smallish regions (like STV), and they also keep the election candidate-based, which other nationally proportional methods tend not to.
Random ballot with just one representative per region guarantees that honest voting is the best strategy, but I tend to think that it becomes too lotteristic at that point. With e.g. five or six chances to be elected (as in the above methods), particularly popular candidates would not be on such a knife-edge of being elected.
I also think that non-deterministic methods send out a good message - that there are no "safe seats", and that representing the electorate is a privilege and not some guaranteed right.
So while non-deterministic methods might be a tough sell, I personally prefer them for national parliaments.