I've always wondered if a hybrid system could work. You'd need a lot of voting infrastructure, and you need online voting, which means you need a reliable and quick method of online identification. Scandinavian countries fill those prerequisites, perhaps other places do too.

The idea is basically that you give a politician a mandate to use your vote. Whatever your chosen politician votes for will count as their and your vote. If you happen to disagree with your chosen politician on a given question, you can manually vote in that question. Your chosen representatives vote in that question will then be worth one vote less, since you've effectively used it yourself.

In the end we get the best of both worlds: voters don't have to vote in every single issue, but they can should they choose to. When they don't vote themselves, a politician they've chosen gets to use their vote, in a representative-like manner.