Not necessarily. You could also punish liars several after the fact, ie after their term, and hope that incentives will do the trick.
Though my favourite idea is to make voting with your feet easier. If you have more issues decided at more local levels, then it's easier to up sticks and move to the next town over, if you disagree with a policy.
I call that the "McDonald's flavour of democracy": McDonald's doesn't let you vote on their menu, but if you don't like it, you can always just head over to Pizza Hut.
You can either (A) do that inside an existing system by aggressively pushing responsibility down. That's what subsidiarity is meant to capture. And also how the US was supposedly meant to be structured; but over time centralisation won out.
Or (B) you can ensure that by having smaller independent countries. Ideally city states.
That's one of the reasons why Singapore is my adopted home.
Moving with your feet is about the most direct democracy you can get, but you also don't have to worry about the usual downsides of direct democracy.