It's not an easy problem to solve, but it is not unsolvable.
I don't think 'solve' is binary. Different solutions come with different tradeoffs. Membership of supreme courts is made up by judges chosen by political majorities. There are advantages to having a powerful fourth estate that's independent of the other three.
As a practical matter getting a parliament to pass legislation that introduces a new class of people that check whether or not the members of that parliament are holding their promises also seems unrealistic.
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