Ie vote on your priorities and what you want to get done. Then use a prediction market (possibly on a very informal level, if it's a small group), to decide on a policy to reach those goals.
And then that party proceeds to blackmail everybody all the time.
Thus all the governments need to pander to this particular party and they get to gridlock the government whenever they feel the smallest slight or displeasure.
Of course they can, they just choose not to. What you are saying is that the parties are choosing a blackmailer over a self-declared "enemy". That's a choice, it's not inevitable.
Besides, if the political landscape is diverse enough, a minority coalition can be a boon for everyone: it means that the ruling parties must actually learn to cooperate with the opposition instead of dictating policy for the duration of their term.
However our political landscape is polarized to a degree where minority coalition has no chance of doing anything.
Not that any political problem could solve people acting as idiots.
How do you currently choose new hires? Decide to ship (go/no go)? Probably something like Roman Evaluation.
How do you triage defects or choose features? Probably something like Approval Voting.