Against Compromise, or, Deciding as a Team without Succombing to Entropy

I've had a similar experience at [large tech firm]. It was becoming clear that an intersecting project with two teams wasn't working. The challenge though was it was stuck in a rotten equilibrium. Each team's true incentive was distinct and contrary to the other team. Yet the mandate was 'thou shalt have the same incentives.' Everyone kept publicly claiming we had aligned incentives, which you shouldn't have to publicly explain if it's actually true.

A lot of social choice theory guys tried to explain this in the context of voting, and the stability of outcomes. Arrow's impossibility theorem can be resolved if you have a dictator. In the end a strong and smart leader can solve so many issues of indecisiveness, and can take ownership of directing the deliberation, and adjusting for variables no one else owns (e.g. the cost of time in making a decision).

Still, I remember thinking about this all while intersecting teams were making obviously bad choices, and thinking that the best way out would just be to make someone sovereign and let them choose.

Leadership gets weird though. Despite all this theory and analysis over group choice dynamics, there is this transformative property of a great leader that seems to inspire people to buy into their vision and work incredibly hard. I don't understand how that works though, other than some handwaving and 'psychology.'