From Jeff Lash’s Ask A Good Product Manager:

I’ve known people who have tried scorecards, ranking systems, voting (see Product Development is not a democracy), but ultimately these are just ways to avoid the responsibility that product managers have to ultimately make the important decisions.

There’s no magic formula, and in the end it might be that what makes a GOOD product manager vs. a BAD one is his/her ability to take these hundreds/thousands of inputs and make good decisions — and learn from bad ones.