"If you assume both people are intelligent and rational, then the only way you can have a disagreement is if you are looking at different data."
This simple statement is at the core of my philosophy as a product manager and coworker. It suggests that the best way to resolve a disagreement is to show the set of data you're looking, encourage the other party to do the same, and then examine both to see where the discrepancies are. Once you find the difference, it becomes a matter of each party incorporating the data into their decision, which hopefully leads to resolving the disagreement with both on the same page.
The data in question is whatever led you to take your current stance, be it an analysis of user behavior, a recent conversation with a customer, a favorite book on product development, the way you were taught, or a deeply-held belief about people's inherent sense of morality. Identifying all the data that led you to your stance takes honest introspection, and there are times when the key piece of different data is something irreconcilable like belief or prior experience. But more often than not, it's something much simpler, and "getting on the same page" is quick and amicable.
I was told this gem by Eric Cattell, my mentor when I was interning at Google. I love its optimism and faith in other people. Eric's version actually went one step further - as a manager, he added "and if we're looking at the same data and still disagree, I assume that the people I work with are smarter than me and so I go along with their approach." Eric was - and I assume still is - a great leader.