Good discussion so far.I would like to shift a focus little bit.What if you do not have option to pick? Which is the situation in most of the time.In such cases one should have to look up for strategies to manage conflict and disagreements. As PMBOK suggests some of the ways to manage conflicts are.

(1) Avoidance
(2) Compromise
(3) Delegation
(4) Listen
(5) Call a meeting
(6) Solve the problem,not symptom
(7) Use the Mediator
(8) Appease