From Jason Fried’s article in Inc some interesting suggestions on dealing with “conflict” or more generally situations where people can’t agree.
Consider trading the decision. If it’s relatively small, consider saying “Ok you win this time, but I’ll take the next decision.”
Determine who wants it more. Let the person with greater passion behind their view take the decision. This is the difference between counting votes and weighing them.
Clearly, for larger decisions these tactics risk worsening the outcome, but for smaller issues, these aren’t bad approaches to finding consensus quickly.
Strategic PPM 
Great. Good post. Thanks