My wife and I try to operate "by common consent" and unanimity. We talk about everything imaginable and, whenever an "important" decision needs to be made we make it together. If we can't agree, we stick with the status quo.
That means our children don't get most of their last-minute requests, since my wife and I haven't had a chance to discuss it - and, in almost all cases, what they are requesting is not a real emergency situation. I simply tell them, "You know I can't give my permission without talking to Mama. You also know we generally don't make decisions like that the same day you ask us. We need time to think and talk about it. What can you do to rearrange it for next week or this weekend?" If it really is an emergency situation and we don't agree, she allows me to decide - knowing I then am the one who has to deal with the consequences if my decision is incorrect or causes unexpected complications. (and I mean it when I say she "allows" it)
Too many people (including parents) think that decisions MUST be made in the moment. I can't think of a single time we've delayed a decision on which we didn't agree and regretted it later.
Having said all of that, she cares more about many things than I do, so I am fine if most of our decisions reflect what she wants. My boys have learned the "Yes, Dearem Theorem". Very few things are worth making a conflicting issue of them that must be resolved immediately by one person over-riding the other.