One needs to think things through clearly, as do those reporting to you. A possible way to do so: Play devil's advocate. In the process, one quickly determines how well others have thought through their recommendations or how strongly they feel about them. It may not endear you to others, but it will give you the benefit of knowing how reliable the recommendations made to you are.
After using your head to try to come to the right conclusions, you are probably better served by then going with your gut. Visceral reactions serve you well because you know yourself and what you want to do.
A controversial case in point involved my desire to increase the number of faculty members of color on campus. Why? Because I was presented one day with the prospect of being left with a single African-American faculty member, since one faculty member told me he wanted to retire and another was, I believe, going to be denied tenure.
I felt that situation was unacceptable, and I decided to address the issue forcefully. So, when the faculty asked me to add four members to their ranks, I agreed -- on the condition the additions were members of underrepresented minority groups.
I clearly understood the questionable legal basis of my position, but I felt both the situation I wanted to address and the signal being sent were important. Some feared a lawsuit; others felt we would be unable to find suitable candidates. Fortunately, they were wrong on both counts.
We added four excellent members to our faculty, and we were not sued. In making my determination, I concluded we would have "won" even if we had been sued and lost the suit because the publicity we would have garnered would have outweighed the financial cost; however, I was glad not to have to find out if I was right in my assessment.
Presidents will always be presented with difficult choices to make. While it may seem sensible to make a decision that pleases the most constituents, it generally is not. One is best served by seeking the input of many so that one -- you -- can make a decision.
In making your decision, you should obviously use your head (and at times your heart). Still, you should generally rely on your gut. Have the guts to do so.