In our candidate-centric political system, every president is a singular figure in his own way, whose appeal to the public is at least a little distinct from that of his party. But presidents still have a relationship to that party, and their choice of Cabinet members and other high-level officials can tell any close observer a good deal about the nature of that relationship.
This is more than the standard observation that personnel is policy; to see who gets what job is to get a better sense of the coalition that put the president into office.
The president who puts a strong rival in a key position, like Abraham Lincoln did for William Seward when he made him secretary of state, might be working to keep a divided party together and a potential critic within the fold of the administration.
The president who taps an ideologue to lead an important agency could be showing his commitment to a set of ideas. That’s what we saw, for example, when Ronald Reagan placed supply-side true believers and conservative evangelicals in key roles in his administration.