Some things just aren't reasons for a choice. For instance, the fact that a portion of ice cream has an odd number of carbon atoms is by itself not a reason at all for eating the ice cream, and the fact that I find hot chocolate unpleasant is by itself not a reason to choose the hot chocolate. (The "by itself" qualifier is needed. I might have some instrumental reason for consuming an odd number of carbon atoms, and I might be ascetically training myself to consume what is unpleasant.)
Sometimes, however, something can be a reason for A without being a reason for A rather than B. For instance, that I enjoy hot chocolate to degree 100 is a reason to have hot chocolate. But if I enjoy ice cream to degree 150 on the very same scale, then my enjoying hot chocolate to degree 100 is not by itself a reason to have hot chocolate rather than ice cream. In the absence of other reasons, it would then make no rational sense to choose hot chocolate over ice cream, since my reason for hot chocolate is strictly dominated by my reason for ice cream.
At least roughly speaking:
- Reason R (not necessarily strictly) dominates reason S if and only if S is not at all a reason for choosing an action supported by S over an action supported by R.
- Reason R strictly dominates reason S if and only if R dominates S and S does not dominate R.
Rational choice between A and B occurs only when one has reason to choose A over B and reason to choose B over A. Thus, rational choice between A and B occurs only when the reasons for neither option dominate the reasons for the other.
Definition: Reasons R and S are incommensurable if and only if neither dominates the other.
Thus, rational choice is possible only given sets of reasons that are incommensurable.