There’s a couple of responses to your question. The first is the “It’s a Contract!” response. Doctors might be contractually bound to their employer and be required to work late to finish operations. The “It’s a Contract!” cards answers all questions for some, and those types will walk away nodding.
But to me, that’s simplistic and not really convincing. So it’s better to ask, “What really is in the self interest of the actor, and is there really a conflict?
Example: The doc acts altruistically when he stays late to finish the operation on a sick patient and so misses that golf game he's been dying to play.
Assuming there is no contractual requirement to finish the operation, is it really in the doctor’s self-interest to play a golf game rather than finishing an operation on a sick patient? What effect will it have on his reputation if a less capable doctor messes it up? How would it affect his relationships with his colleagues to see him “slack off” and leave work behind for others?
Example: The representative acts altruistically when he votes to keep out that waste dump in his constituency's neighborhood and so passes up a huge bribe from the waste dump managers.
Is it really in the representative’s self-interest to accept an illegal kickback and risk criminal prosecution? Is it really altruistic to be a consistent advocate for the concept of property rights?
Life is about making choices and many involve trade-offs. But it’s your own hierarchy of value that determines what’s important. I can’t imagine many doctors that would trade their reputation for an afternoon of golf, but maybe there are and maybe golf is more important to them than their career. But I’d say they’re in the wrong career and that they’d soon be out of a career as a result of dissatisfied customers.
I think you’re over-mathematicizing the triage example. You’re right, the doctor needs a method of choosing who should get immediate treatment. But I wouldn’t call this the choice between winners and losers, and I wouldn’t say that the guy with the sprained wrist is getting “screwed over” for not receiving priority over the guy who’s just had the heart attack. So it’s simply a case of prioritizing in order of who’s closest to death. Because the last thing in a doctor’s self-interest is to be responsible for fatalities.