Philosophers have given significant attention to identifying conflicts of interest in the course of developing theories of justice, accounts of fairness, business ethics, philosophy of law, and even museum ethics. Your focus seems to be on sex and the academy, so I will go right to that topic: in most colleges and universities there is indeed a regulation against professors and students having sexual relations, but I believe this is not primarily a matter of what may called a conflict of interest. I suggest it is more of a matter of preventing exploitation as well as a matter of a common sense approach to professor-student relations. Even if it happens that the sexual relationship does not lead to preferential (or unfair) grading, it is occurring in a relationship in which both parties have responsibilities to each other that sexuality almost cannot help but compromise or overshadow. The primary role of the professor in teaching or practicing philosophy (or any subject) with students is one in which (ideally) there is mutual respect and a host of duties (maintaining the highest standards intellectually, being trustworthy in terms of honesty, promise-keeping, and so on). Adding on to that courtship, flirtation, dating, one-off or regular acts of sexual intimacy (in my view) cannot help undermine or cloud the integrity of the student-professor relationship. I think the same is true in so many relationships where there are professional codes of conduct (e.g. judges not having sex with jurors or defendants, surgeons not having sexual relations with patients prior to operations, and so on). Perhaps I am wrong, but on the worry about 'dehumanization' there is nothing that I am aware of in any college or university that prevents romantic relationships between professors and former students. In fact, I know of at least four cases in my own college when former students have married professors and lived (what appear to be) passionately happy, even joyful lives. If in the course of a class a professor and student fall in love there are many remedies: wait till the class ends before dating (or whatever) or (if time is of the essence) the student can drop the class, the professor can ask for a transfer, and all may be well -- except, of course, for the wonderfully but sometimes painfully complex issues that arise in almost all relations between all persons whether or not any of them were ever in a professor-student relationship.
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Does the idea of "conflict of interest" figure into any contemporary discussion of ethics in philosophy? For example, few would argue that a professor having a sexual relationship with a student in his class is immoral in itself, but why would that necessarily be a conflict of interest? Banning such relationships is what is immoral because it reduces people's humanity by presupposing that humans are totally unable to separate their private lives from their professional ones. Are we to ban family businesses too? Even if empirical studies DO show that a majority of these kinds of relationships result in preferential grading, universities can always discipline such professors--disciplining the student would certainly be excessive. Banning relationships are the worst kinds of bans as without relationships we are dehumanized; it seems to me that if a person personally wishes to jeopardize his career for the sake of a relationship, then we should acknowledge and accept that.