Couldn't the student by taught by "someone" in a program other than that where his father is the boss of every faculty member?

@buoyantforce Are you suggesting that applicants be barred from applying to any program where they have relatives in positions of authority?

I'm not going that far, no. But I can tell you that it's a terrible situation. Other students in the class certainly perceive a potential conflict of interest and they have not found "Move along folks, nothing to see here!" statements convincing. Neither have I.

@buoyantforce You seem to agree that the student has a right to attend the institution. Great. So who is going to teach them? The options are (a) the student's parent (the chair), or (b) a subordinate of the student's parent (someone else in the department who works for the chair). Which is worse? Please note, also, that I did not say "Move along folks, nothing to see here!". What I said was "These kinds of situations occur, and are rarely fraught. You likely have nothing to worry about, but there are steps you can take to further mitigate problems."

In (1), you are suggesting that students with parents in administration should not be admitted into any program which is administered by their parents. You have already agreed that such a policy is inappropriate---a student has a right to attend any institution for which they are qualified and can gain admittance. If the administrator abused their power to get their child into the program, that is an ethical breach, but it has nothing to do with you (it is between the administrator and the institution).

And to suggest (2) is to make a mountain out of a molehill. As several other people have noted, many institutions offer free or reduced tuition for the dependents of institutional employees. I obtained my BA at an institution where I got a 90% discount on tuition because my father taught at a different institution in the state. I am currently teaching in another state where dependents of employees can take classes for free. These kinds of policies encourage the situation you describe. Extraordinary safeguards are not required here---the normal ones suffice.

"Attending an institution" does not imply majoring in a particular field.

@buoyantforce Again, you are suggesting that the children of administrators be barred from certain paths because of who their parents are. I find this highly problematic. A student has a right to attend any program for which they are qualified and can gain admittance. If the administrator abused their power to get their child into the program, that is an ethical breach, but it has nothing to do with you (it is between the administrator and the institution).

Yes I can see that you find it problematic. I don't disagree; but I do find other aspects of it more problematic, which is why I posted.

@buoyantforce I still don't understand what aspect of this you find problematic. Is this a hypothetical problem, where you are worried that this student might be getting unfair advantages? or is this an actual problem, where the student has actually received an unfair advantage because of who their parent is? If this is a hypothetical problem, no problem exists yet. If this is an actual problem, I have already given you advice for dealing with it (grade anonymously, keep meticulous records, and speak to a higher authority).

Having at least a perceived conflict of interest built into the situation is, to me, enough to characterize the situation as problematic. The resulting uncertainty, awkwardness, and discomfort are already "something bad happening." It is not necessary to have, e.g., a conflict over grades actually occur here (although that could easily happen and without prior warning, clearly).

There are two possible situations: (1) the chair's offspring must take one course from an instructor who reports to the chair (your hypothetical); (2) the offspring's major is offered by the chair's department, and in every major course the offspring takes his father will be the boss of the instructor (my situation).

The American educational system is such that this kind of situation is bound to happen from time-to-time. The situation itself does not create ethical violations, and your suggested mitigation (disallowing the student from majoring in this field) is far more problematic situation than what exists now. Yes, there is potential for the chair to abuse their position, but the situation itself is not overly problematic. Maintain vigilance, act in good faith, and if an actual ethical breach occurs, take action from there. Until then, the best advice I have is "stop looking for trouble".

Realizing that awkwardness, discomfort, and swirling questions are built into a situation is not "looking for trouble." The trouble is already there. It bothers you that someone would acknowledge it. Why?

Nothing bothers me about acknowledging the situation, and for you to believe that I am attempting to sweep something under the rug indicates to me that you have not read my answer, which gives you concrete strategies for dealing with an actual ethical violation. However, thus far, you have provided no indication that an actual breach has occurred. You have only repeated that you, personally, feel uncomfortable. I'm sorry, but your discomfort does not rise to the level of an ethical breach, any more than the discomfort of a female student who doesn't want to be taught by men.

I'm content with the answer I chose, which acknowledges the difficulties and risks inherent in the situation. To me, most of the rest of the discussion either hedges too much or sounds like rationalization based on pure expediency.

@buoyantforce Which indicates to me that you haven't really understood the answers which have been given to you, because they all pretty much say the same thing as the answer which you have selected. Yes, there is potential for abuse here, but it is unlikely that abuse will occur. If it does occur, there are actions you can take. I have difficulty understanding why you accept this when Anonymous Physicist says it, but object when either Buffy or I say it.

The difference is that part of the chosen answer was that the faculty member should not be evaluated by the chair in question. The other answers were of the form "just do things ethically yourself and wait until something goes wrong." Anonymous Physicist wisely built in a safeguard against one important thing going wrong.

Again, that you think that my answer is "The other answers were of the form 'just do things ethically yourself and wait until something goes wrong'" indicates that you have not understood my answer. In a previous comment, I suggested that you take some time to look at your faculty handbook and institutional procedures and policies regarding nepotism. Have you done this yet? What do those documents suggest?