You can't ban someone from having a relationship. But you certainly can require them to disclose such a conflict of interest to the board.

It is not a human right to have sex with whomever you wish free of restrictions.

In the US, most employment is at-will, which means they can fire you for any reason they want except for a list of prohibited reasons.

"Having sex with a direct report" is not on that list of prohibited reasons.

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