The phrase “downward nobility” is a pun on “upward mobility.” It usually refers to taking a less lucrative but more admired position. For example, it might be used to describe a stock broker who becomes a teacher in a poor school. (I don’t believe that being a teacher is necessarily more noble than being a stock broker, but many people would think so.)
Daniel Lemire looks at a variation on downward nobility in his blog post Why you may not like your job, even though everyone envies you. He comments on Matt Welsh’s decision to leave a position as a tenured professor at Harvard to develop software for Google. Welsh may not have taken a pay cut — he may well have gotten a raise — but he took a cut in prestige in order to do work that he found more fulfilling.
The Peter Principle describes people how people take more prestigious positions as they become less competent. The kind of downward nobility Daniel describes is a sort of anti-Peter Principle, taking a step down in prestige to move deeper into your area of competence.
Paul Graham touches on this disregard for prestige in his essay How to do what you love.
If you admire two kinds of work equally, but one is more prestigious, you should probably choose the other. Your opinions about what’s admirable are always going to be slightly influenced by prestige, so if the two seem equal to you, you probably have more genuine admiration for the less prestigious one.
Matt Welsh now has a less prestigious position in the assessment of the general public. But in a sense he didn’t give up prestige for competence. Instead, he chose a new environment in which his area competence carries more prestige.