Michael Vassar once suggested: "Status makes people effectively stupid, as it makes it harder for them to update their public positions without feeling that they are losing face."

To the extent that status does, in fact, make people stupid, this is a rather important phenomenon for a society like ours in which practically all decisions and beliefs pass through the hands of very-high-status individuals (a high "cognitive Gini coefficient").

Does status actually make people stupid? It's hard to say because I haven't tracked many careers over time. I do have a definite and strong impression, with respect to many high-status individuals, that it would have been a lot easier to have an intelligent conversation with them, if I'd approached them before they made it big. But where does that impression come from, since I haven't actually tracked them over time? (Fundamental question of rationality: What do you think you know and how do you think you know it?) My best guess for why my brain seems to believe this: I know it's possible to have intelligent conversations with smart grad students, and I get the strong impression that high-status people used to be those grad students, but now it's much harder to have intelligent conversations with them than with smart grad students.

Hypotheses:

Vassar's hypothesis: Higher status increases the amount of face you lose when you change your mind, or increases the cost of losing face.
The open-mindedness needed to consider interesting new ideas is (was) only an evolutionary advantage for low-status individuals seeking a good idea to ride to high status. Once high status is achieved, new ideas are high-risk gambles with less relative payoff - the optimal strategy is to be mainstream. I think Robin Hanson had a post about this but I can't recall the title.
Intelligence as such is a high-cost feature which is no longer necessary once status is achieved. We can call this the Llinas Hypothesis.
High-status individuals were intelligent when they were young; the observed disparity is due solely to the standard declines of aging.
High-status individuals spend more time on dinners and politics, and less time on problem-solving and reading; they exercise their minds less.
High-status individuals are under less pressure to perform, in general.
High-status individuals are just as smart as they ever were, but when you or I try to approach them, the status disparity makes it harder to converse with them - they would sound just as intelligent if we had higher status ourselves.
High-status individuals feel less social pressure to listen to your arguments, respond articulately to them, or change their minds when their own arguments are inadequate, which decreases their apparent or real intelligence.
High-status individuals become more convinced of their ideas' rightness or of their own competence.
High-status individuals get less honest advice from their friends, especially about their own failings.

Did I miss anything important?

Having achieved some small degree of status in certain very limited circles, here's what I do to try to avoid the status-makes-you-stupid effect:

I try to feel a small flash of self-satisfaction whenever I publicly admit that I am wrong, over what a good rationalist I am being and what a good impression I am making. Not so much satisfaction that I forget that it's better to be correct in the first place, but enough to be a counter-force to the fear of losing face.
I consistently refuse to be drawn into running the Singularity Institute. I have an overwhelming sense of doom about what happens if I start going down that road.
I try in general to avoid sending my brain signals which tell it that I am high-status, just in case that causes my brain to decide it is no longer necessary. In fact I try to avoid sending my brain signals which tell it that I have achieved acceptance in my tribe. When my brain begins thinking something that generates a sense of high status within the tribe, I stop thinking that thought.
I remember my low-prestige roots - for example, I remember what it was like to be a child squeezed through the horrors of the elementary school system. I haven't switched sides to declare that children are stupid and need to be overridden for their own good (as would signal my own adulthood and maturity). I remember the battles I fought then, and would still fight them now on behalf of another child if a target of opportunity arose. That is supporting and identifying with the downtrodden - not to be confused with the high-prestige activity of supporting trendy minority causes that other celebrities support. The vast majority of celebrities who "support the downtrodden" don't go so far as to support children against adults. (David Deutsch is a notable exception to this, and earned a huge amount of respect from me for it.)
I refuse to conform to people's expectations of a wise sage who always speaks with kindness and sober deliberation, of which I have said: "I am not bloody Gandalf."