Inequality breaks down communication between different elements of a society. Different economic groups share fewer experiences and have less in common. We know from neuroscience that intelligence arises out of massive numbers of neurons being massively interconnected. If you start disrupting connections between different parts of a brain you are going to get much less intelligent behavior from that brain.
As different groups in society have less and less in common, communication between them is going to to break down and this decrease in connections will lead to the society acting less intelligently. This is not to say that individuals in the society are any more or less intelligent, rather that the collective behavior of the society will be less intelligent. Fewer connections, less information flowing between parts, less intelligence.
We are in a period of massive and growing inequality. Given this we should be seeing less intelligent behavior from our government, and in fact we are. Current policies on global warming, health care, transportation, education and taxes are mind-numbingly stupid.
As inequality grows our collective behavior will probably become even more feather brained. The needs and concerns of the less powerful are likely to be increasingly ignored, leading to decisions that antagonize and alienate large segments of the population. The summer of 2011 riots in the UK should serve as a wake up call but I suspect the powers that be will do everything within their extensive means to dismiss the warning signals.
Lack of communication from the wealthy with the poor also cuts the poor off from developing an understanding of the inevitable hard choices that those governing always need to make. In other words, inequality makes the collective decision making of both the wealthy and the poor less intelligent.
Communities that minimize inequality will have more connectivity between their citizens and therefore better communication and more intelligent behavior. In the long run these more intelligent communities will tend to do better than their stupid cousins, and evolutionary forces will work their magic.
If inequality can't be reduced through peaceful democratic means the future of wealthy elites is likely to turn out very badly. A little reading of history shows that when the inevitable major economic crises occur, elites who are not willing to give up their special status will not be treated kindly.
If you are interested in learning more about inequality, Larry Ferlazzo has provided a great set of links in a blog post here. I particularly recommend the video of Malcolm Gladwell having a conversation with Roger Martin about Capital vsTalent.