Let's leave aside quantitative questions about exactly what percentage of individuals in the highest ranges of intelligence identify with socialist and related ideologies, and take it as given that a significant proportion (not necessarily a majority, mind) of very intelligent people do or have done over the past century or so. This is a fact. And it is a puzzling fact for those of us who are convinced on the basis of the sad history of attempts to implement such ideologies and/or of economic theory that socialism just doesn't work.
Of course, for those with left-wing views there is no puzzle here. They would simply say that bright people gravitate towards the truth. Their puzzle would be the converse of mine - why so many otherwise intelligent people are conservatives (but, of course, the popular image of the conservative as redneck or reactionary obscures this potentially awkward fact).
The first point to make is that 'intelligent' and 'intellectual' may be derived from the same Latin root, but that does not guarantee any congruence of meaning. Put simply, the set of intellectuals may overlap somewhat less than many intellectuals think with the set of highly intelligent people. (This takes us back to the quantitative issues I said I would leave aside, and there may be some research out there which impinges on this question.)
Sure, leftist ideologies flourish amongst intellectuals (especially in universities, and especially within the humanities) but such people are often directly dependent on state funding for their professional income. It is no wonder they tend to support a larger rather than a smaller role for the state and higher rather than lower taxes. There is clearly more to it than this, however.
Idealism no doubt plays a part, but idealism is never as simple as it seems, and its nature and content (or lack thereof) change over time. Current trends (notably the Occupy movement) are rather different from the more sophisticated and intellectually elaborated radical traditions which dominated the 20th century, and my focus here is on the latter.
Could the tendency to left-wing thought amongst intellectuals - who, almost by definition, excelled in the classroom - have something to do with the classroom, with wanting to turn the world into a giant classroom, to perpetuate somehow those positive experiences? To create a world based on the model of a world where violence and money and trading and physical (productive) work were more or less absent, and every boy or girl had an identical desk and wore identical clothes, where a centralized order prevailed, and ideals were fostered... I don't mean to be snarky here: I know the appeal of a world where the struggles are of understanding and ideas rather than related to more mundane concerns.
I realize there are counter-arguments - along the lines that schools have traditionally been authoritarian and patriarchal structures and so might be seen to foster conservatism amongst those who thrived there and radicalism amongst those who didn't. But there are authoritarian and conservative elements evident in socialist theory and practice. The main political divide as I see it is not so much between right and left as between advocates of free-market approaches and advocates of centralized control. In its day, the far right also held great appeal for intellectuals. Think of Heidegger in the 1930s, or Giovanni Gentile in Italy.
Moral and political considerations are generally given prominence but aesthetic factors cannot be ignored. One reason why clever people, and especially intellectuals, are antagonistic to free markets relates to the fact that a market-based system does tend to play to the lowest common denominator. Look at the mass media and entertainment, for instance. Highly cultured people (as academics often are) are naturally repelled by the crassness and vulgarity and mindlessness of the sort of popular culture which develops in a market economy. Such aesthetic factors no doubt play a role in causing intellectuals to reject such societies and to seek out alternatives reflecting their ideal of a civilized and intellectually-advanced community.