Matt Zwolinski has an interesting article which attempts to answer the question "Why Did Hayek Support a Basic Income?". His answer is that Hayek did so because such a minimum endowment of economic means grants people the essential freedom to say "no"--thus making up for "real" freedom of contract. Matt stresses that Hayek was more concerned than most libertarians with the idea that "unbalanced" market relationships may also be a source of coercion.
I think Matt brings together a neat summary of some well-pondered arguments for a guaranteed minimum income. I would have thought, however, that the Hayekian arguments for a basic income were different.
I think that a Hayekian argument for the basic income is that it would minimize state interventions and, thus, discretionary powers on the part of lawmakers as opposed to contemporary welfare systems.
Hayek believed that there was a legitimate role for collective action against "the extremes of indigence or starvation". Certainly, as Matt remarked in a previous article that David Henderson sharply criticized here, "Hayek was not opposed to the welfare state as such (not even in the Road to Serfdom). At the very least, he regarded certain aspects of the welfare state as permissible options that states might pursue".
However, Hayek was also concerned "with the process by which an apparatus originally meant to relieve poverty is generally being turned into a tool of egalitarian redistribution. It is as a means of socializing income, of creating a sort of household state which allocates benefits in money or in kind to those who are thought to be most deserving, that the welfare state has for many become the substitute for old-fashioned socialism" . He saw clearly the limit of a welfare system that ended up in tinkering with economic life. For example, he maintained that "a compulsory scheme of so-called unemployment insurance will always be used to 'correct' the relative remunerations of different groups, to subsidize the unstable trades at the expense of the stable, and to support wage demands that are irreconcilable with a high level of employment" (The Constitution of Liberty).
Hayek feared that "bleeding heart" policies may endanger the market process. He thought the claims for redistribution were by and large built upon a misunderstanding of markets and a sense of nostalgia for societies based on face-to-face interactions, where (very limited) resources were orderly "distributed" rather than generated in the market process. He eloquently remarked that "those who attack great private wealth do not understand is that it is neither by physical effort nor by the mere act of saving and investing, but by directing resources to the most productive uses that wealth is chiefly created" (Law Legislation and Liberty II. The Mirage of Social Justice). In a market society, people get rewarded for their contributions in a restless process of learning, not because of their "just deserts".
The problem with social justice is thus that it embodies "a demand that the members of society should organize themselves in a manner which makes it possible to assign particular shares of the product of society to the different individuals or groups" (Law Legislation and Liberty II. The Mirage of Social Justice). This would imply a series of continuous interventions in the market process - and, ultimately, the demise of those general, uniformly applicable norms that make for the rule of law.
Thus, a basic minimum income is a smart solution to (a) keep our allegiance to the idea we shall accept some sort of poverty mitigation device but (b) refuse to accept the bureaucratization and the social and economic planning that inevitably comes with "organised benevolence", as Hayek repeatedly pointed out. By providing people with a basic income you do not play with prices (including the price of labour), and society spares herself the (self-interested) intermediation of a welfare apparatus. A basic income is less paternalistic, and may have seemed to Hayek a good way to avoid what happened in the years when he was writing, particularly in England: that is, increasing redistribution, nationalizations, and regulation of the economy going hand-in-hand.
Of course, the interesting question is: could this version of the idea of a basic income survive the test of the political process? And what about its unintended consequences? Hayek would have been fine with replacing the welfare state altogether with a basic income. In Europe at least, most advocates of the basic income are for adding it to the existing welfare provisions. If this happened, I suspect Hayek would not be very confortable in the position of the useful idiot (neither would Matt, for that matter).