Tyler Cowen says leftists:

don't have nearly enough Mill in their thought, and not nearly enough emphasis on individual liberty...This is one reason why the commitment of the current Left to free speech just isn't very strong.

This poses the question: what might be the links between leftism and a Millian assertion of the virtues of free speech?

One upon a time, the answer would have been obvious. Liberals believed that free speech and intellectual progress went together. In a fair contest, it was thought, science would beat religion and liberal equality would beat obscurantism, sexism and privilege. This seems no longer plausible. A proliferation of voices allows people to choose to hear whichever ones support their own prejudices. And even when they are confronted with conflicting evidence, people are asymmetric Bayesians: they question opposing arguments more than supporting ones, and so end up reinforcing (pdf) their own prejudices.

One old "progressive" argument for free speech thus seems weak. There are, however, two other reasons why leftists should embrace the principle.

One is simply that laws will be used by the powerful against the powerless. As Nick Cowen says (pdf), laws against extreme pornography can be used to repress sexual minorities. And similarly, restrictions of free speech will be imposed upon people with low-level mental illnesses whilst leaving hate-mongering newspapers free.

But there's something else. One of the enemies of the left should be people's sense of certainty. Bosses' sense that they are certain how to run a business leads to coercion and alienation - and to inequality as he demands mega-millions for his "talents". Neoliberals' certainty that recessions can be avoided with the right policies leads to the erosion of social safety nets. And the denial of complexity leads to a misplaced confidence in "experts" and hence deference to the rich and powerful.

One case for worker democracy is that bosses are very fallible, and so their control of the firm should be tempered by the dispersed and fragmentary knowledge possessed by others. And one argument for redistributive policies is that we are too fallible to predict recession and so we need risk-pooling institutions such as a generous welfare state instead.

It's this same (misplaced) certainty, though, that leads to the repression of speech. One of Mill's objections to such repression that the man who advocates it "assumes infallibility". Those who want to silence an opinion, he wrote...

of course deny its truth; but they are not infallible. They have no authority to decide the question for all mankind, and exclude every other person from the means of judging. To refuse a hearing to an opinion, because they are sure that it is false, is to assume that their certainty is the same thing as absolute certainty. All silencing of discussion is an assumption of infallibility

In this sense, illiberal tendencies spring from the same source as some inegalitarian ones - from the assumption of infallibility by those in power. To this extent, the assertion of freedom and of substantive equality go hand-in-hand.