In recent years the case for free markets has become tainted by association with a defence of the rich - an association which free market think-tanks have done too little to disentangle. It was not always so, however. Adam Smith and David Ricardo (and Thomas Carlyle!) saw free markets as an attack on privilege. Posner and Weyl's Radical Markets is an attempt to return to that older tradition of Philosophical Radicalism. They want to use markets to equalize wealth.

One of their main ideas is what they call COST - a common ownership self-assessed tax. The idea here is that we assess the value of all our possessions and pay an annual tax on that value - the snag being that everybody can see our assessments and force us to sell our property to them at that assessed price. This gives us an incentive to assess our wealth properly - if we over-estimate it we pay too much tax and if we under-estimate it we risk losing our possessions with insufficient compensation. In effect, then, all property becomes commonly owned and we rent it from others - the rent being the tax we pay. You can think of this as a back-dated consumption tax.

Posner and Weyl see the obvious objections to this, and deal with them well. I was almost convinced.

But only almost. For me, it fails the Cushnie principle: is it worth the bother? Ryan Aven rightly says that self-assessment would impose a massive cognitive load onto all of us. And for what? I'm not sure why a COST is much better than a wealth or land value tax accompanied by their incentive-enhancing self-assessment mechanism,

Another of their ideas is quadratic voting; in effect, people are given a budget of "voice credits" each year and can allocate more of them onto issues where they feel strongly. I sympathize with this - I've supported something similar myself - not least because it might, in the long-run, improve the quality of debate by reducing hyperbole: any blowhard trying to exaggerate an issue can be countered with the question: "how many votes will you spend on it?"

But, but, but. I'm not sure this tackles the big failures of our democracy: the fact that the rich have too much influence; the fact that the standard of public discourse is piss-poor; and the fact that some issues get onto the agenda whilst others, sometimes more deserving, do not.

Yet another of their ideas is that data is labour - that we should be paid for the data we provide for free to the internet giants. This is better. What they hint at - but don't quite say explicitly - is that this is a challenge to neoclassical economics. For any individual, the marginal product of our data is negligible. Collectively, however, it is huge. What does this tell us about marginal productivity theory?

I these senses I agree with Diane and with Ryan. Whilst their actual proposals are dubious ("barking mad" is Diane's phrase), their philosophy deserves careful thought, as they are asking good questions about the relationships between property rights and markets.

I feel Posner and Weyl are on stronger ground when they advocate limits on institutional investors' ability to hold shares in companies in the same industry. At the moment, they say, cross-holdings deter firms from competing against each other. This is good. But it's an extension of anti-trust powers, not a radical market.

What's more, there are some odd omissions. For me, a better way of using markets to help ordinary people was proposed years ago by Robert Shiller: we should, in theory, have markets that allow us to insure against recessions, falling house prices or declining wages. Posner and Weyl, however, don't mention this.

And in fact, 26 years after Shiller proposed them, we still don't have them. Which raises a challenge to Posner and Weyl: why do our imperfect actually-existing markets work in favour of the rich so much? Might it be that they have captured the economy (to use Lindsey and Teles' phrase) not because of a lack of intellectual energy by those who want proper markets, but because they have the power? (The issue here is one raised by Dani Rodrik, about the weight of ideas versus interests.) If this is the case, then a free market economy requires an attack upon that power. Free marketers such as Posner and Weyl must then answer the question in that old folk song: which side are you on?