I'm a massive fan of Joseph Heath's work, and in particular his article The Benefits of Cooperation I have found to be remarkably clear and illuminating. However, it occurs to me that the arguments he gives in that essay would justify arranged marriages. Unless he is willing to bite that bullet, there must be a problem with his broader argument for the welfare state.
Arranged marriages have tended to be seen as a way for the men of a society to reinforce their control over the family. Hence, it is precisely the kind of social institution that liberalism was supposed to abolish and feminism to eviscerate. Using Heath's tools, however, we have a powerful defence of this institution. I'm not disputing Heath's account of how such arrangements might be socially beneficial; rather, I wish to challenge the idea that, given the beneficial nature of these arrangements, individuals are morally obliged to comply.
In the article Heath identifies five (somewhat roughly defined) ways in which we benefit from the existence of other people: economies of scale, gains from trade, transmission of information, risk-pooling, and self-binding. He argues (I forget whether he makes this argument here or whether you have to move onto The Welfare State: Three Normative Models) that the imperative of efficiency means people can be bound by rules which are designed to achieve these efficiencies, even if they do not actually consent to these rules. His defence of the welfare state, then, is a means of achieving risk-pooling among society at large and of achieving self-binding among people with poor self-control.
(To be clear, in political theory the welfare state - at least as traditionally understood - is marked by two features, both of which are normally taken to require justification: (1) coercive redistribution of income from wealthier members of a polity to poorer members, and (2) that redistribution to take place in the form of in-kind benefits such as healthcare, pensions and food stamps, rather than in terms of pure money. Heath claims that (1) is really just a massive risk-pooling arrangement, and (2) is about self-binding.)
Here's another area of massive risk: choice of spouse. Making a poor choice of spouse can wreck your life and destroy your happiness, as we all know from innumerable stories. (And that's hardly the worst of it. I sometimes joke that I will propose to my future wife with the words, "I love you. Will you become the person most likely to kill me?")
So we have an area where it is massively important to make the right decision. Furthermore, people who are in love are not exactly known for their judgement. So from an efficiency perspective, perhaps you want someone else making - or at least having significant influence over - who any given person marries.
Obviously you can't just let anyone make that decision. So for a person X, what are the ideal characteristics of X's marital-decision-maker? They should know X well, should be in some way invested in X or otherwise motivated to help X do well, and should have reasonable experience of what makes for a good marriage. Who better than X's parents? Hang on a moment, this is starting to look an awful lot like traditional arranged marriages!
As a sociological account, this is reasonably persuasive as an explanation of why arranged marriages came to be (although I doubt many feminists will be receptive to the idea that women forced into arranged marriages are so coerced "for their own benefit"). And perhaps the modern, more liberal forms of arranged marriages (in which both prospective partners have the option of refusing) aren't really so bad. But it does raise some uncomfortable questions: firstly, given the theorem of the second-best and the fact that a transition towards a more liberal system might be difficult if not to achieve, does this mean that people living in a society with coercive arranged marriages must go along with them? And second, does this mean that advocates of a welfare state ought also to advocate for a return to arranged marriages?
Perhaps one might try denying that parents really do operate in the interests of their children, and instead use arranged marriages as a way to threaten the daughter and to shore up familial alliances. But this problem is limited by the fact that parents who make utterly awful choices of son-in-law or daughter-in-law will have fewer grandchildren and so, over generations, will pass on fewer of their genes. Furthermore, real-world states of the kinds that Heath thinks we must obey are themselves far from ideal. Many regulations have a basis less in promoting efficiency than in creating work for lawyers, both in compliance and in enforcement. Other regulations exist due to regulatory capture (for example, most restrictions upon Uber - most egregiously, the recently proposed law in London which would require Uber drivers to wait five minutes before picking up a given passenger, a law with no possible purpose other than protecting the interests of black cab drivers at the expense of everyone else). Taxes go to fund not only the welfare state that Heath defends, but a whole host of programs of dubious utility (e.g. immigration restrictions, military interventions in the Middle East) and even boondoggles. So Heath faces a choice between either denying the duty to obey the law, or affirming the duty to participate in arranged marriages.
If he were a utilitarian, this would be simple: just say that while there's no actual duty to obey the law, the state is nevertheless justified in compelling obedience - if necessary through outright violence. But when you're a deontologist, it becomes harder to reject the intuitive claim that if you lack a duty to do X, no-one can force you to do X. I don't mean this as an endorsement of utilitarianism - that system has its own weird and unpleasant implications - but it's one possible way out of the dilemma.