Ex-News of the World journalist and phone hacking aficionado Paul McMullan describes the public interest thus:

The public interest, he said, added up to no more than the sheer number of copies the News of the World could sell. “Circulation defines the public interest” – which meant that everything was legitimate as long as the public bought the paper. “You have to appeal to what the reader wants – this is what the people of Britain wants. I was simply serving their need,” he said

Hence, if the people are willing to pay to  read about Hugh Grant’s peccadilloes, then it is O.K. to hack into his phone etc. to give the people what they want.  There is a flavor of a free market argument here.  But we know that prices are necessary for the market to work efficiently – the market is not literally free in terms of commodities being free! There are no prices here so there is no reason why giving the public what they want leads to efficiency.  Hugh Grant may value keeping the identity of the mother of his child secret at v while the public values the information at 0<v'<v . In the absence of a price, the information will get revealed even when it is inefficient (i.e it does not maximize social surplus).

Then there is the reverse scenario where details of Hugh’s shenanigans in L.A. are worth v’ to the public and secrecy is worth v to Hugh but v’>v>0. In this case the ex post efficient outcome will be implemented by the media. But there is ex ante inefficiency in gossip production. As Hugh does not capture any or the surplus he generates from cavorting with ladies of the night, he will not cavort at the socially optimal level. To fix this serious problem, Hugh and the Sun, Daily Mail etc have to begin by consulting the seminal work of Ted Groves and Myerson and Satterthwaite. A mechanism of some sort needs to be set up to maximizes second-best social welfare. I am sure someone has already worked this out in some abstract mechanism design context (Cole, Mailath and Postlewaite or Bergemann and Valimaki?). The basic idea should involve “selling the firm to the agent” or setting up transfers so each agent maximizes social surplus. This is hard to do for all agents simultaneously I would guess unless you accept some inefficiency in terms of dropping budget balance or accepting some underinvestment ex ante.  But this is still better than the ad hoc mechanism we have right now where the court system makes transfers to Hugh. This wastes resources and does not result in the optimal scheme.

While we mull over what the answer might be, we can enjoy this McMullan performace:

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