Chris is mumbling that the notion of the public interest is 'vacuous'. I think he's wrong about this.
1. Here's an analogy to suggest why. Think of a group of people setting up a chess club. They all want to play chess regularly, and forming the club is a way that they can get to do so. Even though they are a diverse bunch of folk, with many different interests among them, in their club they are united by this common purpose: the playing of chess. It makes perfect sense to speak of there being a public interest within the chess club covering at least that point - though it may cover other points as well, such as securing a reasonably pleasant and comfortable venue in which to meet, ensuring that it is not right next door to the Pneumatic Drill Demonstration Parlour, and so forth.
2. Countries, however, are not unified like chess clubs in this clear way, such that one can cite a single purpose shared amongst all their citizens. Never mind. Even for countries, the idea of a public interest isn't vacuous; for there may be needs that are common across the whole population or a very large part of it. A decent sewage system, for example; or adequate vaccination policies to fend off the danger of epidemics. There are forms of public provision and public policy from which there is a general benefit and in the absence of which harm or severe inconvenience would come to large numbers of people. In these circumstances, as much as with the chess club, it makes sense to speak of a public interest.
3. Chris says:
Arrow's impossibility theorem tells us that, under reasonable assumptions, it is impossible to aggregate individual interests or preferences.
I should be cautious here since, as I've said before about Arrow's theorem, I lack full expertise. However, I don't believe it to be the case that the theorem shows what Chris says it shows: that, under reasonable assumptions, it is impossible to aggregate individual preferences. I think it shows that, under reasonable assumptions, there is no method of aggregating individual preferences that doesn't sometimes produce anomalous results.
How could it be impossible in general to aggregate individual preferences? If there are 99 members of the chess club, 98 of whom want to give priority to the playing of chess, and one of whom wants the club to promote drunken brawling, there will be no problem in getting a clear and unambiguous decision about what the club should do. But if the club AGM has to decide between buying new chess sets and clocks (A), getting new tables, chairs and curtains for the club room (B), and repairing the building's plumbing (c), and 33 of the members rank these choices in the preference order ABC, another 33 rank them BCA, and 33 rank them CAB, then you will get the anomalous result that 66 people prefer A to B and 66 people prefer B to C, and yet 66 people prefer C to A - which violates the expectation (which you would have for an individual) that, preferring A to B and B to C, the membership should prefer A to C, because individual preferences are normally transitive.
Arrow's theorem, on my understanding, shows that there's no conceivable decision procedure for which such anomalies don't sometimes occur, given certain distributions of individual preferences. However, it doesn't follow from this that all distributions of preferences will produce irrational results. If 90 members of the club prefer A to B to C, 8 members A to C to B, and one member can't make up her mind, you'll have a clear, huge majority for buying new chess sets and clocks.
4. Happy to dispense with the notion of a public interest, Chris goes for this: 'working class people to have more power and... bankers, bosses and media moguls to have less'. I'm with him on that. But it's not solely an interest of the working class not to be ripped off by bankers and financial institutions. That seems to me a good candidate for something which is a public interest.