One way might be to consider how many people might have seen the article or brand name. Essentially that's what PR and advertising have traditionally done by publishing Opportuities To See (OTS).
The cost of good audience measurement tools like Comscore means that this approach is very rare (apart from being applied to the biggest websites which take part in ABCe). Not only that but it doesn't give useful measurements for the huge audiences in the long tail (e.g. it can't tell you how many people read this blog)
Another way might be to recognise that some eyeballs are more valuable than others. So if you are trying to sell pensions, readership by lots of teenagers is probably irrelevant.
Demographics data is also expensive to buy, and isn't very relevant to most brands. Afterall if you are selling aftershave then you probably want to market to people who buy aftershare.
So a slightly more sophisticated way of social media measurement might be to assess whether potential customers (etc.) have seen your brand online. Again virtually nobody does this.
Amazingly the approaches that social media measurement firms sell essentially come down to two measures:
1. How many times is the brand mentioned online?
This is utterly barking, implicitly saying that the small/exclusive readership of this blog is the same as the BBC's website. Yet I have recently seen major campaigns assessed on the basis of them receiving 250 mentions online - without any idea of the audience of each mention.
2. Is it influential- as measured by the number of links to the article and similar measures?
This is slightly less mad, but you can imagine there's a lot of wriggle room for what 'influential' means. Radian6 - one of the widely used social media monitoring tools allows you to combine 'on topic mentions', links, comments, and a few other things to create a measure of influence.
Still a bit odd, but it doesn't really reflect that who you are trying to influence and why you are trying to influence them may be important. For instance you may find that Burnley football discussion is very influential on Alastair Campbell, but that doesn't imply that you should start in depth lobbying on capital gains tax on Burnley's football discussion forums.