What is the correlation between a company’s size, as measured by market capitalization, and its power? I’m not sure how one would measure power, but I don’t think that market cap is a good proxy for it. ADM is worth $29 billion; Halliburton is worth $33 billion. Both, I think, have more power than, say, Procter & Gamble ($228 billion), and they surely have more power than Berkshire Hathaway ($218 billion) – although since "power" remains undefined, such determinations will always be a bit fuzzy.
All the same, it’s not surprising that Ken Auletta uses Google’s market capitalization as an indicator of its power:
In response to prodding by consumer activists, some government officials–notably Senator Herb Kohl, a Wisconsin Democrat–have begun to ask: Does Google, which today is among America’s ten richest corporations, with a market value of just over two hundred billion dollars, have too much power? (ExxonMobil, valued at just under five hundred billion, is No. 1.)
One problem here, of course, is that market cap is not a great proxy even for how "rich" a company is, and it might well make more sense to use revenues or profits instead. (In which case Google drops down the league tables quite rapidly.) Indeed, according to Justin Fox, using market cap for these kind of comparisons is a relatively new device:
I think it’s fair to say that, over the course of the 1990s, the idea that the stock market knew best gained an awful lot of strength in public discourse. Just think of the tendency to judge companies by their market capitalization. Very few people outside of investing circles did that before the 1990s, but by the end of the decade everybody was talking about Cisco or Microsoft being "worth" $400 billion (or whatever).
I do think that it’s silly to think that a company has much more power than it used to just because speculators have run up its stock price. Yes, the increasing power of the company might be part of the reason why the stock price has risen – but then again, it might not, or it might only be a small part. The classic "strip and flip" strategy employed by private-equity funds, in fact, is based on the idea that it’s possible to increase a company’s value by decreasing its power.
I would explain market cap’s popularity as a function not of increased adoption of the efficient market hypothesis, but rather as a function of the internet. It takes just seconds to find the market cap of any company in the US, and most companies in the world. And once you’ve done that, you have an easy apples-to-apples metric with which you can compare any company to any other. It’s almost impossible to resist.