Depends on your definition of "scrutiny." This subject is much discussed by theorists in what used to be thought of as "law reviews," and the FTC engages in occasional throat-clearing. But it was apparent to all knowledgeable observers even before Christine Varney departed US DoJ? for Cravath that there will be no serious dust-up between this Administration and Google in during this or any second term. Similarly, the EC has no political stomach for, and precious little jurisdictional armament with which to maintain, such a prolonged confrontation.

Many have argued that Google tweaks its algorithm in ways that push down certain sites in search results that compete for eyeballs, allegedly because these sites have unoriginal content. Disgruntled site owners have cited Google giving Yelp the “TripAdvisor treatment” in support of their accusations. Yelp CEO Jeremy Stoppelman, when questioned about Google Places, remarked:

These are two completely different questions being conflated. At the beginning of the paragraph you are discussing the supposed unfairness of Google's algorithmic rankings. Later you are reflecting on a completely different issue; whether a site operator has some reason to object when material that is searchable to Google spiders--and to the entire rest of the universe on the same terms--is re-aggregated by Google in contexts that bring no immediate monetary advantage to the site operator whose page was searched. Whatever analysis is appropriate to each of these questions (about which I suspect in both cases we might differ), there is no appropriate mode of analysis that begins by confusing them.

This sentence doesn't make any actual sense. I'm not aware, at the moment, of any search engine operator proposing to establish service on the basis of transparently published ranking algorithms. If there were such an operator, it's argument in favor of transparency would not be to consumers, except in the general sense that all propaganda in a society where consumption represents the predominant share of GDP is conducted in the meaningless bullshit vocabulary of "consumer welfare." Slight analysis reveals that it's not the consumer of search results who cares whether the algorithm is transparent. The very people who think that free software is unimportant because the bulk of ordinary PC consumers don't use it should see at once why this argument is nonsense. Transparent search algorithms are valuable to prosumers of search: that is, to the creation of a system of federated search technology, in which we all do searching for one another in some fast and efficient manner we haven't devised yet, and no party in the world knows what all the rest of us are thinking about.

But such a system, in which we spread search out throughout the Net, deconcentrating it, would remove the power over advertising that is held by a centralized search engine that knows what lots of people are looking for right now. In other words, the real competition in search is not between parties centralizing search to control advertising, for each of whom ranking algorithms that enable auction markets are quite legitimately and necessarily hypervaluable trade secrets, but between the architecture of centralized search and the architecture of federated search. As I've already explained in class, centralized search architecture—which makes Google, Bing, and almost all the other known variants—has what at present seems an insurmountable lead. The one-way link design of the Web is apparently overwhelmingly in its favor. And no one has yet built a model of successful, general, instantaneous, Web-wide federated search, so there is not even an unviable competitor to the reigning architecture.

On a twenty-year time scale, however, that's not true. The Web is less than 7,000 days old now. When it is 15,000 days old, federated search will be the dominant architecture, and ranking algorithms will be transparent, just as operating system kernel implementations are becoming transparent, because they too will be free software.

That has important implications for the future of advertising, and the distribution of economic power, that are probably the big story here. But you can't find them if you don't look for them.

There's no "dominant theory" of Google's antitrust liability because there's no viable theory. Not one serious party, public or private, has decided to make the vast bet required to test any theory, because there is no theory that demonstrates both harm and causation sufficient to invoke legal process by any party with a claim to propose.

The other problem here is that you aren't discussing ranking algorithms anymore, you're discussing advertising placement algorithms for sponsored links. These are not the same things, not the same algorithms, and not the same analytic issues with regard to transparency. You need to be clear from the beginning that you're not asking anything about search, the purpose of which is to find things in the web that the reader wants to see. You're asking about advertising placement, which is the algorithm matching stuff that wants to be seen to people who could be induced to click on it whether they actually want it or not. There is no analytic case whatever for transparency of the latter algorithms, except the general belief that people should be able to stufy the software they interact with, which is too weak a claim to overset the obvious operator interest in trade secrecy.

But that's about search ranking. The case is weak, but you're not discussing it. Are you? The confusion on technical points is harmful even to basic coherence at this point.