One very simple metric to improve search results is testing how long a user visits a site. When users search for something, click a link and return to google seconds later you can assume that the result did not match what the user was searching for.
Because they're so dominant they can make changes to the system that make it worse. Haven't you noticed the decline in quality of Google search results over these past few years?
i find google is useless at this. They throw out irrelevant results that the Wise Men of Google think you want to see, or that they'd like you to see. DDG pay more attention to your wording. The drawback is they have fewer indexed pages.
I'd also wager this is probably the most useful or close to the most useful metrics you can use. With this metric, plus the user's persona (male or female, teen or elderly, and so forth), you have a fairly accurate user driven ranking system.
because the underlying assumption is that what they'll tell you is the truth, and that's not necessarily the case. Think of a Firefox plugin in, AdNauseam style, that always says NO.
But there's nothing stopping the same people from gaming existing logic that tracks user behavior except security through obscurity. But you also get dirty data via tracking where it's indistinguishable from backend if user found what they want or just gave up on trying for example.