But if a more relevant website is always going to trump a less relevant one (where for relevant I mean: contains the answer to the question the user has submitted) - then what is the effect of bumping mobile friendly websites? None, it would seem - unless there were two websites perfectly identical in every respect except for mobile friendliness, a case that must be pretty rare.
If A and B are identical in all aspects except for mobile-friendliness (A > B), most users are going to like A better than B, given that information is laid out in a more easily consumable format on mobile [1].
User satisfaction not only depends on getting a relevant answer, but also how an answer is presented. Their degree of importance is where the weights come in.
[1] Otherwise, why would anyone build mobile-friendly websites in the first place?
