Say you have a piece of digital content (a song or book), and you sell it on iTunes, Amazon and on your own website. You're interesting in finding out which of those sales outlets your customers prefer.
So, you devise a test: you'll create three splash pages, each has some marketing copy and a single link to one of those sales outlets. Randomly, one third of your visitors will see the iTunes link, one third the Amazon link and the remaining third will see a link to your own website's sale page. The visitor is identifiable, so the same link is presented on subsequent visits.
I don't think this actually tells you about what your customer's like. But I'm having a hard time saying why. If I'm presented with iTunes but I don't like iTunes and never click through, does that really say anything useful about whether I like the alternatives?
That we're even doing the test is a nice change of pace, but I hate the idea of doing a test and claiming the results mean something that they may not. I'm happy to hear that my misgivings are wrong.
You're performing the test on one large group of people, not on lots of individual people. (Does that make sense?)
It doesn't tell you what Bob as an individual likes, but it might tell you what a collection of people prefer.
It's quite important with A/B testing to set a sample size at the beginning of the experiment and stick to it. A statistician will be able to explain why.
Because you're not testing individual people it'll be tricky to disentangle the reasons for preference from the data.