Can quality be inferred by popularity?

It is a fairly standard fallacy known as the appeal to popularity.

The reverse is a form of appeal to spite I think.

As has been pointed out, it’s the word “good” that becomes problematic. More simply, the argumentum ad populum fallacy asserts: "If many believe so, it is so.” This suggests there is no situation where the argument is valid. That is, it is just not logically sound to argue ‘truth by popularity.’

Using the Amazon book example: Is it logical to claim that because a book has hundreds of five-star reviews, it is good? Well, what does “good” mean? Worth reading? Then certainly not. Like me, I’m sure you have often been disappointed when reading “popular” books. (The same goes for movies rated “good” by critics or viewers on Rotten Tomatoes). 

What about “good” in a moral sense? Well, 74% of Amazon reviewers give Adolph Hitler’s Mein Kampf five stars. OK, you say, that’s a bad example because they aren’t saying the content, per se, is good. But what if those reviews were mostly by white supremacists?

Any book can present this problem. Consider Charles Darwin’s On the Origin of Species . Forget “good.” In all senses of the word, it is considered GREAT by millions of people. Unsurprisingly, its Amazon reviews are likewise great. But recently, some commentators have been pointing out that the sub-title of the book is “And the Preservation of Favored Races in the Struggle for Life.” That’s right: Darwin was a racist, one of the worst kinds of people by today’s moral standards. Some have argued, in fact, that his theories were responsible for eugenics and inspired the thinking of ... wait for it ... Adolph Hitler.

So: I submit that the ad populum argument is always fallacious. Among a group of like-minded people, it seduces us into thinking it is a valid argument because we cannot think of any way it could be wrong. But that is often just a failure of our imagination. As shown above, people’s opinions and perspectives are too unstable to ever be the basis of objective truth. The most we can say is that majority opinions suggest, directionally, that something may be so. We might even say that, as a heuristic, it is usually wise to use popularity as a guide for what is good. But I contend the standard of logic is much higher, and that this argument fails that standard in every case.

The fallacy of appeal to popularity is more commonly encountered when deducing truth from the numbers of people agreeing with a proposition. This is fallacious because the two are distinct from one another and thus exist independently (e.g. a large number of people, or even the majority, can be wrong on things).

In terms of "good", as Dr Bo points out, it depends on what is meant by 'good'. If you see a product with high ratings, it seems like for most people who buy it and leave reviews, it does the job they want it to - and thus, it is good for that purpose (just be careful applying this logic to political books, as people often leave favourable reviews when they agree with the author's position).

There is much ambiguity in the words "good" and "bad." When we do say, for example, a product on Amazon has 4 1/2 stars and over 1000 reviews, we can say that people seem to be happy with it. In this sense, it is considered a "good" product. The inverse is more problematic because we can't infer that a new product with no ratings (yet) is bad—we know nothing about it.

So to answer you question, it can be reasonable when applied to certain cases, as long as all parties are clear as to what is meant by "good."