The example uses it to spot a case where most people are wrong, but some large minority of people expect that most people will answer incorrectly, while themsel

The example uses it to spot a case where most people are wrong, but some large minority of people expect that most people will answer incorrectly, while themselves answering correctly. A large enough difference (10%, in the example case) between the "what do you guess others will answer?" and what people actually answered indicates the majority opinion is, in fact, wrong.