Since this is ELI5:
Let’s say you and your friend get a cake. You each get half the cake because that’s fair. You and your friend are asked to come up with the fastest route from his house to your house, and whoever has the better answer gets another cake. He draws a line on the map that’s straight north and then straight east. You draw a map that goes south, then west, then north a bit, then east, then north, then west again. You drew a line past all your other friends’ houses because you want to see how they’re doing. But the question was for the fastest route, so your friend gets a cake and you don’t. Now you’re upset that he got a cake even though you’d always take your route. You might think it’s better to take more time to go past your friend’s houses, but that’s a value judgement.
Anti-intellectualism is the idea that even if his solution is the better one given the problem statement, your answer should have been accepted instead, or at least accepted too. It’s not that you don’t have a good idea, but you solved the problem in a way that doesn’t fit the problem statement. It’s a problem because maybe you could have just gone straight east and then straight north, and also solved the problem just as well, and also gone past your friend’s house. It becomes a big problem when enough people think that the solution isn’t a good solution because they don’t like it. And if somebody decides to give you the cake because they like your solution, even though it’s not the best one, then others start doing the same thing, trying to appeal to the subjective likes of a judge instead of the objective criteria set out in the problem.
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