What is the difference between "decide for yourself" and "decide by yourself," and is the latter idiomatic?
“Decide for yourself” would mean you’re making the decision that is only for you. The consequences of your decision only affect you. For example: “I’m going to order chocolate ice cream, you decide for yourself what you want”
“Decide by yourself” means you’re making the decision on your own without anyone else. The decision may or may not affect others, but they don’t get a say in it. For example “I hear your suggestions, but I’m going to decide by myself what to do” or “the judge will decide by himself who will win the prize”
There are some cases where you could use either and they would be correct. But you couldn’t say “the judge will decide for himself who will win the prize” because the prize isn’t for him, it’s for someone else.