I think 정하다 and 결정하다 are not the best choice of words as they mean "to decide".
"Is that based on your own judgement?" can be said differently.
- 자기의 판단이 그렇다는 건가요? (literal and rather formal)
- 자기 생각이 그렇다는 뜻이에요? (informal, everyday speech)
그렇다는 (short for 그렇다고 하는) is like "saying that/so", which is similar to "say something based on ...".
자기 (self) indicates the person being mentioned, so it can mean he, she, or you.
We never use 너 to another adult (except close friends) as it sounds very rude like treating them like a kid. 당신 also sounds bad in a face-to-face conversation (it's okay in writings, advertisements, song lyrics, and so on). There is no common word corresponding to "you" for adults.