As the title, do you like "thumb down ↓" on italki?
You bet. It adds a little objectivity to the discussion.
Yes, I do.
No, I don't. There are many trolls here with many accounts and they use their multiple accounts to thumbs down the discussion they dislike so it is useless option.
It is a double edged sword!
It can also be useful and informative in the Answer and Notebook sections. A thumbs-down serves as a signal to the person posting that an answer or correction is unreliable.