Board Game Arena

If we get a thumbs down, does it notify us?

No.

Behind closed doors, someone doesn't like you and lets it known all over their own private internet space. smh.

Also, if it was a public red thumb, if there is a notification there will most likely be a retaliatory red thumb given.

But, unless you get a significant number of red thumbs compared to your green thumbs, it doesn't affect anything. Don't worry about it.