What does the phrase "bat an eye" mean?

Question

I am not talking about the action of batting your eyes. This is the sentence it was used in: "If she applied this restriction not to Youtube but to Entertainment Weekly, nobody would bat an eye."

Answer 1

The expression COMES from the action, so it must be mentioned.  'Batting one's eyes', or blinking, is something one does when their attention is caught, when they're surprised. So, NOT batting an eye means whatever it was that you didn't bat an eye at was unremarkable, you wren't surprised, you didn't give it a second thought, you didn't care.

Answer 2

Well, it's related.  To bat an eye is to blink or wink.  It's a very tiny action.  On the one hand, one way to acknowledge something or show interest in it is to wink at it.  On the other hand, one way to show surprise is to blink.

If she applied this restriction, not to YouTube, but to Entertainment Weekly, no one would show the slightest surprise or interest.  Indeed, there wouldn't be any reaction at all.

Answer 3

It means no one would take notice or care.

Answer 4

The phrase was originally "(not) batting an eyelid" - i.e. not blinking. It means that nobody would be even the slightest bit surprised, not even enough to blink or respond in any way at all.