What does an entity that only cares about the kids in its Everett branches even look like?

Example 1: Someone that doesn't know about or believe in many worlds. The don't care about kids in alternate Everett branches, because to their mind they don't exist, so have zero value. In his mind, all value is in this single universe, with a coin that he is 90% sure landed Tails. By his beliefs, "yea" wins. Most people just don't think about entire multiverses.

Example 2: Someone who gets many worlds, but tends inclined to be overwhelmingly more charitable to those that feel Near rather than Far, and to those that feel like Their Responsibility rather than Someone Else's Problem. I hear this isn't too uncommon :-)

This sort of entity would do very well to cut out its eyes and ears so it never learns it's a decider and begin chanting "nay, nay, nay!" wouldn't it?

Actual cutting aside, this is an excellent strategy. Upvoted :)