Instagram is currently hiding likes in Ireland as part of a test, only the person who uploads the photo sees how many people like it. It will be interesting to see if they roll it out everywhere or decide against it.
Personally I think the converse would be more effective hide the score from the uploader. People upload to gauge their popularity (via image proxy).
Basically I don’t think the issue is, hmmm, what pic got the most likes, do I can get likes too. It’s let me see how many likes I can get on my pic. Obviously people will copycat to go for reproducibility of likes, but are mostly interested in the likes.