To recreate, spawn a few pigs, then get a saddle + carrot on stick, ride one of the pigs for a while, and all of a sudden the other pigs start following you too, with or without a saddle.

I expected the carrot on a stick to have individual movement control, I didn't expect it to be the equivalent of a carrot to other pigs, making them all follow the one that is holding the rod while riding a pig.

This breaks the opportunity to hold events such as pig-races, because the pigs simply follow one player if close enough, even if everybody is riding his own pig and holding his own rod.

I could confirm this behavior in both single player and multiplayer, I am not aware of any similar bug reports after searching around for a bit on here, thus I made this report.