:?
I'm really surprised m_e23. Platies are usually one of the more placid species, even though they can occasionally chase each other and other fish. It's never on the scale of cichlids.
I've a group of 9 in one tank that have been there, well, eons it seems. They all get along just fine, so it's definitely not numbers that are the issue.
What size tank do you have? It could be that if it's a small tank (we'd have to be talking less than 10G here for a group size of 3 to be causing problems... :S) then the fish are feeling hemmed in and stressed and are taking it out on each other.
The one and only time, in many years, I've seen a platy get aggressive was when I relocated a tank: a male blue platy, previously submissive to the dominant red coral group, took it upon himself to become 'boss' and harassed my other fish so badly I actually ended up moving him out of the tank (a platy, who'd have thought?!).
You've got the ratio of m:f right, so it's not that either. My only thinking is: tank size, and/or lack of hiding places/vegetation.