Would there be less war?

Nations begin electing candidates based on strength and fighting ability. Government offices become filled with pro boxers and mma fighters.

Russia would probably win as it sits now

Do you want Putin to conquer the world? Because thats how you get Putin to conquer the world.

Or just have the nation's leaders hire big buff guys to go and fight for them instead

In a chess match

Wars aren't just contests of bravado, that won't work.

floyd may weather becomes prez

If their leader is an asshole

Erm...awesome!

I say we have them play mind games, made to whichever the war they are fighting is about. If we have them do it at all.

http://cdn.thinglink.me/api/image/705370105923502080/1024/10/scaletowidth#tl-705370105923502080;1043138249%27
My money's on Barack.