As im not experienced at bo2 i cant help much but i can help with some traces:
1- there should be some event handler probably named endGame(its from mw2)
you can call your start voting script from. it may be in any of _gamelogic or _globallogic
2- you can use good old voting script from Cod4 Royal Soldiers HC mod(available on cfgfactory) however its not as same as design of what you just sent
3- and according to ImVeryTwisted if bo2 using old maprotation system (not the random one) you can easily set sv_mapRotationCurrent dvar after voting completed
hope i helped you. sincerely