During the Zombie Apocalypse, it may be tempting to start some kind of dictatorship, but I think it’s best to set-up an appointed leader by the rest of the group. Maybe their would be a council who would vote on the matters at hand.
Everyone needs a place in this new world with zombies constantly at our throats. During the apocalypse, you and your group will be more worried about this constant threat then about how the new government will function. After the zombies die down after 10-20 years, give or take five years, you will have time to think about rebuilding society. There would never be a better time to come up with a better system. My idea would be a system where everyone had a job, house, etc., and got payed by the central group. The central group would then ration out, for example food, to all the families. The central group would keep a stock pile of all resources and keep track of incoming and outgoing supplies. During the apocalypse, people would not have a good reason to steal food from one an other because the only thing keeping the “town” together would be everyone’s participation. Everyone must realize that after the apocalypse, it will be much the same, just without the constant threat of being chewed to the bone. Well I hope I have given you something to think about. Now if you’ll excuse me, I have some food to manage.