first thing I think of with anarchy is no rules, no laws....it would basically mean "survival of the fittest", as well as "mob rules" meaning the one positive effect would be progression of the self interests of the masses. We wouldn't have some dumbass republican president in office, but rather one that embodies the spirit of the average American. The negative effects on society is the opposite of freedom, by not allowing people to vote for said dumbass presidents (even if they think they are doing the right thing) regardless of their inability to relate to logic and self progression. Law equals stable environments, lack of laws would equate to chaos.

Anarchy is the absence of any type of political authority -- no good president, no bad president -- based on the concept that all governments are oppressive.

In Utopia, perhaps, anarchy would be the ideal system, as there would be no need to delegate duties, citizens would resolve their own problems peacefully, libraries and roads and parks would be freely financed, built and maintained. From what I've read, though, even Heaven operates within a hierarchy.

The most positive effect anarchy can have on society, however, is unleashing rapid and massive change in the midst of havoc and chaos. The old regime is destroyed along with the rich and powerful who both maintained and were maintained by the state.Their benefits and privileges are stripped, and wealth and power bleed from the few to nourish the many. Consider the French revolution and the Russian revolution as prime examples of seemingly entrenched power structures destroyed by the desperate poor and an impassioned middle class. Mexico's vast estates remained in the hands of the elite, however, while the majority of citizens were lucky to receive share-cropper status.

Cultures change, new ideas can flourish, assets and wealth are parceled out, and meritorious and just people can rise to power.

Nature does abhor a vacuum. The power structure will soon be filled, usually by a new boss same as the old boss -- and often not as effective.

In the meantime, however, in the midst of anarchy, civil services almost inevitably are neglected and decay -- food rots while people starve, water stagnates along with commerce, crops and industries are ruined, the strong and vicious terrorize the citizenry, and the weak and victimized have no recourse. You can elaborate from there.

The upheaval of the existing power structures and social orders is not a rare fantasy, however, for those believe the strongest, smartest and most skillful would thrive in an environment without rules and red tape and corporate bullies maintaining the status quo. That is one reason that doomsday novels and movies can be so stimulating.