DeWaal deftly narrates three changes in leadership among the colony of chimps in a zoo in the Netherlands (not Yerkes in GA, as another reviewer claims). Unlike many animals, chimpanzees can not dominate one another by use of brute force. No chimp is so strong that a coalition of two other males (or a coalition of females) can not successfully challenge his dominate position. This means that the dominate (male) chimp can only remain dominate if he succedes in coalition building.
Each of the "coups" DeWaal describes took place either because the dominate male became too greedy, or because another male built a stronger coalition. Similarly, the dominant make needs the cooperation (or at least neutrality) of most of the (more numerous, but weaker individually) females of the colony.
The comparison to human politics is right on the money. While chimpanzee politics does not have the veneer of ideology that covers the nitty gritty of human politics, I strongly suspect that the type of favors, distribution of goodies, and raw sex that DeWaal describes as the "currency" of chimpanzee politics is much closer to the way human politicians actually operate than most of us would like to admit.
If a Martian were to observe the functioning of the U.S. Sentate--without being able to understand a word anyone says, but with the ability to observe every transaction, day and night, over a period of sereral years, I suspect that the Martian's description of our politics would read very similarly to that of DeWaal's. Of course, for all we know, chimps too have a "language" which permits them to cover what appears to us to be raw politics with "political platforms".
One final note--the chimp need for coalitions to maintain primacy has obvious conotations for international relations in our world, where ideology plays less of a role, and coalitions have, at least since the end of WWII, been the key to maintaining a stable heirarchy of nations. Is the US now in danger of becoming the over confident "alpha" male that DeWaals describes?