These papers deal with the world systems theory of Wallerstien's article as well as the other specialists' criticisms on it. They bring up basically three main ideas, which first off, include the significant role of the periphery in the core- periphery relationship. Secondly, the need to focus on internal and local affects on interrelations between different polities instead of concentrating on the external and generalized role of interaction. Lastly, they demand a model that is diversified enough to allow for analyzation of various levels of interaction between different groups.
In Halls article, he points out that this theory has a few weaknesses, such as its basis is on only one situation of modern times, which does not always have applications to past societies. It is necessary to define the difference between "new" linear events that result from progress over time, and those occurrences that can be explained as historical-cyclical tendencies. To illustrate these types of occurrences, he states that there is a cyclical development from unicentric to multicentric organizations or hegemonic shifts. An example is given between the transfer of power or leadership from the British to the American. Although in concerning this shift the more significant change is the rise of capitalism in the first place that aided in the shift of power.
In order to understand the prehistoric past it is necessary for archaeologists to purpose new theories of interregional interactions. First of all, in order to achieve this increased communication between archaeologist and different type of specialists must happen, before arriving at theories that work. Hall's view on the present day situation is the overflow of theories and models where all the various combination of ideas cannot be combined into one theory, and thus he suggests instead that a paradigm or more general approach will offer more resolution. Thus the first step in achieving a paradigm, he states Chase Dunn's suggestion that the empirical denominations of the world system theory's assumptions must be developed. Hall emphasizes other points that should be incorporated in a new methodology, which are not already present to the world systems theory by Wallenstein. One aspect is that each of system's units works in relation to the whole system; they do not develop on their own. Another is that each system is a world within itself; that its internal factors are just as important in its progress as the external factors affecting it. Other points that must be realized to achieve better understanding of past political social interaction, is to learn the positive aspects of expansion and incorporation and the role of peripheral and semi peripheral states, as well as the ramifications of incorporation on the system.
He includes some various world systems theories as examples in order to emphasize the different the facets that they can take such as being based on war, technological innovation,...