Recent evidence shows that in many societies worldwide the relative sizes of
the economic and social elites are continuously shrinking. Is this a natural
social phenomenon? What are the forces that shape this process? We try to
address these questions by studying a Core-Periphery social structure composed
of a social elite, namely, a relatively small but well-connected and highly
influential group of powerful individuals, and the rest of society, the
periphery. Herein, we present a novel axiom-based model for the forces
governing the mutual influences between the elite and the periphery. Assuming a
simple set of axioms, capturing the elite's dominance, robustness, compactness
and density, we are able to draw strong conclusions about the elite-periphery
structure. In particular, we show that a balance of powers between elite and
periphery and an elite size that is sub-linear in the network size are
universal properties of elites in social networks that satisfy our axioms. We
note that the latter is in controversy to the common belief that the elite size
converges to a linear fraction of society (most recently claimed to be 1%). We
accompany these findings with a large scale empirical study on about 100
real-world networks, which supports our results