Inequality and Heights

This chapter discusses opportunities and limitations of height inequality, especially the role of social status and income distribution in determining height inequality. The more unequal the income distribution in a society, the more unequal the corresponding height distribution. At one time, the height gap between rich and poor teenagers in industrializing England was as high as 22 cm (8.7 inches); today, height inequality tends to be much lower (on the order of a few centimeters) because the gap between rich and poor in developed countries tends to be smaller. Results presented here suggest that height inequality is driven by differences in purchasing power, education, physical workload, and epidemiological environment. In a modern setting, social safety and redistribution of income is also relevant. An introduction into the literature helps illustrate opportunities this methodology has to offer to understand better the dynamics of the way populations experience economic development.

Top incomes under finance-driven capitalism, 1990-2010: power resources and regulatory orders

This article examines the impact of financialisation on the income shares of the top 1% from 1990-2010, through a panel analysis of 14 OECD countries. Drawing together literatures stressing the dependence of income inequality on the structural bargaining power of capital relative to labour, and of the dependence of accumulation on underlying institutionalised modes of state regulation, it shows that financialisation has significantly enhanced top income shares net of underlying controls. Whilst the income shares of the top 1% appear responsive to variables typical of wider studies of personal income inequality, we emphasise distinctive mechanisms of top income growth linked to the rising dominance of financial instruments and actors, facilitated by a historically specific regulatory order. These conditions were key to the emergence of a state of ‘asymmetric bargaining’ which disproportionately enhanced the fortunes of the wealthy. Results thus emphasise the importance of class-biased power resources and underlying regulatory structures, as determinants both of income concentration and of the distribution of economic rewards beyond growth capacity alone.

Estimating quantum chromatic numbers

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP algorithm that yields a parameter larger than the Lovász number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.