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This paper analyses the principles underlying the theories of risk and inequality, and the connections between the two. Using two experimental designs, we investigate the structure of individuals’ rankings of uncertain prospects in terms of risk and inequality. We examine these individual perceptions in the light of the conventional principles underlying risk and inequality. We show that, although the principle of mean-preserving spreads and the principle of transfers are often rejected a weaker principle, “lowest-to-highest” is usually supported.

In the case of ordered categorical data, the concepts of minimum and maximum inequality are not straightforward. In this chapter, the authors consider the Cowell and Flachaire (2017) indices of inequality. The authors show that the minimum and maximum inequality depend on preliminary choices made before using these indices, on status and the sensitivity parameter. Specifically, maximum inequality can be given by the distribution which is the most concentrated in the top or bottom category, or by the uniform distribution.

It is well known that taxes on the transfer of wealth typically raise very little revenue. However, this does not mean that they are ineffective as tools for redistribution. In this chapter, we show how important such taxes can be in the long-run distribution of wealth, reducing equilibrium inequality (the “predistribution” effect) by a much larger amount than what is apparent in terms of the immediate impact of the tax (the “redistribution” effect).

Theil's approach to the measurement of inequality is set in the context of subsequent developments over recent decades. It is shown that Theil's initial insight leads naturally to a very general class of decomposable inequality measures. It is thus closely related to a number of other commonly used families of inequality measures.

We establish a general relationship between the standard form of the individualistic social-welfare function and the “reduced-form” version that is expressed in terms of inequality and mean income. This shows the relationship between the property of monotonicity and the slope of the equity-efficiency trade-off. Particularly simple results are available for a large class of inequality measures that includes the Gini. These results do not require differentiability of the social welfare function.

The techniques of simple random sampling are seldom appropriate in the empirical analysis of income distributions. Various types of weighting schemes are usually required either from the point of view of welfare-economic considerations (the mapping of household/family distributions into individual distributions) or from the point of view of sample design. The different types of weights have different implications for the sampling distribution of estimators of welfare indices.

In this paper, we examine the concept of “vulnerability” within the context of income mobility of the poor. We test for the dynamics of vulnerable households in the UK using waves 1–12 of the British Household Panel Survey and find that, of three different types of risks that we test for, household-specific shocks and economy-wide aggregate shocks have the greatest impact on consumption, in comparison to shocks to the income stream.