JOB MARKET PAPER
Median-Preserving Transfers and Inequality Measurement
Inequality indices such as the Gini coefficient rely on the mean and are therefore ill-defined for ordinal variables like health status or life satisfaction. In the cardinal case, mean-preserving transfers allow one to distinguish a change in inequality from a change in the overall level of outcomes. This paper develops their ordinal counterpart: median-preserving transfers, which reduce dispersion while leaving the median unchanged. I show that, when populations of different sizes are compared through replication, these transfers characterize double dominance — a recently proposed criterion for ordinal inequality comparisons — among distributions sharing the same unique median. The result rests on a first theorem: double dominance holds if and only if one distribution can be reached from another through a finite sequence of Hammond transfers, which bring better-off and worse-off individuals closer together without reversing their relative ranking. The proof provides an explicit algorithm operating within the initial population. Together, these results provide a transfer-based foundation for empirically comparing inequality when the variable we study is ordinal.
Presented at: AMSE PhD Seminar (2024, 2025); Eighteenth Winter School on Inequality and Social Welfare Theory (2025); Workshop on Individual and Collective Decisions and Inequalities (2025); ECINEQ 11th Meeting (2025); ASSET (2025).
WORKING PAPERS
Appraising Central Tendency in Distributions of Cardinal and Ordinal Variables
Joint with Nicolas Gravel — Reject and Resubmit at Social Choice and Welfare
This paper provides an axiomatic justification to the mean and the median as measures of central tendency of a cardinally and ordinally measurable variable respectively. The axioms satisfied by the criteria are the anonymity and Pareto principles as well as the property that an inversion in the scale of measurement of the variable leads to an inversion of the ranking of distributions. Mean and median rankings appear essentially to be the only orderings that satisfy the three properties when the latter is applied to a cardinal and an ordinal scale respectively.
Presented at: AMSE PhD Seminar (2026); ADRES (2026).
On Decomposable Inequality Indices for Ordinal Data
Decomposing health inequality by population subgroups into within- and between-group components is a standard tool in health economics. When health is measured on an ordinal scale, such as self-reported health, the mean is not a meaningful measure of central tendency, and the literature has replaced it with the median. I show that no non-trivial inequality index can be fully decomposable in this setting, contrary to Kobus and Miłoś (2012). I show that decomposability can be achieved only across groups sharing a common median. Under this more limited notion, inequality rankings must be representable as weighted sums of category shares, with weights that depend on the median. Requiring spreads away from the median to raise inequality then characterizes the Allison–Foster index. In the Health Survey for England (2004–2019), where all regions share the same median in every year, I show that the South contributes most to health inequality under the Allison–Foster index.
Presented at: LSE International Inequalities Institute Smoothie Seminar (2026); 18th Meeting of the Society for Social Choice and Welfare (2026).