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Shannon-Theil-Rawls: Information Theory, Inequality and the Veil of Ignorance

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  • Ravi Kanbur

    (Cornell University)

Abstract

This paper shows the power of applying Shannon’s (1948) information theory perspective to inequality measurement by considering the thought experiment of drawing a dollar at random from an income distribution and asking who the dollar came from. The surprise at being told who the dollar came from, and the task of designing a set of questions with yes/no answers which will get us to the person, are two sides of the same coin but with interesting interpretations. The Theil index of inequality, which Theil (1967) himself derived with reference to information theory and entropy but did not then explore further, is shown to have interpretations beyond its simple Daltonian properties such as satisfying the principle of transfers or being sub-group decomposable. It can be interpreted as a statistical test of the hypothesis of fairness, and as a quantitative measure of the difficulty of achieving Rawls’s (1971) original position behind the veil of ignorance.

Suggested Citation

  • Ravi Kanbur, 2024. "Shannon-Theil-Rawls: Information Theory, Inequality and the Veil of Ignorance," Working Papers 669, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2024-669
    as

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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2024-669.pdf
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    References listed on IDEAS

    as
    1. Cowell, Frank, 2003. "Theil, inequality and the structure of income distribution," LSE Research Online Documents on Economics 2288, London School of Economics and Political Science, LSE Library.
    2. Ravi Kanbur & Andy Snell, 2019. "Inequality Indices as Tests of Fairness," The Economic Journal, Royal Economic Society, vol. 129(621), pages 2216-2239.
    3. Paulo L. dos Santos & Noé Wiener, 2020. "By the content of their character? Discrimination, social identity, and observed distributions of income," The Journal of Mathematical Sociology, Taylor & Francis Journals, vol. 44(1), pages 12-41, January.
    4. Paul Hufe & Ravi Kanbur & Andreas Peichlifo, 2022. "Measuring Unfair Inequality: Reconciling Equality of Opportunity and Freedom from Poverty [Multidimensional Poverty and Inequality]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3345-3380.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Information Theory; Inequality; Veil of Ignorance;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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