The principles of inequality measurement are a set of fundamental axioms that a measure of inequality should ideally satisfy to be considered ethically sound and practically useful. These principles ensure that the measure reflects genuine differences in distribution and is not unduly influenced by irrelevant factors. The four main principles are:
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Anonymity Principle: The inequality measure should be independent of any specific characteristics of the individuals within the distribution (e.g., names, gender, race). It treats all individuals equally, focusing solely on the distribution of the variable of interest. In simpler terms, swapping the incomes of two people should not change the measured level of inequality.
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Scale Independence Principle (or Homogeneity): The inequality measure should be independent of the overall size of the variable being measured (e.g., income, wealth). If all incomes in a distribution are multiplied by a constant factor (e.g., doubled due to inflation), the inequality measure should remain unchanged. This ensures that inequality measures relative differences, not absolute differences. For example, if everyone's income doubles, inequality remains the same.
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Population Independence Principle: The inequality measure should be independent of the size of the population. If the population is replicated (e.g., by merging two identical distributions), the inequality measure should remain unchanged. This ensures that inequality measures are comparable across different populations sizes. For instance, merging two identical populations should not alter the measured inequality.
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Transfer Principle (or Pigou-Dalton Principle): This is the most crucial principle. It states that a transfer of income from a richer person to a poorer person, without reversing their relative positions, should reduce the measured inequality. This principle captures the essence of what is meant by inequality: a more equitable distribution is considered less unequal. For example, if person A gives $1 to person B, and A was richer than B before the transfer, inequality should decrease.
In summary, these four principles provide a framework for evaluating and selecting appropriate inequality measures. A good inequality measure should ideally satisfy all these principles to provide a robust and ethically defensible assessment of inequality in a given distribution.
