|**Table 1.1. Use of Poverty and Welfare**|**Measures in Ac**<br>|**ademic, Policy, and Public**<br>|**Discourse**<br>|
|---|---|---|---|
||**Academic Use**|**Policy Use**|**Public Discourse**|
||_EconLit*_|_Multilateral Development_<br>_Banks at nlp4dev.org* _|_Google Ngram**_|
|**Poverty Measures**||||
|Poverty Rate OR Poverty Headcount ***|40832|26730|40.49|
|Poverty Gap|4438|4609|6.84|
|Squared Poverty Gap|473|681|0.32|
|Watts Index|47|52|0.09|
|**Welfare Measures**||||
|Average income|61493|15492|36.11|
|Atkinson Index|744|122|0.49|
|Sen Index|258|70|0.12|

**Notes** : * Number of documents. ** 1 million times fraction of corpus in 2019. *** Search results in last column for “poverty rate” only as Ngram viewer does not support Boolean search. Search results retrieved March 22-24, 2023.

One plausible reason for the limited uptake of distribution sensitive measures is that they are difficult to explain in non-technical terms. For example, it is challenging to define the Atkinson index as anything other than a constant elasticity of substitution aggregate of individual incomes. Compounding the problem, distribution sensitive measures also often have non-intuitive units. For example, the squared poverty gap is measured in squared percent deviations from the poverty line, while the Watts poverty index is measured in log-point differences from the poverty line that cannot easily be interpreted as percent differences unless they are small. While these complications of interpretation and units are of little concern to mathematically minded users, they represent only a small proportion of the audience for welfare measures. For the wider audience of policymakers and the public, “average income in dollars” or “the number of poor people” are far more understandable, and therefore far more effective in influencing policy and public opinion despite their shortcomings. This dilemma is well-summarized by the succinct remark in Watts (1969) that the headcount has “ _little but its simplicity to recommend it.”_ To address this problem, we propose a new distribution sensitive welfare index with a simple mathematical formulation and intuitive units. Our basic measure, described more formally in Section 2.1, is the average across all individuals of z/yi, where yi is the income of individual i and z is a reference income level. As an average, its formulation is simple to describe. Moreover, the average has very intuitive units. Each term in the average is the factor by which the income of the corresponding individual needs to be multiplied to attain the reference level of income, and the index simply is _the average factor by which individual incomes need to be multiplied to reach the reference level of income_ .

In addition to being extremely simple to explain, this measure has several desirable properties. In Section 2.3, we show that it satisfies all three definitions of distribution sensitivity in the literature: Pigou-Dalton sensitivity, transfer sensitivity, and growth sensitivity. In addition, the new index is subgroup decomposable with population weights, which means for example that its value at the world level is simply a population-weighted average of its value in each country in 2