# Inequality (fairness measures) in Julia

**URL:** <https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732>\
**Category:** Optimization (Mathematical)\
**Tags:** economics\
**Created:** [January 27, 2017, 10:19pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732 "2017-01-27T22:19:03Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![gavelasq](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@gavelasq](https://discourse.julialang.org/u/gavelasq)\
**Post date:** [January 27, 2017, 10:19pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/1 "2017-01-27T22:19:03Z")

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Is there a Julia package that calculates inequality measures like Gini Index, Theil Index, Atkinson Index, Hoover Index?

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**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [January 27, 2017, 10:32pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/2 "2017-01-27T22:32:25Z")

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I don’t know but I’d be totally up for writing one together! This is part of my PhD topic. P.S. Atkinson is the best obviously

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**Author:** ![gavelasq](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@gavelasq](https://discourse.julialang.org/u/gavelasq)\
**Post date:** [January 27, 2017, 10:54pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/3 "2017-01-27T22:54:57Z")

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I am planning to use the inequality index as a constraint in a linear problem. I have not quite looked closely at Atkinson Index so could you tell me if the Atkinson index can be used in an LP?

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**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [January 27, 2017, 10:56pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/4 "2017-01-27T22:56:24Z")

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I’ve never done linear programming, sorry. I’m more interested in the ethics side of things.

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**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [January 27, 2017, 11:02pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/5 "2017-01-27T23:02:38Z")

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However, if you’re doing some sort of optimization, I’d just maximize social welfare and skip the inequality measure. So if you’re working with income, just maximize total income \* (1 - the atkinson index for income). You can do a bit of cancellation to simplify this expression.

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**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [January 27, 2017, 11:06pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/6 "2017-01-27T23:06:49Z")

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P.P.S. don’t pick one for the risk aversion parameter if you’re going to use the Atkinson index. Usually you’ll want a higher number; look for an estimate of mean RELATIVE risk aversion (there’s a ton of studies on this).

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**Author:** ![ZacLN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/zacln/32/2748_2.png) [@ZacLN](https://discourse.julialang.org/u/ZacLN)\
**Post date:** [January 27, 2017, 11:27pm UTC](https://discourse.julialang.org/t/inequality-fairness-measures-in-julia/1732/7 "2017-01-27T23:27:03Z")

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I have a bunch of these written up for Gini, Theil, Atkinson and a few other common measures including functions to calculate them from common distribution families, mixture models and kernel density estimates. I’ll hunt them out and post them in a gist

EDIT : [code](https://gist.github.com/ZacLN/fd34052b6a17ea9274f1e92cf82d6472)