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For the moment let's ignore distribution models like meritocracy. Suppose a group has decided to divide their money in a certain way. What are the different formulas to measure how even or equal their division is, (irrespective of their personal needs, efforts, etc.), strictly mathematically speaking?

For instance, we could calculate an "index of inequality" as:

  • the sum of all the differences in the incomes of people,
  • Or as the sum of all differences from the average.
  • Or from the median.

In short, there are many ways such an index might be defined, which affects how big a priority it is for the group. What are the main approaches of measuring the rate of equality of allocation of resources in general?

  • "Strictly matyematically" makes no sense .... Divide the total amount of money for the number of people. – Mauro ALLEGRANZA Jan 15 '17 at 11:34
  • @MauroALLEGRANZA You're right, I'll edit it,m I jusat wanted to express I'm asking for the theories that are, indeed, subjective models of equality but models still possible to describe mathematically. – Probably Jan 15 '17 at 12:11
  • @MauroALLEGRANZA But there's one more important thing you might miss: It's not about total equality but the degrere of equality. Of course, total equality is when everybody gets the average. Though, it's not so clear for example if you compare one situation where there are three equal groups, one with 1$, one with 2$ and one with 3$ and when you compare the situation when most people get 2$, a little people get 0$ and a few people get 4$. – Probably Jan 15 '17 at 12:16
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    I think you mean to ask "what mathematical models of equality are there", or maybe even "what mathematical models of social equality are there". Is that right? I think the question is a little clearer if posed that way. – Eliran Jan 16 '17 at 10:14
  • @EliranH Yeah, thank you I've used the formulation I've been given when asking on Politics. – Probably Jan 16 '17 at 11:07
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To give a terribly unphilosophical answer informed rather by economics:

As purely mathematical and for wealth distribution only (as per OP) the Gini coefficient and normally nothing else, really.

It is the most popular inequality index.

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The work of John Rawls is probably the major effort of the twentieth century in analyzing the questions of freedom and equality. I recommend Justice as Fairness. The book is not an easy read, but Rawls lays out his arguments in detail.

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