Editing Gini coefficient (section)

===Mathematical limitations===
Gini has some mathematical limitations as well. It is not additive and different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets.

{| class="wikitable" style="float: right; margin-left:1em;"
|+ Table A. Different income distributions with the same Gini index<ref name="fao gini"/>
|-
! style=max-width:4em | Household group !! style=max-width:5em | Country A annual income ($) !! style=max-width:5em | Country B annual income ($)
|-
| 1 || 20,000 || 9,000
|-
| 2 || 30,000 || 40,000
|-
| 3 || 40,000 || 48,000
|-
| 4 || 50,000 || 48,000
|-
| 5 || 60,000 || 55,000
|-
| Total income || $200,000 || $200,000
|-
| Country's Gini || '''0.2''' || '''0.2'''
|}

Even when the total income of a population is the same, in certain situations two countries with different income distributions can have the same Gini index (e.g. cases when income Lorenz Curves cross).<ref name="fao gini"/> Table A illustrates one such situation. Both countries have a Gini coefficient of 0.2, but the average income distributions for household groups are different. As another example, in a population where the lowest 50% of individuals have no income, and the other 50% have equal income, the Gini coefficient is 0.5; whereas for another population where the lowest 75% of people have 25% of income and the top 25% have 75% of the income, the Gini index is also 0.5. Economies with similar incomes and Gini coefficients can have very different income distributions. Bellù and Liberati claim that ranking income inequality between two populations is not always possible based on their Gini indices.<ref name=Maio2007>{{cite journal|title=Income inequality measures|first=Fernando G.|last=De Maio|journal=Journal of Epidemiology and Community Health|year=2007|volume=61|issue=10|pages=849–852|doi=10.1136/jech.2006.052969|pmid=17873219|pmc=2652960}}</ref> Similarly, computational social scientist Fabian Stephany illustrates that income inequality within the population, e.g., in specific socioeconomic groups of same age and education, also remains undetected by conventional Gini indices.<ref>{{Cite journal |last=Stephany |first=Fabian |date=2017-12-01 |title=Who are Your Joneses? Socio-Specific Income Inequality and Trust |url=https://doi.org/10.1007/s11205-016-1460-9 |journal=Social Indicators Research |language=en |volume=134 |issue=3 |pages=877–898 |doi=10.1007/s11205-016-1460-9 |issn=1573-0921 |pmc=5684274 |pmid=29187771}}</ref>