Inequality in Death from Social Conflicts: A Gini & Kolkata indices-based Study

TL;DR

This study quantifies inequality in human deaths from conflicts and natural disasters using Gini and Kolkata indices, revealing extremely high inequality levels in man-made conflicts and their similarity to inequalities in academic citations.

Contribution

It introduces a novel application of Lorenz curve-based inequality indices to compare social inequalities in conflict-related deaths and academic citations.

Findings

High inequality indices ($g$=0.82, $k$=0.84) in conflict-related deaths.

Natural disasters show even higher inequality measures.

Man-made conflicts' inequality levels are comparable to those in academic citation distributions.

Abstract

Human deaths caused by individual man-made conflicts (e.g., wars, armed-conflicts, terrorist-attacks etc.) occur unequally across the events (conflicts) and such inequality (in deaths) have been studied here using Lorenz curve and values of the inequality indices Gini ($g$) and Kolkata ($k$) have been estimated from it. The data are taken from various well-known databases maintained by some Universities and Peace Research Institutes. The inequality measures for man-made conflicts are found to have very high values ($g$ = $0.82 ~\pm~ $0.02, $k$ = $0.84~ \pm~ $0.02), which is rarely seen in economic (income or wealth) inequality measures across the world ($g \leq 0.4$, $k \leq 0.6$; presumably because of various welfare measures). We also investigated the inequalities in human deaths from natural disasters (like earthquakes, floods, etc.). Interestingly, we observe that the social inequality measures ($g$ and $k$ values) from man-made conflicts compare well with those of academic centers (inequality in citations; found in earlier studies) of different institutions of the world, while those for natural disasters can be even higher. We discuss about the `similarity classes' of social inequality (similar higher values of $g$ and $k$ indices) for man-made competitive societies like academic institutions and man-made social conflicts, and connect our observations with that of the growing recent trend of economic inequality across the world (with rapid disappearance of welfare strategies).

Figures

Tables

Table 1. Table 1 : Dataset description of social damages (i.e. human deaths) used in our study

Disaster type	Data source	Data coverage	Time period	Dataset length	human death count
					Min.	Max.	Avg.	Total
	war CoW data (v.4.0) Sarkees and Weyman ((2016)	worldwide	1816-2007	538	0	1250000	28553	15361249
	battle UCDP data (v.18.1) encyclopedia Data Program version 18.1 ((2014)	worldwide	1989-2017	4695	25	500000	783	3674068
man-made	armed-conflict PRIO data(v.3.1) Lacina ((2009)	worldwide	1946-2008	1186	13	497500	7175	8510077
	murder (violent-crime) NCRB data Bureau	India	1967-2016	1583	0	10776	902	1427276
	terrorism GTD data Database ((2018)	worldwide	1970-2017	172109	0	1570	2-3	414537
	earthquake NCEI-NOAA data Database (a)	worldwide	1000-2018(July)	1321	1	830000	3312	4375172
natural	flood EMDAT dataDatabase (b)	worldwide	1900-2018(July)	3540	1	3700000	1965	6957472
	tsunami NCEI-NOAA data Database (c)	worldwide	1000-2018(July)	372	1	167540	1038	386275

Table 2. Table 2 : Estimated inequality (in death counts) index values for man-made conflicts (see, Table I and Fig. 2)

Type of conflicts	$g$-index	$k$-index
war	$0.83\pm$0.02	$0.85\pm$0.02
battle	$0.82\pm$0.02	$0.85\pm$0.02
armed-conflict	$0.85\pm$0.02	$0.87\pm$0.02
terrorism	$0.80\pm$0.03	$0.83\pm$0.02
murder	$0.66\pm$0.02	$0.75\pm$0.02

Table 3. Table 3 : Estimated inequality (in death counts) index values for natural disasters (see, Table I and Fig. 3)

Type of disasters	$g$-index	$k$-index
earthquake	$0.94\pm$0.02	$0.95\pm$0.02
flood	$0.98\pm$0.02	$0.98\pm$0.02
tsunami	$0.93\pm$0.02	$0.94\pm$0.02

Table 4. Table 4 : Inequality (in terms of physical damages) index values of physical damages caused by natural disasters

Data source	Data coverage	Time period	Dataset length	Damage measures				Measured in	$g$-index value	$k$-index value
				Min.	Max.	Avg.	Total
earthquake USGS data Program	worldwide	2013-2018(July)	519959	0.5	8.3	1.96	1022601	Richter magnitude	0.35	0.64
flood EMDAT dataDatabase (b)	worldwide	1900-2018(July)	1719	0	2857000	87868.28	151045575	areas affected (sq-km)	0.76	0.79
tsunami NCEI-NOAA data Database (c)	worldwide	1000-2018(July)	374	1	524.26	10.16	3803	maximum water height (m)	0.53	0.69

Table 5. Table 5 : Values of the inequality indices ( g 𝑔 g and k 𝑘 k ) for some of the academic institutions (from Ghosh et al. ( (2014 ) , see also Chatterjee et al. ( (2017 ) ; source-data taken from the Web of Science)

Inst./Univ.	Year	Index values for		Inst./Univ.	Year	Index values for
		Gini ($g$)	Kolkata ($k$)			Gini ($g$)	Kolkata ($k$)
Cambridge	1980	0.74	0.78	BHU	1980	0.68	0.76
	1990	0.74	0.78		1990	0.71	0.77
	2000	0.71	0.77		2000	0.64	0.74
	2010	0.70	0.76		2010	0.63	0.73
Harvard	1980	0.73	0.78	Calcutta	1980	0.74	0.78
	1990	0.73	0.78		1990	0.64	0.74
	2000	0.71	0.77		2000	0.68	0.74
	2010	0.69	0.76		2010	0.61	0.73
MIT	1980	0.76	0.79	Delhi	1980	0.67	0.75
	1990	0.73	0.78		1990	0.68	0.76
	2000	0.74	0.78		2000	0.68	0.76
	2010	0.69	0.76		2010	0.66	0.74
Oxford	1980	0.70	0.77	IISC	1980	0.73	0.78
	1990	0.73	0.78		1990	0.70	0.76
	2000	0.72	0.77		2000	0.67	0.75
	2010	0.71	0.76		2010	0.62	0.73
Stanford	1980	0.74	0.78	Madras	1980	0.69	0.76
	1990	0.70	0.76		1990	0.68	0.76
	2000	0.73	0.80		2000	0.64	0.73
	2010	0.70	0.76		2010	0.78	0.79
Stockholm	1980	0.70	0.76	SINP	1980	0.72	0.74
	1990	0.66	0.75		1990	0.66	0.73
	2000	0.69	0.76		2000	0.77	0.79
	2010	0.70	0.76		2010	0.71	0.76
Tokyo	1980	0.69	0.76	TIFR	1980	0.70	0.76
	1990	0.68	0.76		1990	0.73	0.77
	2000	0.70	0.76		2000	0.74	0.77
	2010	0.70	0.76		2010	0.78	0.79

Full text

I Introduction

While studying social systems, we come across various stabilized inequalities, as results of inherent social dynamics. Sociophysics Sen and Chakrabarti ((2014); Castellano et al. ((2009); Galam ((2012) attempts to study such inequalities and capture them in various models of social dynamics. Though not inevitable, death to mortal life in natural or man-made disasters seems to be a significant possibility in our life. Since ancient times, both of man-made conflicts as well as natural disasters have played their role in shaping the structure of human society. Sometimes of course the distinction between man-made disasters and natural disasters are not very clear: Malthus suggested Malthus ((1888) that (in absence of any birth control) the population grows with time in geometric progression (exponentially), while food-grain supply (cultivable land, the basic ingredient for food-grain production) grows in algebraic progression (linear in time), suggesting that famines or wars will occur almost periodically. This and similar arguments suggest that even the events like wars, armed-conflicts or in some cases the famines, may be natural and not directly man-made. We will, however, not consider such arguments and distinguish them using commonly used criteria (as given in various datasets studied here).

We study here the inequality measures (from the corresponding human death distributions) for all kinds of social conflicts (wars, violent crimes, etc.) and also the same for natural disasters (earthquakes, floods, etc.). The detailed nature of the death count distributions (fat tails in particular) in such conflicts and disasters have already been studied earlier Chatterjee and Chakrabarti ((2017). We utilized the data publicly available from various established data-sources maintained by various universities and Peace Research centers. We find, the extent of inequality (using the specific measures defined later) is much higher in social conflicts when compared with those observed for the economic inequalities (for income, wealth) in earlier decades. We find that the ‘similarity classes’ of social inequality (similar values of $g$ and $k$ indices, defined in the next section) for man-made competitive societies like academic institutions and for social conflicts are the same. We connect our observations about extreme inequalities in various social institutions and in social conflicts with that of the growing recent trend of economic inequality across the world (with rapid disappearance of welfare strategies).

II Inequality indices

Generally for measuring (income or wealth) inequality, Gini index ($g$) Gini ((1921) is used by the economists who constructs first the Lorenz curve (see Fig. 1), which gives the cumulative fraction of the wealth against the fraction of population (possessing that wealth), when they are arranged in increasing order of income or wealth. The equality line corresponds to the case when the people have equal income or wealth each. We have used the equivalent Lorenz curve (see, Fig. 1), where cumulative number of deaths (instead of wealth) are plotted against the fraction of events/conflicts (instead of population), when arranged in increasing order of size of the events or conflicts. The area between the equality line and Lorenz curve (when normalised) gives the Gini index ($g$). We will also consider the Kolkata index $k$ Ghosh et al. ((2014); Chatterjee et al. ((2015, (2017) here, which is given by the value of the $x$-coordinate of the crossing point of the diagonal perpendicular to the equality line and the Lorenz curve (see Fig. 1). It may be noted that $g$ takes values within the range 0 (representing complete equality) and 1 (representing complete inequality), while the corresponding $k$ values range from 0.5 to 1, and the values of $2k-1$ ranges from 0 to 1. In view of the fact that ($1-k$) fraction of people, papers or wars do posses, capture or cause exactly $k$ fraction of wealth, citations or deaths respectively, we give the $k$ index values in various cases considered here. Also, $k$ index corresponds to a non-trivial fixed point of the complementary (non-linear) Lorenz function $\tilde{F}(n)\equiv 1-F(n)$ (see Fig. 1): $\tilde{F}(k)=k$. It may be mentioned in this context that in  Sreenivasan ((2010), a decomposition of $g$ in terms of a quantity equal in magnitude of $k$ was attempted. There are several other social inequality measuring indices Eliazar and Sokolov ((2010); Eliazar and Cohen ((2012, (2014); Eliazar ((2015, (2016), based on the Lorenz curve properties, which we will not consider here.

III DATASET DESCRIPTION

We have studied here the statistics of human death in various man-made events or conflicts and natural disasters like earthquake etc. using the extensive and publicly available death count datasets from various universities and public research organisations for a long period of collections. Few data are found missing, and obviously get ignored in this study. The details of the used datasets are given below in Table I:

IV ANALYSIS AND ESTIMATES OF $g$ , $k$ VALUES

IV.1 For man-made conflicts

We used the human death data in various kinds of social conflicts, as recorded in various datasets e.g., CoWSarkees and Weyman ((2016), UCDPencyclopedia Data Program version 18.1 ((2014), PRIOLacina ((2009), NCRBBureau and GTDDatabase ((2018). The estimated Lorenz curves (shown in Figs. 2a, 2b, 2c) give the values of the Gini ($g$) and Kolkata ($k$) indices. These indices have quite high values (see Table II).

IV.2 For natural disasters

Analyzing the data for human death distribution in various natural disasters, as obtained from the datasets mentioned in Table I, we find the Lorenz curves (see, Fig. 3) to be even more steeply curved and the corresponding $g\simeq 0.95\simeq k$ values are even higher (see, Table III).

However, when the damages are measured in physical quantities (in Richter magnitude for earthquakes, areas affected in floods and water level heights in case of tsunamis) both of the Gini and Kolkata indices assume much lower values (see Fig. 3 and Table IV).

V Discussion & Summary

Assuming the Lorenz curve to be given by $y=x^{\alpha}$ for a positive real number $\alpha$, passing through (0,0) and (1,1) points, we get $g$ = $[\frac{1}{2}-\int_{0}^{1}x^{\alpha}\;\mathrm{d}x]/({\frac{1}{2}})=1-\frac{2}{(\alpha+1)}$ and self-consistent equation $k^{\alpha}=1-k$ (in Fig. 1, $y$ $\equiv$ $F$ and $x$ $\equiv$ $n$). This gives $g=0$ and $k=\frac{1}{2}$ for the equality line ($\alpha=1$) and $g=k=1$ for extreme inequality ($\alpha\to\infty$). In the social conflict cases studied here, such high values of inequality-index values suggest $\alpha\simeq 10$, giving $g\simeq 0.82$ and $k\simeq 0.84$ (when both $g$ and $k$ are high and close enough in magnitude, as observed). Indeed, even for the so called Pareto 80/20 law (80% wealth possessed by 20% of the population Lipovetsky ((2009)) suggesting $k=0.8$, one gets $\alpha\simeq 7$ ($[0.8]^{\alpha}=0.2$, giving $\alpha\simeq 7$) and hence $g$ = $1-\frac{1}{4}\simeq 0.75$, which also compares well with our earlier observation Ghosh et al. ((2014) for citation distribution in academic institutions ($g\simeq 0.75$ and $k\simeq 0.8$). As mentioned before, such high values of $g$ and $k$ are not usually seen for income or wealth distributions in societies (economic inequalities; see e.g., Ghosh et al. ((2014)) though, of late, these values are rapidly increasing Piketty ((2013). Human death inequality index values for natural disasters ($g\simeq 0.95\simeq k$) are even higher. Of course we found that when the social counts (of deaths) are replaced by physical quantities measuring damages in natural disasters (e.g., Richter magnitude in case of earthquakes, amount of areas affected in case of floods or maximum water level heights in case of tsunamis etc.) the inequality index values ($g\leq 0.76$ and $k\leq 0.79$; see Table IV) become somewhat lower. Fig. 4 shows the variations of the quantity $2k-1$ and $g$ for all the cases analysed use (see Table II-IV). Both $2k-1$ and $g$ have identical ranges [0,1]. These seems to be two distinct slopes of the $2k-1$ vs $g$ curves: about 0.73 (for lower $g$ range) and about 1.50 (for higher $g$ range). It may be mentioned that the mapping of Lorenz curve as the quadrant of an unit circle, gives Chatterjee et al. ((2017) $(2k-1)/g\simeq 0.73$, which compares well with the observed initial slope value in Fig. 4. It may be interesting to note that a recent data analysis study on the relationship between Gini index ($g$) and Kolkata index ($k$) has been reported Il’inskii and Mierzwa ((2019) in the context of economic inequality in the bitcoin market.

In summary, we find deaths from social conflicts are quite inequally distributed. From Table II, we find death inequality measures ($g\simeq 0.82$ and $k\simeq 0.84$) for man-made social conflicts, while from Table III those for natural disasters are $g\simeq 0.95$ and $k\simeq 0.96$. As already mentioned earlier, the citations of the papers produced by various universities or institutes of the world, can be viewed as the wealth created by the respective institutions and these wealths are also found to be quite unequally distributed across the contributions or papers. Our earlier study in Ghosh et al. ((2014) (see Table V in the Appendix) suggested high level of inequality across the institutions: $g\simeq 0.75$, $k\simeq 0.80$. As the institutions encourage competitiveness (and do not always take care for those who may fall behind or become unsuccessful), the social inequality is very high. Such high values of inequality indices had however not been seen in socio-economic systems earlier ($g\leq 0.4$, $k\leq 0.6$ Ghosh et al. ((2014)). These may be due the various welfare measures usually taken by various governments. Also, some entropic considerations suggest Venkatasubramanian ((2017) that some amount of inequality may not be unfair in capitalistic societies. Recently the economic inequality has started growing rapidly (since 1950’s; see e.g., Piketty ((2013)of Family Income Gini Index ) and index values for both $g$ and $k$ are increasing. This may be because of the fast disappearance of social welfare measures across the world. Our study here indicates a ‘natural’ tendency towards extreme inequality ($g\simeq 0.90\simeq k$) in our societies, unless some appropriate welfare measures are taken.

Acknowledgement: We are thankful to Arnab Chatterjee, Asim Ghosh, Manipushpak Mitra, Sudip Mukherjee for many useful inputs and discussions. AS acknowledges kind hospitality at Saha Institute of Nuclear Physics, Kolkata and BKC acknowledges JC Bose Fellowship (DST) for support.

APPENDIX