1. Model of Power Distribution
Gourav Kumar Vani

2. Rhetoric that is resonating in every society from time in memorial
Rich Becoming Richer day by day at the expense of poor who is becoming poorer day by day.
Rich people use their money to control the power in the country and make the policies and regulations in their favour leading to increase in inequality in society.

3. All the things are centred around Power. So what decides your power?
Lets assume certain things about what decides power of a person/institution/group, before we proceed further
Basic idea power is partially a function of no. of people under your command.
𝑃𝑜𝑤𝑒𝑟=𝑓 𝑛𝑜. 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑢𝑛𝑑𝑒𝑟 𝑐𝑜𝑚𝑚𝑎𝑛𝑑,….

4. All the things are centred around Power. So what decides your power?
For example is that if you can control 10 people then it shows you have some amount of power over those ten and if you can control 100 then your power increases and continue to increase as you command a control over many and many more.
Hence it is the no. of people you control that shows your power.

5. All the things are centred around Power. So what decides your power?
To hold power money is needed to control the subjects or to keep the subjects engaged.
In past it was feudalism and dictatorships which required money to maintain army to suppress subjects.

6. All the things are centred around Power. So what decides your power?
But we are in modern time where democracy prevails on vast majority of countries and countries are more focused on technology, fuelled by elite’s funding them.
Ownership and/or control of TV channel, search engines allows elites to control subjects by keeping people engaged with television and computers.

7. All the things are centred around Power. So what decides your power?
For example, all kinds of propaganda can be channelled to the mass of subjects worldwide with help of mass media.
Actually political parties are in existence for two reasons
One is that people unit by the ideology of the parties thereby making it a more powerful way to contest elections against the others who either have no ideology or have different and/or opposite ideology.

8. All the things are centred around Power. So what decides your power?
Transaction cost is the second reason why political parties are existing.
Since political parties provide a cost effective platform to contest election with greater power than would be contesting independently.

9. All the things are centred around Power. So what decides your power?
That’s why in contemporary world we see more people contesting elections under the aegis and banner of political parties.
But if you see the candidates who contest from political parties then you find most of them rich enough to fund themselves.
It is rare to see a person belonging to poor family contesting election. Even share of candidates from middle class families is very less.

10. All the things are centred around Power. So what decides your power?
Poor people can’t make it to assembly on their own because hardly few are ready to fund them.
But rich people (the elite) can fund the people to go to assembly and work on behalf of them or else the rich people can themselves stand in election to get elected to assembly.

11. All the things are centred around Power. So what decides your power?
Even if none of the candidate funded by rich people make it to assembly then rich people can buy the favour of those assembly members in exchange for money.

12. Modelling the Power of Elite and Rest
𝝁= 𝟏−𝒏 𝑾 𝒓 𝒈 𝜶 𝑫 ; 𝜷= 𝑾 𝒑 𝟏−𝒈 𝟏−𝜶 𝑫 𝒏
𝑾 𝒑 =𝐓𝐨𝐭𝐚𝐥 𝐰𝐞𝐚𝐥𝐭𝐡 𝐨𝐟 𝐫𝐞𝐬𝐭 𝐨𝐟 𝐭𝐡𝐞 𝐩𝐨𝐩𝐮𝐥𝐚𝐭𝐢𝐨𝐧𝐬 𝐍𝐨𝐧 𝑬𝒍𝒊𝒕𝒆
𝝁=𝑷𝒐𝒘𝒆𝒓 𝒐𝒇 𝑬𝒍𝒊𝒕𝒆
𝜷=𝑷𝒐𝒘𝒆𝒓 𝒐𝒇 𝒕𝒉𝒆 𝑹𝒆𝒔𝒕
𝒏=Population of Elites as % of National Population
𝑾 𝒓 =𝑻𝒐𝒕𝒂𝒍 𝑾𝒆𝒂𝒍𝒕𝒉 𝒐𝒇 𝑬𝒍𝒊𝒕𝒆𝒔 𝒂𝒔 % 𝒐𝒇 𝑻𝒐𝒕𝒂𝒍 𝑾𝒆𝒂𝒍𝒕𝒉
𝒈= Gini Coefficient
𝜶= 𝐸𝑙𝑖𝑡𝑒′ 𝑠 M𝑒𝑚𝑏𝑒𝑟𝑠ℎ𝑖𝑝 𝑖𝑛 Constitutional A𝑠𝑠𝑒𝑚𝑏𝑙𝑦 𝑎𝑠 % 𝑜𝑓 T𝑜𝑡𝑎𝑙 S𝑖𝑧𝑒 𝑜𝑓 A𝑠𝑠𝑒𝑚𝑏𝑙𝑦 𝑖𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔 𝑡ℎ𝑒 Members Working in Favour of Elite.
D=Dummy Variable for Democracy,
D=1, if state is democratic and
D=0, if state is autocratic.

13. Consider a Utopian Society.
All persons have equal income so 𝑔=0.
Also no elite rules society so 𝛼=0 and also 𝐷=1 because Utopian societies are expected to be democratic.
Then for any value of 𝑊 𝑟 and 𝑛 we get 𝜇=0 and also 𝛽≠0.
This is because such societies are not run based on economic principles but on religious principles.
Thus each individual has some power but not against the institution of “Religion”.

14. Consider a Communist Country
Let there be a “Central Planning Authority” (CPC) which decides everything from food, cloth, time schedule (including even hours of sleep) and also family matters like size of family, etc.
So there is no choice even literally. Hence Gini coefficient can be taken as zero.

15. Consider a Communist Country
Regarding wealth, since all wealth belongs to nation and CPC is the care taker of the National Wealth. So 𝑊 𝑟 =1 𝑎𝑛𝑑 𝑊 𝑝 =0.
Since the nation has no democratic rule so 𝐷=0.
Since CPC is the only powerful body that exists so 𝑛=𝑜. CPC itself act as elite.
Hence for such countries we get 𝜇=1, 𝛽=0.
So CPC has complete power and all the people are powerless against the ruling of CPC.