Indian Lok Sabha Redistribution (850 Total Seats)

A special session of parliament has been convened to discuss Constitutional Amendments for implementing wowen’s reservation in parliament. The proposed amendements, among other things, seek to modify the maximum number of Lok Sabha seats and adjust inter-state distribution seats as well. In order to understand the implications of seat adjustment exercise, this analysis focuses on redistributing seats across India based on the 2011 Census population data.

Objectives:

1. Total Seats: 850 (States: 815, Union Territories: 35).
2. States Allocation: 815 seats distributed among States.
3. UTs Allocation: 35 seats distributed among Union Territories.
4. No Decrease Rule: No state or UT will receive fewer seats than its current strength.
5. Method: Proportional allocation (Largest Remainder Method) within each group (States and UTs).
6. Relative Strength: Compare the percentage of the House each entity holds before and after redistribution.

Data

For each state and union territory– current seats in Lok Sabha, population as per 2011 census and a boolean variable flagging UT status–are recorded.

import pandas as pd
import numpy as np
import json

raw_data = {
    "Uttar Pradesh": {
        "pop": 199812341,
        "current": 80,
        "is_ut": False
    },
    "Maharashtra": {
        "pop": 112374333,
        "current": 48,
        "is_ut": False
    },
    "Bihar": {
        "pop": 104099452,
        "current": 40,
        "is_ut": False
    },
    "West Bengal": {
        "pop": 91276115,
        "current": 42,
        "is_ut": False
    },
    "Madhya Pradesh": {
        "pop": 72626809,
        "current": 29,
        "is_ut": False
    },
    "Tamil Nadu": {
        "pop": 72447030,
        "current": 39,
        "is_ut": False
    },
    "Rajasthan": {
        "pop": 68548473,
        "current": 25,
        "is_ut": False
    },
    "Karnataka": {
        "pop": 61095297,
        "current": 28,
        "is_ut": False
    },
    "Gujarat": {
        "pop": 60439692,
        "current": 26,
        "is_ut": False
    },
    "Andhra Pradesh": {
        "pop": 49577103,
        "current": 25,
        "is_ut": False
    },
    "Odisha": {
        "pop": 41974218,
        "current": 21,
        "is_ut": False
    },
    "Telangana": {
        "pop": 35003674,
        "current": 17,
        "is_ut": False
    },
    "Kerala": {
        "pop": 33406061,
        "current": 20,
        "is_ut": False
    },
    "Jharkhand": {
        "pop": 32988134,
        "current": 14,
        "is_ut": False
    },
    "Assam": {
        "pop": 31205576,
        "current": 14,
        "is_ut": False
    },
    "Punjab": {
        "pop": 27743338,
        "current": 13,
        "is_ut": False
    },
    "Chhattisgarh": {
        "pop": 25545198,
        "current": 11,
        "is_ut": False
    },
    "Haryana": {
        "pop": 25351462,
        "current": 10,
        "is_ut": False
    },
    "Uttarakhand": {
        "pop": 10086292,
        "current": 5,
        "is_ut": False
    },
    "Himachal Pradesh": {
        "pop": 6864602,
        "current": 4,
        "is_ut": False
    },
    "Tripura": {
        "pop": 3673917,
        "current": 2,
        "is_ut": False
    },
    "Meghalaya": {
        "pop": 2966889,
        "current": 2,
        "is_ut": False
    },
    "Manipur": {
        "pop": 2855794,
        "current": 2,
        "is_ut": False
    },
    "Nagaland": {
        "pop": 1978502,
        "current": 1,
        "is_ut": False
    },
    "Goa": {
        "pop": 1458545,
        "current": 2,
        "is_ut": False
    },
    "Arunachal Pradesh": {
        "pop": 1383727,
        "current": 2,
        "is_ut": False
    },
    "Mizoram": {
        "pop": 1097206,
        "current": 1,
        "is_ut": False
    },
    "Sikkim": {
        "pop": 610577,
        "current": 1,
        "is_ut": False
    },
    "Delhi": {
        "pop": 16787941,
        "current": 7,
        "is_ut": True
    },
    "Jammu & Kashmir": {
        "pop": 12267013,
        "current": 5,
        "is_ut": True
    },
    "Puducherry": {
        "pop": 1247953,
        "current": 1,
        "is_ut": True
    },
    "Chandigarh": {
        "pop": 1055450,
        "current": 1,
        "is_ut": True
    },
    "Dadra & Nagar Haveli and Daman & Diu": {
        "pop": 586956,
        "current": 2,
        "is_ut": True
    },
    "Andaman & Nicobar Islands": {
        "pop": 380581,
        "current": 1,
        "is_ut": True
    },
    "Ladakh": {
        "pop": 274289,
        "current": 1,
        "is_ut": True
    },
    "Lakshadweep": {
        "pop": 64473,
        "current": 1,
        "is_ut": True
    }
}

df = pd.DataFrame.from_dict(raw_data, orient='index').reset_index()
df.columns = ['Entity', 'Population', 'Current Seats', 'is_ut']

CURRENT_TOTAL_SEATS = 543
NEW_STATE_SEATS_TOTAL = 815
NEW_UT_SEATS_TOTAL = 35
NEW_HOUSE_TOTAL = NEW_STATE_SEATS_TOTAL + NEW_UT_SEATS_TOTAL

print(f"Current Strength: {CURRENT_TOTAL_SEATS}")
print(f"Target New Strength: {NEW_HOUSE_TOTAL} (States: {NEW_STATE_SEATS_TOTAL}, UTs: {NEW_UT_SEATS_TOTAL})")

Current Strength: 543
Target New Strength: 850 (States: 815, UTs: 35)

Allocation Logic for States and UTs

At one level the seat allocation is simple: One has to calculate the population proportion as per 2011 and allocate 815 seats to states and 35 seats to union territories in the same proportion. However, a staightforward application of this logic will create two complications: resulting seats will be fractional; and seats of some states may decrease in the exercise. Both are unrealistic.

For converting floats to integers, one can use functions like floor, ceiling or round (nearest integer). Rounding off using these methods is not guaranteed to result in sum of seats being equal to 815 and 35 for states and UTs however. If we use floor for rounding off, we will be left with surplus seats. These surplus seats can be allocated to the states in the order of remainder. This is called ‘Largest Remainder Method’. We define a function for the Largest Remainder Method with the ‘No Decrease’ constraint.

def allocate_seats(sub_df, target_total):
    total_pop = sub_df['Population'].sum()
    quota = total_pop / target_total
    
    sub_df = sub_df.copy()
    sub_df['Exact Share'] = sub_df['Population'] / quota
    sub_df['Base Seats'] = sub_df['Exact Share'].apply(lambda x: max(1, int(x)))
    sub_df['Remainder'] = sub_df['Exact Share'] - sub_df['Base Seats']
    
    sub_df['New Seats'] = sub_df.apply(lambda x: max(x['Base Seats'], x['Current Seats']), axis=1)
    
    current_total = sub_df['New Seats'].sum()
    surplus = target_total - current_total
    
    if surplus > 0:
        top_remainders = sub_df.sort_values(by='Remainder', ascending=False).index[:surplus]
        sub_df.loc[top_remainders, 'New Seats'] += 1
    elif surplus < 0:
        can_reduce = sub_df[sub_df['New Seats'] > sub_df.apply(lambda x: max(x['Current Seats'], 1), axis=1)].index
        to_reduce = sub_df.loc[can_reduce].sort_values(by='Remainder').index[:abs(surplus)]
        sub_df.loc[to_reduce, 'New Seats'] -= 1
        
    return sub_df

states_df = allocate_seats(df[~df['is_ut']], NEW_STATE_SEATS_TOTAL)
uts_df = allocate_seats(df[df['is_ut']], NEW_UT_SEATS_TOTAL)

final_df = pd.concat([states_df, uts_df])
print(f"Total State Seats: {states_df['New Seats'].sum()}")
print(f"Total UT Seats: {uts_df['New Seats'].sum()}")
print(f"Total House Seats: {final_df['New Seats'].sum()}")

Total State Seats: 815
Total UT Seats: 35
Total House Seats: 850

Final Results and Relative Strength Comparison

For comparision, we define relative stregth change. Gainers and losers in this exercise are highlighted using pandas conditional formatting.

Relative Strength Change = (New Seats / 850 * 100) - (Current Seats / 543 * 100). Highlighted in green (increase) or red (decrease).

final_df['Current %'] = (final_df['Current Seats'] / CURRENT_TOTAL_SEATS * 100).round(4)
final_df['New %'] = (final_df['New Seats'] / NEW_HOUSE_TOTAL * 100).round(4)
final_df['Rel. Strength Change'] = (final_df['New %'] - final_df['Current %']).round(4)

def highlight_change(val):
    if val > 0.005:
        return 'color: green; font-weight: bold'
    elif val < -0.005:
        return 'color: red; font-weight: bold'
    return ''

display_df = final_df[['Entity', 'Population', 'Current Seats', 'New Seats', 'Current %', 'New %', 'Rel. Strength Change']]
display_df = display_df.sort_values(by=['New Seats', 'Population'], ascending=False)

styled_df = display_df.style.map(highlight_change, subset=['Rel. Strength Change'])
styled_df

	Entity	Population	Current Seats	New Seats	Current %	New %	Rel. Strength Change
0	Uttar Pradesh	199812341	80	138	14.733000	16.235300	1.502300
1	Maharashtra	112374333	48	78	8.839800	9.176500	0.336700
2	Bihar	104099452	40	72	7.366500	8.470600	1.104100
3	West Bengal	91276115	42	63	7.734800	7.411800	-0.323000
4	Madhya Pradesh	72626809	29	50	5.340700	5.882400	0.541700
5	Tamil Nadu	72447030	39	50	7.182300	5.882400	-1.299900
6	Rajasthan	68548473	25	47	4.604100	5.529400	0.925300
7	Karnataka	61095297	28	42	5.156500	4.941200	-0.215300
8	Gujarat	60439692	26	42	4.788200	4.941200	0.153000
9	Andhra Pradesh	49577103	25	34	4.604100	4.000000	-0.604100
10	Odisha	41974218	21	29	3.867400	3.411800	-0.455600
11	Telangana	35003674	17	24	3.130800	2.823500	-0.307300
12	Kerala	33406061	20	23	3.683200	2.705900	-0.977300
13	Jharkhand	32988134	14	23	2.578300	2.705900	0.127600
14	Assam	31205576	14	21	2.578300	2.470600	-0.107700
15	Punjab	27743338	13	19	2.394100	2.235300	-0.158800
16	Chhattisgarh	25545198	11	17	2.025800	2.000000	-0.025800
17	Haryana	25351462	10	17	1.841600	2.000000	0.158400
28	Delhi	16787941	7	16	1.289100	1.882400	0.593300
29	Jammu & Kashmir	12267013	5	12	0.920800	1.411800	0.491000
18	Uttarakhand	10086292	5	7	0.920800	0.823500	-0.097300
19	Himachal Pradesh	6864602	4	5	0.736600	0.588200	-0.148400
22	Manipur	2855794	2	3	0.368300	0.352900	-0.015400
20	Tripura	3673917	2	2	0.368300	0.235300	-0.133000
21	Meghalaya	2966889	2	2	0.368300	0.235300	-0.133000
24	Goa	1458545	2	2	0.368300	0.235300	-0.133000
25	Arunachal Pradesh	1383727	2	2	0.368300	0.235300	-0.133000
32	Dadra & Nagar Haveli and Daman & Diu	586956	2	2	0.368300	0.235300	-0.133000
23	Nagaland	1978502	1	1	0.184200	0.117600	-0.066600
30	Puducherry	1247953	1	1	0.184200	0.117600	-0.066600
26	Mizoram	1097206	1	1	0.184200	0.117600	-0.066600
31	Chandigarh	1055450	1	1	0.184200	0.117600	-0.066600
27	Sikkim	610577	1	1	0.184200	0.117600	-0.066600
33	Andaman & Nicobar Islands	380581	1	1	0.184200	0.117600	-0.066600
34	Ladakh	274289	1	1	0.184200	0.117600	-0.066600
35	Lakshadweep	64473	1	1	0.184200	0.117600	-0.066600

Final Diagnostics and Tests

It is never a good idea to trust your calculations without validation. So we throw in some tests here, asserting that total allocated seats are equal to 850; total allocated seats to UTs are equal to 35; percentages sum to 100: and gains and losses net out. Our estimates pass all the tests, validating the analysis.

print("### Final Diagnostics")
curr_total = final_df['Current Seats'].sum()
curr_ut_total = final_df.query('is_ut')['New Seats'].sum()
new_total = final_df['New Seats'].sum()
pct_total = final_df['New %'].sum()
rel_change_total = final_df['Rel. Strength Change'].sum()

print(f"Total Current Seats: {curr_total} (Expected: 543)")
print(f"Total New Seats (Total): {new_total} (Expected: 850)")
print(f"Total New Seats (UT): {curr_ut_total} (Expected: 35)")
print(f"Total New %: {pct_total:.2f}% (Expected: 100.00%)")
print(f"Total Relative Change: {rel_change_total:.4f} (Expected: 0.0000)")

assert curr_total == 543
assert new_total == 850
assert curr_ut_total == 35
assert abs(pct_total - 100.0) < 0.1
assert abs(rel_change_total) < 0.1

### Final Diagnostics
Total Current Seats: 543 (Expected: 543)
Total New Seats (Total): 850 (Expected: 850)
Total New Seats (UT): 35 (Expected: 35)
Total New %: 100.00% (Expected: 100.00%)
Total Relative Change: -0.0003 (Expected: 0.0000)