1 Methodology

1.1 Notation

Symbol Meaning
\(i\) candidate / party index
\(k\) constituency index
\(\text{share}_{ik}\) vote share of candidate \(i\) in constituency \(k\)
\(\bar{\text{share}}_i\) candidate \(i\)’s vote-weighted average share (national / state-wide)
\(N\) number of candidates / parties in the election-year

1.2 Formulas

Election Polarization (EP) — Within-Antagonism (territorial sorting):

\[EP_k = \sum_i \frac{|\text{share}_{ik} - \bar{\text{share}}_i|}{N-1}\]

Election Competitiveness (EC) — Between-Antagonism (within-constituency closeness):

\[EC_k = \sum_i \sum_j \frac{1 - |\text{share}_{ik} - \text{share}_{jk}|}{N(N-1)}\]

Both are bounded \([0,\, 1]\). Higher EP = more sorted strongholds. Higher EC = tighter races.

1.3 Key Methodological Fixes

Two important corrections are applied relative to naive implementations:

Fix 1 — Aggregate to party level for \(\bar{\text{share}}_i\): Original candidate-level benchmarks produce misleading EP because ~97% of candidates contest only one seat, making their national share ≈ 0. The correct approach pools all votes for party \(X\) nationally to compute \(\bar{\text{share}}_{X}\).

Fix 2 — Treat IND candidates as unique individuals: “IND” in the data represents thousands of unrelated people. Aggregating them creates a spurious national IND benchmark. Each IND is assigned a unique tag so their deviation = 0 (they have no national identity to deviate from), while still counting toward \(N\) for the EC calculation.

2 Data Sources

  • Lok Sabha (1962–2019): All_States_GE.csv
  • Lok Sabha (2024): merged_cand7724.csv
  • State Assembly (1961–2026): tcpd_merged.csv

3 Core Computation Functions

4 Part 1: Lok Sabha & State Assembly Violin Plots

4.1 Load & Prepare Data

4.2 Compute EP & EC

4.3 Bin State Assembly into 5-Year Intervals

4.4 Theme & Plot Helper

4.5 Figure A — Lok Sabha EP

Lok Sabha Election Polarization (EP), 1962–2024

Lok Sabha Election Polarization (EP), 1962–2024

4.6 Figure B — Lok Sabha EC

Lok Sabha Election Competitiveness (EC), 1962–2024

Lok Sabha Election Competitiveness (EC), 1962–2024

4.7 Figure C — State Assembly EP (5-Year Intervals)

State Assembly Election Polarization (EP), 1962–2026

State Assembly Election Polarization (EP), 1962–2026

4.8 Figure D — State Assembly EC (5-Year Intervals)

State Assembly Election Competitiveness (EC), 1962–2026

State Assembly Election Competitiveness (EC), 1962–2026

4.9 Three-Period Analysis — State Assembly

State Assembly EP by Three-Period Regime

State Assembly EP by Three-Period Regime

State Assembly EC by Three-Period Regime

State Assembly EC by Three-Period Regime

4.10 Three-Period Analysis — Lok Sabha

Lok Sabha EP by Three-Period Regime

Lok Sabha EP by Three-Period Regime

Lok Sabha EC by Three-Period Regime

Lok Sabha EC by Three-Period Regime

5 Part 2: Multi-State Assembly Analysis (Post-2009)

5.1 Load & Filter Data

5.2 Compute State-Level Party Benchmarks

5.3 State Labels & Region Mapping

5.4 State-Level Violin Plots

6 Part 3: EP & EC Predictor Analysis

6.1 Load & Prepare Data

6.2 Compute EP & EC

6.3 Build Predictors

6.4 Global Tertile Classification

6.5 Tertile Threshold Summary Table

Global Tertile Thresholds
Low = below 33rd pctile | High = above 67th pctile
Level Metric Low / Medium boundary Medium / High boundary
AC (Assembly) EP 0.061 0.095
AC (Assembly) EC 0.835 0.880
PC (Lok Sabha) EP 0.044 0.074
PC (Lok Sabha) EC 0.862 0.897

6.6 Summary Tables by Tertile

6.6.1 AC Level — EP Tertile

AC Level — Mean Predictors by EP Tertile
19 states, pooled post-2009 elections
EP Tertile N Turnout (mean) N Candidates (mean) Margin % (mean) Win Share % (mean) Electorate (mean)
Low EP 4066 65.3 16.2 11.8 43.1 263,151
Medium EP 4065 66.4 11.3 12.3 45.1 246,758
High EP 4066 74.4 8.0 13.1 48.3 220,089

6.6.2 AC Level — EC Tertile

AC Level — Mean Predictors by EC Tertile
19 states, pooled post-2009 elections
EC Tertile N Turnout (mean) N Candidates (mean) Margin % (mean) Electorate (mean)
Low EC 4066 73.7 7.0 14.0 219,847
Medium EC 4065 67.2 11.2 12.1 245,466
High EC 4066 65.0 17.2 11.2 264,744

6.6.3 PC Level — EP Tertile

PC Level — Mean Predictors by EP Tertile
Lok Sabha 2009–2024
EP Tertile N Turnout (mean) N Candidates (mean) Margin % (mean) Win Share % (mean) Electorate (mean)
Low EP 728 61.8 20.4 15.4 48.8 1,633,682
Medium EP 727 64.0 14.6 14.1 48.3 1,632,605
High EP 728 70.1 11.0 12.6 48.5 1,486,571

6.7 Regressions

6.7.1 AC Level — EP (with State FE)

OLS: EP ~ Predictors | AC Level (State FE) | R² = 0.57 | N = 12106
Term Estimate Std. Error t-stat p-value Sig
(Intercept) 0.3731 0.0252 14.8031 0.0000 ***
Turnout 0.0000 0.0000 −1.9023 0.0572 .
N_Cand −0.0054 0.0001 −67.1295 0.0000 ***
Margin_Pct −0.0002 0.0000 −3.8269 0.0001 ***
Winner_VoteShare 0.0006 0.0001 10.5922 0.0000 ***
log(Electorate) −0.0186 0.0020 −9.0894 0.0000 ***

6.7.2 AC Level — EC (with State FE)

OLS: EC ~ Predictors | AC Level (State FE) | R² = 0.791 | N = 12106
Term Estimate Std. Error t-stat p-value Sig
(Intercept) 0.7956 0.0168 47.3161 0.0000 ***
Turnout 0.0003 0.0000 19.7390 0.0000 ***
N_Cand 0.0076 0.0001 141.8516 0.0000 ***
Margin_Pct 0.0004 0.0000 13.5717 0.0000 ***
Winner_VoteShare −0.0014 0.0000 −35.3328 0.0000 ***
log(Electorate) 0.0008 0.0014 0.5895 0.5555

6.7.3 PC Level — EP (with State FE)

OLS: EP ~ Predictors | PC Level (State FE) | R² = 0.522 | N = 2183
Term Estimate Std. Error t-stat p-value Sig
(Intercept) 0.2308 0.0501 4.6053 0.0000 ***
Turnout 0.0001 0.0001 1.2829 0.1997
N_Cand −0.0019 0.0001 −19.4648 0.0000 ***
Margin_Pct −0.0006 0.0001 −6.5505 0.0000 ***
Winner_VoteShare 0.0012 0.0001 8.5525 0.0000 ***
log(Electorate) −0.0179 0.0039 −4.5714 0.0000 ***

6.7.4 PC Level — EC (with State FE)

OLS: EC ~ Predictors | PC Level (State FE) | R² = 0.731 | N = 2183
Term Estimate Std. Error t-stat p-value Sig
(Intercept) 0.6999 0.0428 16.3416 0.0000 ***
Turnout 0.0000 0.0001 0.5712 0.5680
N_Cand 0.0039 0.0001 45.3124 0.0000 ***
Margin_Pct 0.0011 0.0001 12.7229 0.0000 ***
Winner_VoteShare −0.0021 0.0001 −17.3726 0.0000 ***
log(Electorate) 0.0169 0.0033 5.0653 0.0000 ***

6.8 State-by-State Coefficients Table

State-by-State Regression Coefficients
Estimate with significance: * p<0.05 | ** p<0.01 | *** p<0.001
State Turnout (%) No. of candidates Winner margin (%) Winner vote share (%) Electorate size (log)
EP
Andhra_Pradesh -1e-04* -0.0063*** -2e-04* 0.001*** 0.0121*
Assam 7e-04 -0.0148*** 2e-04 0.0017** 0.0344*
Bihar -2e-04*** -0.0045*** 1e-04 1e-04 -0.028***
Chhattisgarh -2e-04* -0.0029*** -1e-04 4e-04** -0.0155***
Delhi -8e-04*** -0.0071*** -8e-04*** 0.0021*** -0.0027
Gujarat 4e-04* -0.0067*** 1e-04 2e-04 -0.0102
Haryana 4e-04** -0.0033*** 0 5e-04** -0.0389***
Jharkhand 0 -0.003*** 2e-04. -2e-04. -0.0042
Karnataka 2e-04** -0.0038*** 1e-04 1e-04 -0.0207***
Kerala 0.0028*** -0.0185*** -0.002*** 0.0042*** -0.023
Madhya_Pradesh -1e-04 -0.0043*** -2e-04* 3e-04** 0.0053
Maharashtra 3e-04*** -0.0055*** 1e-04 1e-04 -0.0096*
Odisha -3e-04. -0.0099*** -3e-04. 0.0011*** 0.0027
Punjab 7e-04*** -0.0086*** -4e-04* 9e-04*** 0.0185*
Rajasthan 1e-04 -0.0048*** -1e-04 3e-04** 0.0094*
Tamil_Nadu 0.0016*** -0.0035*** 7e-04*** -9e-04*** -0.0404***
Telangana 1e-04 -0.0027*** -4e-04** 0.0012*** -0.0033
Uttar_Pradesh -2e-04. -0.0039*** -5e-04*** 7e-04*** -0.0169***
West_Bengal 0.0029*** -0.0174*** -0.0021*** 0.0048*** -0.1576***
EC
Andhra_Pradesh 2e-04*** 0.0068*** 3e-04*** -0.001*** 0.0036
Assam 1e-04 0.0145*** 0.0013*** -0.0039*** -0.0115
Bihar 7e-04*** 0.0063*** 5e-04*** -0.0012*** -0.002
Chhattisgarh 0 0.006*** 9e-04*** -0.0021*** 0.0132*
Delhi 7e-04*** 0.0106*** 3e-04* -0.0015*** 0.0073*
Gujarat -6e-04** 0.0109*** 7e-04*** -0.0025*** 0.0129.
Haryana -1e-04 0.006*** 5e-04*** -0.0014*** 0.0159***
Jharkhand 4e-04*** 0.0047*** 2e-04* -9e-04*** -0.006*
Karnataka 2e-04* 0.0081*** 7e-04*** -0.0016*** 0.0159***
Kerala -4e-04** 0.0174*** 0.0012*** -0.0034*** 0.0234***
Madhya_Pradesh 1e-04 0.0081*** 6e-04*** -0.0017*** -0.0104.
Maharashtra -3e-04*** 0.0073*** -3e-04*** -6e-04*** -0.011**
Odisha 1e-04 0.0119*** 1e-04 -0.001*** -0.0485***
Punjab 0 0.0105*** 0.0014*** -0.0027*** 0.0018
Rajasthan -2e-04 0.0088*** 9e-04*** -0.0024*** -0.0142*
Tamil_Nadu -3e-04** 0.0052*** 3e-04* -0.0013*** 0.0283***
Telangana -1e-04 0.004*** 2e-04 -5e-04* -0.0033
Uttar_Pradesh 0 0.0061*** 4e-04*** -0.0011*** 0.0043
West_Bengal -7e-04*** 0.0155*** 0.0016*** -0.0039*** 0.0298***

6.9 Heatmaps

Share of High-EP and High-EC constituencies by state and election year

Share of High-EP and High-EC constituencies by state and election year

Share of High-EP and High-EC constituencies by state and election year

Share of High-EP and High-EC constituencies by state and election year

6.10 EP × EC Tertile Grid

EP × EC 3×3 tertile grid for AC and PC levels

EP × EC 3×3 tertile grid for AC and PC levels

7 How EP is Different from ER and GP

EP (Election Polarization in this paper) asks: “How much are parties’ voters separated across space?”

For EP, you need party vote shares in each constituency:

  • If a party gets about the same share everywhere, EP for that party is low.
  • If a party has strongholds and deserts (very high in some constituencies, very low in others), EP for that party is high.
  • EP is the sum of that “unevenness across places” over all parties.

So:

  • ER and GP only look at overall party vote shares — unchanged if you shuffle constituencies around while keeping party totals the same.
  • EP looks at how those shares are distributed in space — changes a lot if you move a party’s support from being evenly spread to being concentrated in a few regions.