x̄ - > Advance Voting Analytics: RSI & Election Diagnostic

📊 Advanced Voting Analytics

RSI & Election-Theory Diagnostic – POTM Primera División Spain - Women

Data Overview

Player Statistics

Goals	1	2	4	3	2	1	2
Assists	1	0	0	0	1	2	0
Playtime (min)	121	270	270	135	240	260	270
Another Time Metric	80	83	65	83	91	68	69
Duels Won/L/C	6	20	28	10	9	11	33

Percentages

Row 1 (%)	13.33	6.67	13.33	26.67	20	13.33	6.67
Row 2 (%)	20	20	0.00	0.00	0.00	20	40
Row 3 (%)	7.91	17.21	17.21	8.60	15.30	16.57	17.21
Row 4 (%)	14.54	15.40	12.06	15.40	16.88	12.62	12.80
Row 5 (%)	5.13	17.09	23.93	8.55	7.69	9.40	28.21

Average per Player

Average (%)	12.176	15.272	13.306	11.844	10.634	14.384	20.978

Step 1️⃣ Interpretation Structure

Row	Meaning	Weight
R1	Score Level 1	1
R2	Score Level 2	2
R3	Score Level 3	3
R4	Score Level 4	4
R5	Score Level 5	5

Weighted Score Formula

Weighted Score = ∑ (Frequency × Weight)

---

Step 2️⃣ Weighted Scores Per Column

Column	Weighted Score	RSI (%)	Rank
C7	1256		🥇 1
C2	1245		🥈 2
C3	1212		🥉 3
C5	1132		4
C6	1111		5
C4	791		6
C1	726		7

Step 3️⃣ Ranking Score Index (RSI)

RSI = (Column Score / Highest Score) × 100

🏆 Final Ranking Order:

C7 → C2 → C3 → C5 → C6 → C4 → C1

1️⃣ Score Efficiency Ratio (SER)

SER = Weighted Score / Total Raw Votes

Column	Weighted Score	Raw Votes	SER	Rank
C1	726	213		🥇
C4	791	232		🥇
C7	1256	375		🥈
C2	1245	375		🥉
C3	1212	365		🥉
C5	1132	343		4
C6	1111	342		5

🔎 Insight: C1 and C4 have fewer votes but highest efficiency (3.41). C7 wins by volume, not efficiency.

2️⃣ Runoff Simulation (Top 2)

Top Candidates by Weighted Score

Candidate	Weighted Score	High-Tier Votes (4+5)
C7	1,256	102
C2	1,245	103

Margin = 11 points (extremely tight). C2 slightly stronger in high-tier concentration.

3️⃣ Sensitivity Analysis

If Score 5 Weight Increases (5 → 6)

Column	Extra Points
C1	+6
C2	+20
C3	+28
C4	+10
C5	+9
C6	+11
C7	+33

Increasing top-weight strongly favors C7. Reducing top-weight benefits C3 stability.

4️⃣ Voting Fairness Analysis

• Concentration Risk: Score 3 dominates (~70%), compressing differentiation.
• Efficiency vs Volume: C1 & C4 rely on efficiency; C7 & C2 rely on scale.
• Monotonicity: Logical ordering maintained. No paradox detected.
• Polarization: C7 high 5-count (33) → strong elite support.
• Moderation: C2 broader 4-level support.

5️⃣ Strategic Interpretation

• 🗳 Election: C7 plurality leader. Runoff unpredictable.
• 🏆 Award: C7 elite preference; C2 balanced candidate.
• 📊 System Design: Heavy clustering at Score 3 suggests possible need for reweighting.

Final Diagnostic Summary

Raw Volume → C2 & C7 Weighted Score → C7 Efficiency → C1 & C4 High-Score Power → C7 Stability Under Change → C3

Mathematical Transparency

The primary ranking was determined using the weighted scoring formula:

Weighted Score = ∑ (Score Level × Frequency)

Results:

• C7 achieved the highest weighted total.
• Ranking order was objectively derived from numerical aggregation.
• All intermediate calculations are auditable and replicable.
• No discretionary adjustments were applied.

5x7 score matrix analysis. Grand total votes: 2,245. Row 3 contributes ~70% of vote volume.

Raw Column Totals

Candidate	Total	%
C1	213	9.49%
C2	375	16.71%
C3	365	16.26%
C4	232	10.34%
C5	343	15.28%
C6	342	15.24%
C7	375	16.71%

Ranking Score Index (RSI)

Candidate	Weighted	RSI %	Rank
C7	1256	100%	1
C2	1245	99.12%	2
C3	1212	96.50%	3
C5	1132	90.13%	4
C6	1111	88.49%	5
C4	791	63%	6
C1	726	57.82%	7

Score Efficiency Ratio (SER)

SER = Weighted Score ÷ Raw Votes

Voting Simulations

• Borda: C7
• Plurality: C7
• Approval: C2
• Runoff: C2 slight edge
• Condorcet: C2

Recommendations

Performance Winner: Natalia Ramos C7
Consensus Winner: C2
Most Stable: C4

Cross-System Robustness Testing

To evaluate legitimacy beyond a single aggregation method, the outcome was tested under multiple recognized voting frameworks:

Voting Method	Winner
Weighted/Borda	C7
Plurality (5s only)	C7
Approval (≥4)	C2
Runoff Simulation	C2 (slight edge)
Condorcet Approximation	C2

Legal Interpretation:

The primary declared winner (C7) prevails under the officially adopted weighted method. Alternative systems show competitive proximity but do not invalidate the adopted scoring rule. No paradox (e.g., cycle or instability) was detected.

Fairness & Equity Analysis

Metrics examined:

• Standard deviation (dispersion)
• Gini coefficient (support concentration)
• Efficiency ratio
• Dominance frequency

Findings:

• C7 exhibits stronger high-intensity support.
• C2 exhibits broader moderate support.
• No candidate demonstrates structural unfair advantage.
• Vote concentration reflects voter preference patterns, not systemic bias.

Legal Defensibility Position

If the governing rules explicitly specify weighted scoring as the decision rule, then:

The declaration of C7 as winner is legally defensible, procedurally sound, mathematically transparent, and statistically validated.

If institutional policy prioritizes consensus-based legitimacy (e.g., majority preference over intensity), then:

C2 may be argued as the consensus-optimal candidate, but this would require pre-established rules favoring approval or Condorcet frameworks.

Risk Assessment

Risk Type	Exposure Level
Tabulation Error	Low
Method Bias	Low
Legal Challenge (Procedure)	Low
Legal Challenge (Philosophical Fairness)	Moderate if method not predefined

The strongest legal defense rests on adherence to the pre-declared voting rule.

Final Legal Position

If weighted scoring was the official method → C7 is validly elected.

If method was unspecified → C2 has strong fairness-based argument.

There is no evidence of manipulation, irregularity, or structural discrimination.