Financial & Economic Analysis
Hoover Index (Robin Hood / Schutz Index) & Exact Parity Reallocation Share
Calculate the Hoover (Robin Hood / Pietra) index 0.5 * SUM(|resource_share - population_share|) and the exact volume that must shift from surplus to deficit units to reach equal per-capita parity.
Operational meaning of the Hoover / Robin Hood index
Geometrically equal to the maximum vertical distance between the Lorenz curve and the 45-degree line of equality, the Hoover index (also called the Robin Hood, Schutz, or Pietra index) has the most direct physical interpretation of any inequality metric: it equals the exact fraction of total income, budget, or server capacity that would have to be transferred from above-average units to below-average units to achieve uniform per-capita allocation.
Given headcount or demand weights p_i and allocated resources x_i, each unit’s share gap is (x_i / SUM(x)) - (p_i / SUM(p)). Because positive surpluses and negative deficits sum to zero, summing ABS(share_gap) counts every transferred dollar twice—so multiplying by 0.5 yields the exact Hoover index H in [0, 1).
| District | Headcount Share | Budget Share | Absolute Gap |s_x - s_p| |
|---|---|---|---|
| North (30 staff, 150K) | 0.3000 | 0.1500 | 0.1500 (Deficit -150K) |
| East (30 staff, 210K) | 0.3000 | 0.2100 | 0.0900 (Deficit -90K) |
| South (20 staff, 240K) | 0.2000 | 0.2400 | 0.0400 (Surplus +40K) |
| West (20 staff, 400K) | 0.2000 | 0.4000 | 0.2000 (Surplus +200K) |
Row-Level Absolute Share Gap & Hoover Index Formula
Compute each district’s absolute share gap ABS((C2 / SUM($C$2:$C$5)) - (B2 / SUM($B$2:$B$5))) in Column D and take half the column sum.
=ROUND(0.5 * SUM(D2:D5), 4)Exact Reallocation Volume Required for Per-Capita Parity
Multiply the Hoover index by total resource pool SUM(C2:C5) (equivalently summing MAX(0, C_i - target_i) across surplus rows) to quantify the exact transfer amount.
=ROUND(G2 * SUM(C2:C5), 2)Try the example
Use the original values or change them to test your understanding.