Tiebout Capitalization & Median Voter Spending Formula

Why majority-rule referendums select MEDIAN (not average!) spending — and capitalize fiscal surplus into home prices!

In local public finance, two classic theorems govern municipal budgets and property values. First, Howard Bowen (1943) and Duncan Black (1948) proved that when voters have single-peaked preferences over a single-dimensional municipal budget G, pairwise majority voting selects the MEDIAN voter’s ideal budget G_med = MEDIAN(G_1:G_N) — NOT the arithmetic mean AVERAGE(G_1:G_N), which right-skewed high-wealth estates pull upward! Second, Charles Tiebout (1956) and Wallace Oates (1969) showed that when mobile households "vote with their feet" across jurisdictions, an annual local public-service benefit advantage Delta_B minus annual municipal bill difference Delta_Bill at real discount rate r capitalizes into residential home values by Delta_P_house = (Delta_B - Delta_Bill) / r!

Build a 5-cohort municipal roll FIRST: Tier_1 (B2 = 100,000 property, C2 = 4,000 ideal per-cohort budget), Tier_2 (B3 = 150,000, C3 = 6,000), Tier_3_Median (B4 = 200,000, C4 = 8,000), Tier_4 (B5 = 350,000, C5 = 12,000), and Tier_5_Estate (B6 = 700,000, C6 = 25,000), plus school-quality benefit gap Delta_B = 1,800 (F2), local bill gap Delta_Bill = 600 (F3), and real discount rate r = 0.04 (F4). Naive averaging predicts 11,000 per cohort, whereas majority voting passes G_med = MEDIAN(C2:C6) = 8,000 (total budget 5 * 8,000 = 40,000 across 1,500,000 assessed base -> millage rate 0.0267 = 26.67 mills), and Tiebout-Oates capitalization adds (1,800 - 600) / 0.04 = 30,000.00 per home!

Equilibrium Majority-Rule Municipal Millage Rate Formula

Notice that changing top-tier estate demand C6 from 25,000 to 50,000 changes AVERAGE(C2:C6) dramatically while leaving G_med = 8,000 and the winning referendum rate completely unchanged!

=LET(tot_base, SUM(B2:B6), g_med, MEDIAN(C2:C6), n_coh, ROWS(C2:C6), IF(OR(tot_base <= 0, g_med < 0), "Invalid Municipal Roll", ROUND((n_coh * g_med) / tot_base, 4)))

Tiebout-Oates Fiscal-Surplus Property Capitalization Formula

Before accepting a district boundary proposal in a shared Arte Sheets workbook, ask a hint-first AI prompt: "How does partial capitalization k in [0, 1] scale (Delta_B - Delta_Bill) / r when elastic housing supply expands?"

=LET(db_ben, F2, dt_bil, F3, r_cap, F4, IF(r_cap <= 0, "Require Discount Rate r > 0", ROUND((db_ben - dt_bil) / r_cap, 2)))

Further reading

• Arte Sheets Lesson — Samuelson Public-Good Sum of MRS & Lindahl Prices
• Microsoft Support — MEDIAN function