prop-prob

NHW non-NHW · Residents of two tracts (V) mix at the destination (θ). Naive expectation misses.

Origins

80 neighborhoods — high cluster on top, low on bottom.

target V = 0.450 realized V = 0.450 p̄ = 0.50

V segregation (variance ratio) 0.45 0 = identical tracts · 1 = fully sorted p̄ citywide NHW share 0.50 0.5 = symmetric (closed-form) N neighborhoods 80 more tracts — smoother realized V φ⁻¹ cluster spread deterministic 0 = two-point · >0 = Beta-distributed within each cluster

Flows

Each row node emits two flows — blue to NHW pool, orange to non-NHW pool.

8 rows · θ = 0.40 dest NHW = 70.0%

θ mobility sorting 0.40 0 = proportional · +1 = NHW-preferred destination · −1 = non-NHW-preferred

Destination

Observed vs. what proportionality predicts.

observed composition π_true = 70.0%

proportional prediction π_prop = 59.0%

destination diversity (Herfindahl, 0–0.5)

predicted

observed

0.000.250.50

proportionality bias 0.000 − 0.000

0.000

Bias surface

Analytical bias over (V, θ). Click to teleport. Contours at 0.02, 0.05, 0.10, 0.20, 0.35.

V = 0.450 θ = 0.400 bias (sim) = 0.064 bias (closed) = 0.064

θ=+1 θ=0 θ=−1

V=0

V=1

bias · viridis · √-scaled

0.000

0.500