The Hardest Interview 2 __link__ May 2026

[ \Delta U = \mathbbE\left[ \fracb'g' - \fracbg \right] - \lambda \cdot 1 ]

Set (\Delta U = 0) → threshold (p_\textthresh = 2\lambda). the hardest interview 2

The fixed point (R^ ) satisfies (p(R^ ) = 0.5) → (R^* = 1). So long-term ratio tends to 1 even with feedback. Families compute (\Delta U) using their noisy (\hatR). For a family with ((b,g)): [ \Delta U = \mathbbE\left[ \fracb'g' - \fracbg

If (\Delta U < 0), they stop even if formal stopping rule not met (early stop). [ U_\texttotal = \sum_\textfamilies \left( \fracb_fg_f - \lambda \cdot t_f \right) ] Families compute (\Delta U) using their noisy (\hatR)

| (\lambda) | Final national (E[b/g]) | Avg. children per family | Avg. utility per family | |-------------|----------------------------|--------------------------|--------------------------| | 0.05 | 1.023 | 2.91 | 0.955 | | 0.10 | 1.007 | 2.68 | 0.891 | | 0.15 | 0.994 | 2.44 | 0.847 |