Table 4.

Utility-weighted sampling explains the Allais paradox.

	ΔU	p	$\mathbb{E}\left[\stackrel{\sim }{q}\right]$	$\mathbb{E}\left[\stackrel{\sim }{q}\right]$/p
	0	0.66	0	0
z = 2400:
	u(2500) − u(2400)	0.33	0.58	1.8
	−u(2400)	0.01	0.42	42
	ΔU	p	$\mathbb{E}\left[\stackrel{\sim }{q}\right]$	$\mathbb{E}\left[\stackrel{\sim }{q}\right]$/p
	0	0.66 · 0.67	0	0
z = 0 :	−u(2400)	0.67 · 0.34	0.5	2.19
	u(2500) −u(2400)	0.33 · 0.34	0.01	0.08
	u(2500)	0.33 · 0.66	0.49	2.26

Note: The agent’s simulation yields ΔU = Δ u with probability $\stackrel{\sim }{q}(\mathrm{\Delta }u)\propto p(\mathrm{\Delta }u)\cdot \left|\mathrm{\Delta }u\right|$ where p is Δ u’s objective probability.