Table C1.

Two worked examples of UWS applied to the choice between a gamble ($x with probability p) versus its expected value (p · × dollars for sure) for a linear utility function without noise. These predictions change significantly when UWS takes into account that outcome valuation is noisy, as discussed in the text.

Samples	Decision	Frequency	Freq. if p = 0.01	Freq. if p = 0.99
(win, win)	gamble	$\stackrel{\sim }{q}{(x-p\cdot x)}^2$	0.5 · 0.5 = 0.25	0.5 · 0.5 = 0.25
(lose, lose)	sure option	$\stackrel{\sim }{q}{(0-p\cdot x)}^2$	0.5 · 0.5 = 0.25	0.5 · 0.5 = 0.25
(win, lose)	choose randomly	$\stackrel{\sim }{q}(x-p\cdot x)\cdot \stackrel{\sim }{q}(-p\cdot x)$	0.5 · 0.5 = 0.25	0.5 · 0.5 = 0.25
(lose, win)	choose randomly	$\stackrel{\sim }{q}(-p\cdot x)\cdot \stackrel{\sim }{q}(x-p\cdot x)$	0.5 · 0.5 = 0.25	0.5 · 0.5 = 0.25
P(choose gamble) :		$\stackrel{\sim }{q}(x-p\cdot x)$	0.5	0.5