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""" ...the example I've seen is that a loss-averse agent may evaluate a sequence of say ten coinflips with -$15/+$20 payoffs positively at the same time as evaluating each individual such coinflip negatively. - steven, http://lesswrong.com/lw/gi/dissenting_views/dlu?context=3 """ from math import log def util(x): if x > 0: return log(x + 1) elif x < 0: return -2 * log(abs(x) + 1) else: return 0. print "single flip EU =", print 0.5 * util(20) + 0.5 * util(-15) fac = lambda x: 1 if x==0 else x*fac(x-1) binom = lambda n,k: fac(n) / (fac(n-k) * fac(k)) eu = 0. for n_wins in xrange(11): payoff = 20 * n_wins - 15 * (10 - n_wins) p = binom(10, n_wins) / 1024. eu += util(payoff) * p print "multi-flip EU =", eu
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