tests/Test_Birnbaum_1999.R
In gary-au/pt: Computational models for prospect theory and other theories of risky decision making
library("pt")
########################
# Birnbaum, M. H. (1999). The paradoxes of Allais, stochastic dominance, and decision weights. In J. Shanteau, B. A. Mellers & D. A. Schum (Eds.), Decision science and technology: Reflections on the contributions of Ward Edwards (pp. 27-52). Norwell, MA: Kluwer Academic Publishers.
########################
########################
# common ratio paradox
########################
########################
# Choice problem 1, p.28,33,36,48
# A = (3000, 1.0)
# ~ 24.6 SWU(A) (p.33)
# ~ 3000 SWAU (p.36)
# ~ 3000 TAX (p.48)
# B = (4000, 0.8; 0, 0.2)
# ~ 11.33 SWU(B) (p.33)
# ~ 1566 SWAU (p.36)
# ~ 1934 TAX (p.48)
# A > B
choice_ids <- c(1, 1, 1)
choice_ids <- c(1, 1, 1)
gamble_ids <- c(1, 2, 2)
outcome_ids <- c(1, 1, 2)
objective_consequences <- c(3000, 4000, 0)
probability_strings <- c("1.0", "0.8", "0.2")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 3000 24.6 3000 -0.000000000001819
# 2 1 2 3200 11.33 431.9 2768
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 3000 24.6 3000 -0.000000000001819
# 2 1 2 3200 18.96 1566 1634
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 3000 3000 3000 0
# 2 1 2 3200 1934 1934 1266
########################
# Choice problem 2, p.28,33,36,48
# A' = (3000, 0.25; 0, 0.75)
# ~ 5.04 SWU(A') (p.33)
# ~ 215.2 SWAU (p.36)
# ~ 633 TAX (p.48)
# B' = (4000, 0.2; 0, 0.8)
# ~ 5.16 SWU(B') (p.33)
# ~ 218.8 SWAU (p.36)
# ~ 733 TAX (p.48)
# B' > A'
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(3000, 0, 4000, 0)
probability_strings <- c("1/4", "3/4", "0.2", "0.8")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 750 5.04 57.04 693
# 2 1 2 800 5.155 60.34 739.7
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 750 8.573 215.2 534.8
# 2 1 2 800 8.63 218.8 581.2
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 750 633.4 633.4 116.6
# 2 1 2 800 732.8 732.8 67.2
########################
# common consequence paradox
########################
########################
# Choice problem 3, p.29,33,36,48
# C = (500000, 1.0)
# ~ 190.4 SWU(C) (p.33)
# ~ 500000 SWAU (p.36)
# ~ 500000 TAX (p.48)
# D = (1000000, 0.1; 500000, 0.89; 0, 0.01)
# ~ 127.16 SWU(D) (p.33)
# ~ 474156 SWAU (p.36)
# ~ 405106 TAX (p.48)
# C > D
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 2, 2, 2)
outcome_ids <- c(1, 1, 2, 3)
objective_consequences <- c(500000, 1000000, 500000, 0)
probability_strings <- c("1.0", "0.1", "0.89", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 500000 190.4 500000 -0.0000000004075
# 2 1 2 545000 127.2 182326 362674
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 500000 190.4 500000 -0.0000000004075
# 2 1 2 545000 186.4 474156 70844
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 500000 500000 500000 0
# 2 1 2 545000 405106 405106 139894
########################
# Choice problem 4, p.29,33,36,48
# C' = (500000, 0.11; 0, 0.89)
# ~ 28.12 SWU(G) (p.34)
# ~ 13432 SWAU (p.36)
# ~ 62643 TAX (p.48)
# D' = (1000000, 0.1; 0, 0.9)
# ~ 35.8 SWU(H) (p.34)
# ~ 24011 SWAU (p.36)
# ~ 117879 TAX (p.48)
# D' > C'
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(500000, 0, 1000000, 0)
probability_strings <- c("0.11", "0.89", "0.1", "0.9")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 55000 28.12 4194 50806
# 2 1 2 100000 35.78 7657 92343
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 55000 44.8 13432 41568
# 2 1 2 100000 56.51 24011 75989
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 55000 62643 62643 -7643
# 2 1 2 100000 117879 117879 -17879
########################
# stochastic dominance
########################
########################
# Choice problem 5, p.34,36,48
# E = (100, 0.5; 200, 0.5)
# ~ 4.18 SWU(G) (p.34)
# ~ 145 SWAU (p.36)
# ~ 133 TAX (p.48)
# F = (100, 0.99; 200, 0.01)
# ~ 5.01 SWU(H) (p.34)
# ~ 106 SWAU (p.36)
# ~ 103 TAX (p.48)
# E > F
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(100, 200, 100, 200)
probability_strings <- c("1/2", "1/2", "0.99", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 150 4.181 35.75 114.2
# 2 1 2 101 5.012 56.24 44.76
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 150 7.318 144.8 5.151
# 2 1 2 101 6.465 106.3 -5.28
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 150 133.3 133.3 16.67
# 2 1 2 101 102.6 102.6 -1.57
########################
# Choice problem 6, p.34,36,48
# G = (110, 0.5; 120, 0.5)
# ~ 3.81 SWU(G) (p.34)
# ~ 115 SWAU (p.36)
# ~ 113 TAX (p.48)
# H = (101, 0.01; 102, 0.01; 103, 0.98)
# ~ 4.94 SWU(H) (p.34)
# ~ 102 SWAU (p.36)
# ~ 102 TAX (p.48)
# G > H
choice_ids <- c(1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 1, 2, 3)
objective_consequences <- c(110, 120, 101, 102, 103)
probability_strings <- c("1/2", "1/2", "0.01", "0.01", "0.98")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 115 3.812 28.37 86.63
# 2 1 2 103 4.941 54.26 48.71
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 115 6.671 114.9 0.06525
# 2 1 2 103 6.379 102.8 0.2028
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 115 113.3 113.3 1.667
# 2 1 2 103 102.2 102.2 0.7854
########################
# violations of branch independence
########################
########################
# Choice problem 7, p.39,48
# S = (5, 1/3; 40, 1/3; 44, 1/3)
# ~ 23.17 TAX
# R = (5, 1/3; 10, 1/3; 98, 1/3)
# ~ 22.16 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(5, 40, 44, 5, 10, 98)
probability_strings <- c("1/3", "1/3", "1/3", "1/3", "1/3", "1/3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 29.67 23.17 23.17 6.5
# 2 1 2 37.67 22.17 22.17 15.5
########################
# Choice problem 8, p.39,48
# S' = (40, 1/3; 44, 1/3; 107, 1/3)
# ~ 52.49 TAX
# R' = (10, 1/3; 98, 1/3; 107, 1/3)
# ~ 55.51 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(40, 44, 107, 10, 98, 107)
probability_strings <- c("1/3", "1/3", "1/3", "1/3", "1/3", "1/3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 63.67 52.5 52.5 11.17
# 2 1 2 71.67 55.5 55.5 16.17
########################
# violations of lower cumulative independence
########################
########################
# Choice problem 9, p.43,48
# S = (3, 0.8; 48, 0.1; 52, 0.1)
# ~ 14.05 TAX
# R = (3, 0.8; 10, 0.1; 98, 0.1)
# ~ 11.67 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(3, 48, 52, 3, 10, 98)
probability_strings <- c("0.8", "0.1", "0.1", "0.8", "0.1", "0.1")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 12.4 14.05 14.05 -1.654
# 2 1 2 13.2 11.67 11.67 1.531
########################
# Choice problem 10, p.43,48
# S'' = (10, 0.8; 52, 0.2)
# ~ 17.69 TAX
# R'' = (10, 0.9; 98, 0.1)
# ~ 20.37 TAX
# R'' > S''
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(10, 52, 10, 98)
probability_strings <- c("0.8", "0.2", "0.9", "0.1")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 18.4 17.69 17.69 0.7056
# 2 1 2 18.8 20.37 20.37 -1.573
########################
# violations of upper cumulative independence
########################
########################
# Choice problem 11, p.43,48
# S' = (40, 0.1; 44, 0.1; 110, 0.8)
# ~ 65.03 TAX
# R' = (10, 0.1; 98, 0.1; 110, 0.8)
# ~ 69.59 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(40, 44, 110, 10, 98, 110)
probability_strings <- c("0.1", "0.1", "0.8", "0.1", "0.1", "0.8")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 96.4 65.03 65.03 31.37
# 2 1 2 98.8 69.59 69.59 29.21
########################
# Choice problem 12, p.43,48
# S''' = (40, 0.2; 98, 0.8)
# ~ 68.04 TAX
# R''' = (10, 0.1; 98, 0.9)
# ~ 58.29 TAX
# S''' > R'''
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(40, 98, 10, 98)
probability_strings <- c("0.2", "0.8", "0.1", "0.9")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 86.4 68.04 68.04 18.36
# 2 1 2 89.2 58.29 58.29 30.91
########################
# violations of stochastic dominance
########################
########################
# Choice problem 13, p.44,48
# G+ = (12, 0.05; 14, 0.05; 96, 0.9)
# ~ 45.77 TAX
# G- = (12, 0.1; 90, 0.05; 96, 0.85)
# ~ 63.10 TAX
# G- > G+
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(12, 14, 96, 12, 90, 96)
probability_strings <- c("0.05", "0.05", "0.9", "0.1", "0.05", "0.85")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 87.7 45.77 45.77 41.93
# 2 1 2 87.3 63.1 63.1 24.2
########################
# coalescing & event splitting effects
########################
########################
# Choice problem 14, p.45,48
# S1 = (8, 0.7; 0, 0.3)
# ~ 3.44 TAX
# R1 = (24, 0.3; 0, 0.7)
# ~ 5.69 TAX
# R1 > S1
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(8, 0, 24, 0)
probability_strings <- c("0.7", "0.3", "0.3", "0.7")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 5.6 3.435 3.435 2.165
# 2 1 2 7.2 5.695 5.695 1.505
########################
# Choice problem 15, p.45,48-49
# S2 = (8, 0.3; 8, 0.4; 0, 0.3)
# ~ 4.14 TAX
# R2 = (24, 0.3; 0, 0.4; 0, 0.3)
# ~ 3.72 TAX
# S2 > R2
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(8, 8, 0, 24, 0, 0)
probability_strings <- c("0.3", "0.4", "0.3", "0.3", "0.4", "0.3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 5.6 4.138 4.138 1.462
# 2 1 2 7.2 3.723 3.723 3.477
########################
# violations of distribution independence
########################
########################
# Choice problem 16, p.46,49
# S = (4, 0.59; 45, 0.2; 49, 0.2; 110, 0.01)
# ~ 21.70 TAX
# R = (4, 0.59; 11, 0.2; 97, 0.2; 110, 0.01)
# ~ 20.56 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 4, 1, 2, 3, 4)
objective_consequences <- c(4, 45, 49, 110, 4, 11, 97, 110)
probability_strings <- c("0.59", "0.2", "0.2", "0.01", "0.59", "0.2", "0.2", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 22.26 21.7 21.7 0.5595
# 2 1 2 25.06 20.56 20.56 4.501
########################
# Choice problem 17, p.46,49
# S' = (4, 0.01; 45, 0.2; 49, 0.2; 110, 0.59)
# ~ 49.85 TAX
# R' = (4, 0.01; 11, 0.2; 97, 0.2; 110, 0.59)
# ~ 50.03 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 4, 1, 2, 3, 4)
objective_consequences <- c(4, 45, 49, 110, 4, 11, 97, 110)
probability_strings <- c("0.01", "0.2", "0.2", "0.59", "0.01", "0.2", "0.2", "0.59")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 83.74 49.85 49.85 33.89
# 2 1 2 86.54 50.03 50.03 36.51
gary-au/pt documentation built on May 16, 2019, 5:41 p.m.
R Package Documentation
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library("pt")
########################
# Birnbaum, M. H. (1999). The paradoxes of Allais, stochastic dominance, and decision weights. In J. Shanteau, B. A. Mellers & D. A. Schum (Eds.), Decision science and technology: Reflections on the contributions of Ward Edwards (pp. 27-52). Norwell, MA: Kluwer Academic Publishers.
########################
########################
# common ratio paradox
########################
########################
# Choice problem 1, p.28,33,36,48
# A = (3000, 1.0)
# ~ 24.6 SWU(A) (p.33)
# ~ 3000 SWAU (p.36)
# ~ 3000 TAX (p.48)
# B = (4000, 0.8; 0, 0.2)
# ~ 11.33 SWU(B) (p.33)
# ~ 1566 SWAU (p.36)
# ~ 1934 TAX (p.48)
# A > B
choice_ids <- c(1, 1, 1)
choice_ids <- c(1, 1, 1)
gamble_ids <- c(1, 2, 2)
outcome_ids <- c(1, 1, 2)
objective_consequences <- c(3000, 4000, 0)
probability_strings <- c("1.0", "0.8", "0.2")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 3000 24.6 3000 -0.000000000001819
# 2 1 2 3200 11.33 431.9 2768
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 3000 24.6 3000 -0.000000000001819
# 2 1 2 3200 18.96 1566 1634
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 3000 3000 3000 0
# 2 1 2 3200 1934 1934 1266
########################
# Choice problem 2, p.28,33,36,48
# A' = (3000, 0.25; 0, 0.75)
# ~ 5.04 SWU(A') (p.33)
# ~ 215.2 SWAU (p.36)
# ~ 633 TAX (p.48)
# B' = (4000, 0.2; 0, 0.8)
# ~ 5.16 SWU(B') (p.33)
# ~ 218.8 SWAU (p.36)
# ~ 733 TAX (p.48)
# B' > A'
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(3000, 0, 4000, 0)
probability_strings <- c("1/4", "3/4", "0.2", "0.8")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 750 5.04 57.04 693
# 2 1 2 800 5.155 60.34 739.7
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 750 8.573 215.2 534.8
# 2 1 2 800 8.63 218.8 581.2
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 750 633.4 633.4 116.6
# 2 1 2 800 732.8 732.8 67.2
########################
# common consequence paradox
########################
########################
# Choice problem 3, p.29,33,36,48
# C = (500000, 1.0)
# ~ 190.4 SWU(C) (p.33)
# ~ 500000 SWAU (p.36)
# ~ 500000 TAX (p.48)
# D = (1000000, 0.1; 500000, 0.89; 0, 0.01)
# ~ 127.16 SWU(D) (p.33)
# ~ 474156 SWAU (p.36)
# ~ 405106 TAX (p.48)
# C > D
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 2, 2, 2)
outcome_ids <- c(1, 1, 2, 3)
objective_consequences <- c(500000, 1000000, 500000, 0)
probability_strings <- c("1.0", "0.1", "0.89", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 500000 190.4 500000 -0.0000000004075
# 2 1 2 545000 127.2 182326 362674
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 500000 190.4 500000 -0.0000000004075
# 2 1 2 545000 186.4 474156 70844
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 500000 500000 500000 0
# 2 1 2 545000 405106 405106 139894
########################
# Choice problem 4, p.29,33,36,48
# C' = (500000, 0.11; 0, 0.89)
# ~ 28.12 SWU(G) (p.34)
# ~ 13432 SWAU (p.36)
# ~ 62643 TAX (p.48)
# D' = (1000000, 0.1; 0, 0.9)
# ~ 35.8 SWU(H) (p.34)
# ~ 24011 SWAU (p.36)
# ~ 117879 TAX (p.48)
# D' > C'
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(500000, 0, 1000000, 0)
probability_strings <- c("0.11", "0.89", "0.1", "0.9")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 55000 28.12 4194 50806
# 2 1 2 100000 35.78 7657 92343
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 55000 44.8 13432 41568
# 2 1 2 100000 56.51 24011 75989
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 55000 62643 62643 -7643
# 2 1 2 100000 117879 117879 -17879
########################
# stochastic dominance
########################
########################
# Choice problem 5, p.34,36,48
# E = (100, 0.5; 200, 0.5)
# ~ 4.18 SWU(G) (p.34)
# ~ 145 SWAU (p.36)
# ~ 133 TAX (p.48)
# F = (100, 0.99; 200, 0.01)
# ~ 5.01 SWU(H) (p.34)
# ~ 106 SWAU (p.36)
# ~ 103 TAX (p.48)
# E > F
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(100, 200, 100, 200)
probability_strings <- c("1/2", "1/2", "0.99", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 150 4.181 35.75 114.2
# 2 1 2 101 5.012 56.24 44.76
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 150 7.318 144.8 5.151
# 2 1 2 101 6.465 106.3 -5.28
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 150 133.3 133.3 16.67
# 2 1 2 101 102.6 102.6 -1.57
########################
# Choice problem 6, p.34,36,48
# G = (110, 0.5; 120, 0.5)
# ~ 3.81 SWU(G) (p.34)
# ~ 115 SWAU (p.36)
# ~ 113 TAX (p.48)
# H = (101, 0.01; 102, 0.01; 103, 0.98)
# ~ 4.94 SWU(H) (p.34)
# ~ 102 SWAU (p.36)
# ~ 102 TAX (p.48)
# G > H
choice_ids <- c(1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 1, 2, 3)
objective_consequences <- c(110, 120, 101, 102, 103)
probability_strings <- c("1/2", "1/2", "0.01", "0.01", "0.98")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swu ce rp
# 1 1 1 115 3.812 28.37 86.63
# 2 1 2 103 4.941 54.26 48.71
my_utility <- Utility(fun="power",
par=c(alpha=0.4, beta=0.4, lambda=1))
my_pwf <-
ProbWeight(fun="linear_in_log_odds",
par=c(alpha=0.4, beta=0.4))
compareSWAU(my_choices,
prob_weight=my_pwf,
utility=my_utility,
digits=4)
# cid gid ev swau ce rp
# 1 1 1 115 6.671 114.9 0.06525
# 2 1 2 103 6.379 102.8 0.2028
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 115 113.3 113.3 1.667
# 2 1 2 103 102.2 102.2 0.7854
########################
# violations of branch independence
########################
########################
# Choice problem 7, p.39,48
# S = (5, 1/3; 40, 1/3; 44, 1/3)
# ~ 23.17 TAX
# R = (5, 1/3; 10, 1/3; 98, 1/3)
# ~ 22.16 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(5, 40, 44, 5, 10, 98)
probability_strings <- c("1/3", "1/3", "1/3", "1/3", "1/3", "1/3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 29.67 23.17 23.17 6.5
# 2 1 2 37.67 22.17 22.17 15.5
########################
# Choice problem 8, p.39,48
# S' = (40, 1/3; 44, 1/3; 107, 1/3)
# ~ 52.49 TAX
# R' = (10, 1/3; 98, 1/3; 107, 1/3)
# ~ 55.51 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(40, 44, 107, 10, 98, 107)
probability_strings <- c("1/3", "1/3", "1/3", "1/3", "1/3", "1/3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 63.67 52.5 52.5 11.17
# 2 1 2 71.67 55.5 55.5 16.17
########################
# violations of lower cumulative independence
########################
########################
# Choice problem 9, p.43,48
# S = (3, 0.8; 48, 0.1; 52, 0.1)
# ~ 14.05 TAX
# R = (3, 0.8; 10, 0.1; 98, 0.1)
# ~ 11.67 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(3, 48, 52, 3, 10, 98)
probability_strings <- c("0.8", "0.1", "0.1", "0.8", "0.1", "0.1")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 12.4 14.05 14.05 -1.654
# 2 1 2 13.2 11.67 11.67 1.531
########################
# Choice problem 10, p.43,48
# S'' = (10, 0.8; 52, 0.2)
# ~ 17.69 TAX
# R'' = (10, 0.9; 98, 0.1)
# ~ 20.37 TAX
# R'' > S''
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(10, 52, 10, 98)
probability_strings <- c("0.8", "0.2", "0.9", "0.1")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 18.4 17.69 17.69 0.7056
# 2 1 2 18.8 20.37 20.37 -1.573
########################
# violations of upper cumulative independence
########################
########################
# Choice problem 11, p.43,48
# S' = (40, 0.1; 44, 0.1; 110, 0.8)
# ~ 65.03 TAX
# R' = (10, 0.1; 98, 0.1; 110, 0.8)
# ~ 69.59 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(40, 44, 110, 10, 98, 110)
probability_strings <- c("0.1", "0.1", "0.8", "0.1", "0.1", "0.8")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 96.4 65.03 65.03 31.37
# 2 1 2 98.8 69.59 69.59 29.21
########################
# Choice problem 12, p.43,48
# S''' = (40, 0.2; 98, 0.8)
# ~ 68.04 TAX
# R''' = (10, 0.1; 98, 0.9)
# ~ 58.29 TAX
# S''' > R'''
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(40, 98, 10, 98)
probability_strings <- c("0.2", "0.8", "0.1", "0.9")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 86.4 68.04 68.04 18.36
# 2 1 2 89.2 58.29 58.29 30.91
########################
# violations of stochastic dominance
########################
########################
# Choice problem 13, p.44,48
# G+ = (12, 0.05; 14, 0.05; 96, 0.9)
# ~ 45.77 TAX
# G- = (12, 0.1; 90, 0.05; 96, 0.85)
# ~ 63.10 TAX
# G- > G+
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(12, 14, 96, 12, 90, 96)
probability_strings <- c("0.05", "0.05", "0.9", "0.1", "0.05", "0.85")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 87.7 45.77 45.77 41.93
# 2 1 2 87.3 63.1 63.1 24.2
########################
# coalescing & event splitting effects
########################
########################
# Choice problem 14, p.45,48
# S1 = (8, 0.7; 0, 0.3)
# ~ 3.44 TAX
# R1 = (24, 0.3; 0, 0.7)
# ~ 5.69 TAX
# R1 > S1
choice_ids <- c(1, 1, 1, 1)
gamble_ids <- c(1, 1, 2, 2)
outcome_ids <- c(1, 2, 1, 2)
objective_consequences <- c(8, 0, 24, 0)
probability_strings <- c("0.7", "0.3", "0.3", "0.7")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 5.6 3.435 3.435 2.165
# 2 1 2 7.2 5.695 5.695 1.505
########################
# Choice problem 15, p.45,48-49
# S2 = (8, 0.3; 8, 0.4; 0, 0.3)
# ~ 4.14 TAX
# R2 = (24, 0.3; 0, 0.4; 0, 0.3)
# ~ 3.72 TAX
# S2 > R2
choice_ids <- c(1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 1, 2, 3)
objective_consequences <- c(8, 8, 0, 24, 0, 0)
probability_strings <- c("0.3", "0.4", "0.3", "0.3", "0.4", "0.3")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 5.6 4.138 4.138 1.462
# 2 1 2 7.2 3.723 3.723 3.477
########################
# violations of distribution independence
########################
########################
# Choice problem 16, p.46,49
# S = (4, 0.59; 45, 0.2; 49, 0.2; 110, 0.01)
# ~ 21.70 TAX
# R = (4, 0.59; 11, 0.2; 97, 0.2; 110, 0.01)
# ~ 20.56 TAX
# S > R
choice_ids <- c(1, 1, 1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 4, 1, 2, 3, 4)
objective_consequences <- c(4, 45, 49, 110, 4, 11, 97, 110)
probability_strings <- c("0.59", "0.2", "0.2", "0.01", "0.59", "0.2", "0.2", "0.01")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 22.26 21.7 21.7 0.5595
# 2 1 2 25.06 20.56 20.56 4.501
########################
# Choice problem 17, p.46,49
# S' = (4, 0.01; 45, 0.2; 49, 0.2; 110, 0.59)
# ~ 49.85 TAX
# R' = (4, 0.01; 11, 0.2; 97, 0.2; 110, 0.59)
# ~ 50.03 TAX
# R' > S'
choice_ids <- c(1, 1, 1, 1, 1, 1, 1, 1)
gamble_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)
outcome_ids <- c(1, 2, 3, 4, 1, 2, 3, 4)
objective_consequences <- c(4, 45, 49, 110, 4, 11, 97, 110)
probability_strings <- c("0.01", "0.2", "0.2", "0.59", "0.01", "0.2", "0.2", "0.59")
my_choices <- Choices(choice_ids=choice_ids,
gamble_ids=gamble_ids,
outcome_ids=outcome_ids,
objective_consequences=objective_consequences,
probability_strings=probability_strings)
my_choices
my_utility <- Utility(fun="linear",
par=c(lambda=1))
my_pwf <-
ProbWeight(fun="power",
par=c(alpha=0.7, beta=1.0))
compareTAX(my_choices,
prob_weight=my_pwf,
utility=my_utility,
delta=-1, digits=4)
# cid gid ev tax ce rp
# 1 1 1 83.74 49.85 49.85 33.89
# 2 1 2 86.54 50.03 50.03 36.51
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