Tradeo Contrast Eect in Choices Between Lotteries Yuval Heller (Preliminary Draft) School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel. Phone: 972-3-640-5386. Fax: 972-3-640-9357. Email:
[email protected]
Abstract Simonson and Tversky
(Journal of Marketing Research, 1992) demonstrated that the
tendency to choose an alternative is enhanced or hindered depending on whether the tradeos within the set under consideration are favorable or unfavorable to that option (tradeo contrast eect). The existing literature experimentally tested this eect mostly in choices between multi-attribute products. In this note we present experimental evidence that suggests that the tradeo contrast eect also exists for choices between lotteries.
1 Introduction Choice behavior is often in uenced by the set of alternatives under consideration (menu eects). Speci cally, Itamar Simonson and Amos Tversky (1992) presented and experimentally tested the in uence of
tradeo contrast
eect.
According to this eect, the tendency to choose an alternative is enhanced or hindered depending on whether the tradeos within the set under consideration are favorable or unfavorable to that option. Consider, for example, the choice between the three objects displayed in Figure 1 (where each axis represents a positive attribute). Because the contrast between the the
x -z
and
y -z
tradeos is unfavorable to
z, z
x -y
tradeo and
is expected to fare worse (to
be chosen less often) in the triple than in the pairs. On the other hand, if was above the
x- y
z
line, then it would be expected to fare better in the triple.
Simonson and Tversky (1992, 1993) present an experimental support for this eect for choices between dierent multi-attribute products. Recently (Heller, 2010), we presented an axiomatic formulation for this eect for choices between lotteries (the framework of John von-Neumann and Oscar Morgenstern, 1944). In this note we present experimental evidence that suggests that the tradeo contrast eect also exists in choices between lotteries.
August 3, 2010
Figure 1. Contrast Tradeo Detraction
This note is is organized as follows. In the next section we describe the experimental design. Section 3 presents the main results. Further results and the raw data are found in the Appendix.
2 Experimental Design Participants in the experiment included 153 undergraduate students in TelAviv University (from economics, computer science and physics). The students were asked to participate in a short experiment (that lasted about 10 minutes) in the beginning of the class. The experiment did not include monetary payments (i.e., an hypothetical treatment). Each subject was being asked to answer 6 questions (see appendix B). In each question, the subject had to choose a single alternative out of 2-3 alternatives. These 6 questions dealt with 4 dierent choice problems. Each of these problem was presented in one of two possible framings, and with one of two somewhat dierent sets of values. Two of these problems dealt with choices over lotteries as described in Table 1 (the other two problems, which dealt with choices over 1 dierent remuneration plans, are described in Appendix A). For each choice problem, one half of the subjects received a single 3-alternative question (with either of the two framings/values), while the other half received two 2-alternative questions: the rst question included alternatives and the second question included alternatives
y
and
z.
x
and
z,
In order to hide the
1 During the experiment time (June 2010), one NIS (new Israeli Shekel) was worth approximately 0.25 dollar or 0.2 euro.
2
Table 1 Problems of Choices Between Lotteries Problem
1
2
Framing 1
Lottery for a
public transportation
Lottery of
Framing 2
period of free:
photocopy services
monetary payos
x
y
Set of
z
Values 1
- 20% for 15,000 NIS
y
- 25% for half year
z
- total 19% for a free period:
- 50% for 5,000 NIS
- total 37% for a prize:
7% for one year and 12% for
11% for 15,000 NIS,
half year
and 26% for 5,000 NIS
x
- 17% for one year
x
y
- 31% for half year
y
Set of
z
Values 2
x
- 15% for one year
z
- total 23% for a free period:
8% for 1 year and 15% for
1 2 year
- 18% for 20,000 NIS - 45% for 7,000 NIS
- total 33% for a prize: 10% for 20,000 NIS,
and 23% for 7,000 NIS
relation between the two related questions (the
x−z
choice and the
y−z
choice), these two questions had dierent framings (in Problem 1), dierent sets of values, and were located at dierent pages of the questionnaire (see Appendix B). An analysis of the results shows that the framing and the set of values had no direct substantial in uence on the choices of the subjects. In both problems, alternative prize with respect to
y.
x
has a lower probability for gaining a better
Thus the choice between
x
and
y
depends on the
tradeo between winning probability and prize's quality. Alternative compromise between symmetric mixture of Problem 2
z
x x
y: and y
and
in Problem 1
z
z
is a
is a little bit worse than the
(similar to the description of Figure 1); in
is a little bit better than the symmetric mixture. According to
the tradeo contrast eect,
z
should be fare worse in the triple than in the
pairs in Problem 1, and fare better in the triple in Problem 2.
3 Results Table 2 compares the frequency in which the compromise alternative z was 2 chosen in the triple and in the two pairs in each of the problems. It indicates that the tradeo contrast eect exists in choice between lotteries:
z
worse in the triple when it was inferior to the symmetric mixture of
2 That is the frequency of subjects who chose (i.e.,
z
was chosen both in
{x, z}
and in
z
{y, z}).
3
fared
x
and
in both the 2-alternative questions
Table 2 Choice frequency of
Problem 1
Problem 2
inferior to mixture
superior to mixture
Choice frequency in the triple
29% (80 subjects)
27% (73 subsets)
Choice frequency in the two pairs
22% (73 subsets)
36% (80 subsets)
p-value
12%
17%
z
y
z
relative to the symmetric mixture
(its choice frequency dropped from 29% in the pairs to 22%), and it fared
better when it was superior to the symmetric mixture of
x
and
y
(its choice
frequency raised from 27% to 36%). Observe, however, that the statistical signi cance of these results is somewhat limited (respective
p-values
of 12%
and 17%), and we plan to replicate this experiment again with more subjects,
REFERENCES Heller, Yuval.
2010. Justi able Choice.
http://www.tau.ac.il/~helleryu/weaker.pdf
Simonson, Itamar, and Amos Tversky.
contrast and extremeness aversion.
1992. Choice in context: tradeo
Journal of Marketing Research,
XXIX:
281-95.
Simonson, Itamar, and Amos Tversky.
erences.
1993. Context-Dependent Pref-
Management Science, 39(10): 1179-1189.
von Neumann, John, and Oscar Morgenstern.
1944.
Theory of Games
and Economic Behavior, Princeton: Princeton University Press.
Appendix A Results for Remuneration Plans Two of the four problems (Problems 3 and 4) in the questionnaire dealt with choices over dierent remuneration plans as described in Table A.1. As in Problems 1-2, one half of the subjects received a single 3-alternative question (with either of the two framings/values), while the other half received two 2-alternative questions:
x−z
choice and the
4
y−z
choice. In order to
Table A.1 Problems of Choices Between Remuneration Plans Problem
3
4
Framing 1
Paying annual tuition
Scholarship award
Framing 2
Paying for Plasma TV
Severance Payment
x
- installments: 1,000 NIS *
10 months (total 10,000 NIS) Set of
Values 1
y
- down payment: 9,500 NIS
z
- down payment: 4,700 NIS,
and installments: 500 NIS *
x y
- 6,000 NIS in 2 months
- 6,500 NIS in 14 months
z
- 6,200 NIS in 8 months
x
- 5,400 NIS in 2 months
10 months (total 9,700 NIS)
x
- installments: 950 NIS * 10 months (total 9,500 NIS)
Set of
Values 2
y
- down payment: 9,000 NIS
z
- down payment: 4,500 NIS,
and installments: 470 NIS *
y z
- 5,900 NIS in 13 months
- 5,600 NIS in 7 months
10 months (total 9,200)
hide the relation between these two related questions, these two questions had dierent framings, dierent set of values, and were located at dierent pages of the questionnaire. Problem 3 dealt with dierent remuneration plans for paying about 9,500 NIS. The total payment of alternative installments, while in Alternative value (of
y ),
z
y
x
is higher and it is divided into 10 monthly
the total payment is lower but it is paid immediately.
is a good compromise: the total amount is closer to the low
about half of it is paid as a down payment, and the other half is
paid with 10 monthly installments. Problem 4 dealt with dierent alternatives
x includes a lower amount that is given
to receive about 6,000 NIS. Alternative in 2 months, while
y
includes a higher amount that is given after more than
a year (13-14 months). Alternative closer to the low value (of
x),
z
is a bad compromise: the amount is
and the waiting period is 7-8 months.
Table A.2 compares the frequency in which the compromise alternative
z
was chosen in the triple and in the two pairs in each of the problems. It indicates that the tradeo contrast eect may exist in choices between dierent remuneration plans:
z fared worse in the triple when it was a bad compromise
in Problem 4 (its choice frequency dropped from 10% in the pairs to 6%), and it fared better when it was a good compromise(its choice frequency raised from 20% to 25%). Observe, however, that the statistical signi cance of these results is low (respective
p-values
of 22% and 24%), and we plan to replicate
5
Table A.2 Choice frequency of
z Problem 3
Problem 4
z
good compromise
bad compromise
Choice frequency in the triple
20% (80 subsets)
10% (73 subsets)
Choice frequency in the two pairs
25% (73 subsets)
6% (80 subsets)
p-value
24%
22%
this experiment again with more subjects.
B Questionnaires In this appendix we present an English translation of the four versions of the questionnaire (approximately one quarter of the subjects received each version).
Version 1a You are being asked to answer the following questions. Answers will be analyzed anonymously for a research on decision making. Please choose a single answer to each question. Thank you for you cooperation. (1) Sex (a) Male (b) Female (2) You have to pay annual tuition for the university in one of the following alternatives. Which alternative would you choose? (a) 10 monthly installments of 950 NIS each (total amount - 9,500 NIS). (b) A down payment of 4,500 NIS, and 10 monthly installments of 470 NIS each (total amount - 9,200 NIS). (3) You may participate in a lottery for free public transportation. Which lottery would you choose? (a) Probability 17% of winning free transportation for one year (and nothing with probability 83%). (b) Probability of 23% of winning free transportation, out of which: 8% for one year and 15% for half year (and nothing with probability 77%). (4) You are being oered to get a scholarship award in a few alternatives. Which alternative would you choose?
6
(a) 6,000 NIS in two months. (b) 6,200 NIS in eight months. (c) 6,500 NIS in one year and two months. (5) You may participate in one of the following lotteries. Which lottery would you choose? (a) Probability 20% to get 15,000 NIS (and nothing with probability 80%). (b) Probability 37% to get a prize, out of which 11% for 15,000 NIS and 26% of 5,000 NIS (and nothing with probability 63%). (c) Probability 50% to get 5,000 NIS (and nothing with probability 50%). [ 2 more questions are in the next page. ] (6) You decided to buy a plasma TV. The store oers you two remuneration plans. Which plan would you choose? (a) Paying a down payment of 4,700 NIS, and additional 10 monthly installments of 500 NIS (total amount 9,700 NIS). (b) Paying a single payment of 9,500 NIS. (7) You may participate in a lottery for free photocopy services. Which lottery would you choose? (a) Probability 19% of winning free services, out of which: 7% for one year and 12% for half year (and nothing with probability 81%). (b) Probability 25% of winning free services for half year (and nothing with probability 75%).
Version 1b You are being asked to answer the following questions. Answers will be analyzed anonymously for a research on decision making. Please choose a single answer to each question. Thank you for you cooperation. (1) Sex (a) Male (b) Female (2) You decided to buy a plasma TV. The store oers you two remuneration plans. Which plan would you choose? (a) 10 monthly installments of 1,000 NIS each (total amount - 10,000 NIS). (b) A down payment of 4,700 NIS, and 10 monthly installments of 500 NIS each (total amount - 9,700 NIS). (3) You may participate in a lottery for free photocopying services. Which lottery would you choose? (a) Probability 15% of winning free services for one year (and nothing with probability 85%). (b) Probability of 19% of winning free services, out of which: 7% for one
7
year and 12% for half year (and nothing with probability 81%). (4) You are being oered to get a severance payment in a few alternatives. Which alternative would you choose? (a) 5,400 NIS in two months. (b) 5,600 NIS in eight months. (c) 5,900 NIS in one year and two months. (5) You may participate in one of the following lotteries. Which lottery would you choose? (a) Probability 18% to get 20,000 NIS (and nothing with probability 82%). (b) Probability 33% to get a prize, out of which 10% for 20,000 NIS and 23% of 7,000 NIS (and nothing with probability 67%). (c) Probability 45% to get 7,000 NIS (and nothing with probability 55%). [ 2 more questions are in the next page. ] (6) You have to pay annual tuition for the university in one of the following alternatives. Which alternative would you choose? (a) Paying a down payment of 4,500 NIS, and additional 10 monthly installments of 470 NIS (total amount 9,200 NIS). (b) Paying a single payment of 9,000 NIS. (7) You may participate in a lottery for free public transportation. Which lottery would you choose? (a) Probability 23% of winning free transportation, out of which: 8% for one year and 15% for half year (and nothing with probability 77%). (b) Probability 31% of winning free transportation for half year (and nothing with probability 69%).
Version 2a You are being asked to answer the following questions. Answers will be analyzed anonymously for a research on decision making. Please choose a single answer to each question. Thank you for you cooperation. (1) Sex (a) Male (b) Female (2) You are being oered to get a scholarship award in a few alternatives. Which alternative would you choose? (a) 5,400 NIS in two months. (b) 5,600 NIS in seven months. (3) You may participate in one of the following lotteries. Which lottery would you choose? (a) Probability 18% to get 20,000 NIS (and nothing with probability 82%).
8
(b) Probability 33% to get a prize, out of which 10% for 20,000 NIS and 23% of 7,000 NIS (and nothing with probability 67%). (4) You have to pay annual tuition for the university in one of the following alternatives. Which alternative would you choose? (a) 10 monthly installments of 1,000 NIS each (total amount - 10,000 NIS). (b) A down payment of 4,700 NIS, and 10 monthly installments of 500 NIS each (total amount - 9,700 NIS). (c) Paying a single payment of 9,500 NIS. (5) You may participate in a lottery for free public transportation. Which lottery would you choose? (a) Probability 15% of winning free transportation for one year (and nothing with probability 85%). (b) Probability of 19% of winning free transportation, out of which: 7% for one year and 12% for half year (and nothing with probability 81%). (c) Probability 25% of winning free transportation for half year (and nothing with probability 75%). [ 2 more questions are in the next page. ] (6) You are being oered to get a severance payment in a few alternatives. Which alternative would you choose? (a) 6,200 NIS in eight months. (b) 6,500 NIS in one year and two months. (7) You may participate in one of the following lotteries. Which lottery would you choose? (a) Probability 37% to get a prize, out of which 11% for 15,000 NIS and 26% of 5,000 NIS (and nothing with probability 63%). (b) Probability 50% to get 5,000 NIS (and nothing with probability 50%).
Version 2b You are being asked to answer the following questions. Answers will be analyzed anonymously for a research on decision making. Please choose a single answer to each question. Thank you for you cooperation. (1) Sex (a) Male (b) Female (2) You are being oered to get a severance payment in a few alternatives. Which alternative would you choose? (a) 6,000 NIS in two months. (b) 6,200 NIS in eight months. (3) You may participate in one of the following lotteries. Which lottery would
9
you choose? (a) Probability 20% to get 15,000 NIS (and nothing with probability 82%). (b) Probability 37% to get a prize, out of which 11% for 15,000 NIS and 26% of 5,000 NIS (and nothing with probability 63%). (4) You decided to buy a plasma TV. The store oers you two remuneration plans. Which plan would you choose? (a) 10 monthly installments of 950 NIS each (total amount - 9,500 NIS). (b) A down payment of 4,500 NIS, and 10 monthly installments of 470 NIS each (total amount - 9,200 NIS). (c) Paying a single payment of 9,000 NIS. (5) You may participate in a lottery for free photocopying services. Which lottery would you choose? (a) Probability 17% of winning free services for one year (and nothing with probability 83%). (b) Probability 23% of winning free services, out of which: 8% for one year and 15% for half year (and nothing with probability 77%). (c) Probability 31% of winning free services for half year (and nothing with probability 69%). [ 2 more questions are in the next page. ] (6) You are being oered to get a scholarship award in a few alternatives. Which alternative would you choose? (a) 5,600 NIS in seven months. (b) 5,900 NIS in one year and one month. (7) You may participate in one of the following lotteries. Which lottery would you choose? (a) Probability 33% to get a prize, out of which 10% for 20,000 NIS and 23% of 7,000 NIS (and nothing with probability 67%). (b) Probability 45% to get 7,000 NIS (and nothing with probability 55%).
C Raw Data We describe below the variable names used in Table C.1:
# Department Economics C.S. Physics Version Sex Q2-Q7
subject number subject's department: Economics
Computer Science Physics
questionnaire's version (see appendix B).
subject's sex (question 1) subject's answer to each question
10
Table C.1 Raw Data
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
1
c.s.
1b
m
b
a
c
b
b
a
2
c.s.
1a
f
a
b
a
c
b
b
3
c.s.
1b
f
b
b
c
b
b
a
4
c.s.
1b
f
b
a
c
b
b
b
5
c.s.
1b
m
b
b
c
c
b
b
6
c.s.
1b
m
a
b
c
c
a
b
7
c.s.
1b
m
b
b
c
c
b
b
8
c.s.
1b
m
b
b
a
b
b
a
9
c.s.
1b
m
b
b
a
b
b
b
10
c.s.
1b
m
b
b
a
c
b
b
11
c.s.
1b
m
a
b
c
b
b
a
12
c.s.
1b
f
a
b
c
c
b
b
13
c.s.
1b
m
b
a
a
b
a
b
14
c.s.
1b
m
b
b
a
c
b
b
15
c.s.
1b
m
b
a
c
c
b
b
16
c.s.
1b
f
b
b
a
c
a
a
17
c.s.
1b
f
b
b
c
c
b
b
18
c.s.
1b
f
b
b
c
a
b
b
19
c.s.
1a
f
b
b
c
c
b
a
20
c.s.
1a
m
b
b
c
c
b
b
21
c.s.
1a
m
b
b
a
c
b
b
22
c.s.
1a
f
a
b
a
a
b
b
23
c.s.
1a
m
a
a
c
c
a
a
24
c.s.
1a
m
a
a
c
c
a
a
25
c.s.
1a
f
b
b
c
b
a
a
26
c.s.
1a
f
a
b
c
b
b
a
27
c.s.
1a
m
a
a
a
c
b
b
28
c.s.
1a
m
a
a
a
c
a
b
29
c.s.
1a
f
a
b
c
c
b
b
11
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
30
c.s.
1a
m
a
b
c
b
a
a
31
c.s.
1a
m
b
a
c
c
b
a
32
c.s.
1a
m
b
b
a
b
a
a
33
c.s.
1a
m
b
b
a
b
b
a
34
c.s.
1a
m
a
b
a
b
a
a
35
c.s.
1a
f
a
b
a
c
a
b
36
c.s.
1a
m
b
b
c
c
b
b
37
c.s.
1a
f
b
b
c
b
b
b
38
c.s.
1a
m
b
b
a
b
b
a
39
c.s.
1b
f
b
b
a
b
a
a
40
c.s.
1b
m
a
b
a
c
b
a
41
c.s.
1b
m
a
a
a
b
a
a
42
c.s.
1b
m
b
a
c
c
a
b
43
c.s.
1b
m
b
b
c
b
b
a
44
c.s.
1b
f
a
b
a
c
a
b
45
physics
1b
m
b
a
a
c
b
b
46
physics
1b
m
a
b
a
c
a
b
47
physics
1b
m
b
b
a
b
b
b
48
physics
1b
m
b
a
c
c
b
b
49
physics
1b
f
b
b
c
c
b
b
50
physics
1b
m
a
a
c
b
a
b
51
physics
1b
m
a
b
b
a
b
b
52
physics
1a
m
b
b
a
a
a
a
53
physics
1a
m
a
a
a
a
b
b
54
physics
1a
m
b
b
c
c
b
a
55
physics
1a
m
b
a
c
c
a
b
56
physics
1a
m
b
b
c
a
b
b
57
physics
1a
f
a
b
a
c
b
b
58
physics
1a
m
a
b
a
c
a
b
59
physics
1a
m
b
b
a
c
b
a
12
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
60
economics
1a
m
a
b
c
c
a
b
61
economics
1a
f
a
b
a
c
a
b
62
economics
1a
m
a
b
a
c
a
b
63
economics
1a
f
b
b
c
a
b
b
64
economics
1a
f
b
b
a
a
b
a
65
economics
1b
f
b
b
c
b
a
a
66
economics
1b
f
a
b
a
c
a
b
67
economics
1b
m
a
b
b
b
a
b
68
economics
1b
f
a
a
a
a
a
b
69
economics
1b
f
b
b
b
b
a
b
70
economics
1a
m
b
a
a
c
b
a
71
economics
1a
f
b
b
a
c
b
b
72
economics
1a
m
b
b
c
b
a
a
73
economics
1b
m
b
a
b
b
a
b
74
economics
1b
f
b
b
c
c
a
b
75
economics
1b
f
a
a
a
c
a
b
76
economics
1a
m
b
b
a
b
a
b
77
economics
1a
m
b
b
c
b
b
b
78
economics
1a
m
b
b
a
c
a
a
79
economics
1b
m
b
a
c
b
a
a
80
economics
1b
m
b
b
c
b
b
a
81
c.s.
2b
m
a
b
a
c
b
a
82
c.s.
2b
m
a
b
b
b
b
b
83
c.s.
2b
m
a
b
a
b
a
b
84
c.s.
2b
m
a
a
b
a
a
a
85
c.s.
2a
f
a
b
a
c
b
b
86
c.s.
2a
m
a
b
c
c
a
a
87
c.s.
2b
m
b
b
c
c
b
b
88
c.s.
2a
m
a
b
b
c
a
b
89
c.s.
2a
m
a
a
b
a
a
a
13
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
90
c.s.
2b
f
b
b
c
c
b
b
91
c.s.
2a
m
a
b
b
c
a
b
92
c.s.
2a
f
b
a
c
a
a
a
93
c.s.
2a
m
a
b
c
a
a
a
94
c.s.
2a
m
b
b
c
c
b
b
95
c.s.
2b
m
a
b
b
a
b
b
96
c.s.
2a
m
b
a
c
c
b
b
97
c.s.
2b
m
a
a
c
c
b
b
98
c.s.
2a
f
a
b
c
a
a
b
99
c.s.
2b
m
a
b
a
c
b
b
100
c.s.
2b
m
a
b
a
c
a
b
101
c.s.
2b
m
a
b
a
c
a
a
102
c.s.
2b
m
a
b
a
c
a
a
103
c.s.
2a
m
a
b
a
c
b
b
104
c.s.
2a
m
b
b
b
c
b
b
105
c.s.
2b
m
a
b
a
c
a
a
106
c.s.
2b
m
a
b
b
b
b
a
107
c.s.
2a
m
a
a
c
b
a
b
108
c.s.
2a
m
a
b
c
a
a
a
109
c.s.
2a
m
a
b
c
b
a
a
110
c.s.
2b
f
a
b
c
c
a
a
111
c.s.
2b
f
b
a
c
c
b
b
112
c.s.
2b
m
b
b
c
c
b
b
113
c.s.
2a
m
b
b
c
b
b
b
114
c.s.
2a
m
a
b
c
c
b
b
115
c.s.
2a
m
b
b
b
b
b
a
116
c.s.
2a
m
a
b
c
c
a
b
117
c.s.
2a
m
b
b
c
b
b
b
118
c.s.
2b
f
a
b
b
b
b
b
119
c.s.
2a
m
b
b
c
c
b
a
14
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
120
c.s.
2b
f
b
b
c
b
b
b
121
physics
2a
f
a
b
c
c
b
b
122
physics
2a
m
b
a
b
c
a
b
123
physics
2a
m
b
a
c
a
b
b
124
physics
2a
m
a
b
c
c
b
b
125
physics
2a
m
a
b
c
a
a
a
126
physics
2b
m
b
b
c
b
b
b
127
physics
2b
f
b
b
c
c
b
b
128
physics
2b
f
b
a
a
c
b
a
129
physics
2b
m
b
b
b
a
b
b
130
physics
2b
m
b
b
c
c
b
b
131
physics
2b
m
b
b
c
c
b
b
132
physics
2b
m
a
b
a
a
b
a
133
physics
2b
f
b
b
c
c
b
b
134
economics
2a
f
a
b
c
a
a
b
135
economics
2a
f
a
b
c
b
a
a
136
economics
2a
m
a
a
a
b
b
a
137
economics
2a
m
a
b
c
c
b
b
138
economics
2a
m
b
b
a
c
b
b
139
economics
2b
m
b
a
c
c
b
a
140
economics
2b
m
b
b
b
c
a
a
141
economics
2b
f
a
b
a
c
a
b
142
economics
2b
m
a
a
a
a
a
a
143
economics
2b
m
b
b
c
b
b
a
144
economics
2a
m
a
b
a
c
a
b
145
economics
2a
m
a
b
b
b
a
a
146
economics
2b
m
b
b
b
b
a
b
147
economics
2b
f
b
b
b
c
a
b
148
economics
2a
m
b
a
c
c
a
b
149
economics
2a
f
a
b
a
c
a
a
15
#
Department
Version
Sex
Q2
Q3
Q4
Q5
Q6
Q7
150
economics
2a
f
b
a
b
c
a
b
151
economics
2b
m
a
a
c
a
a
a
152
economics
2b
f
a
b
b
c
a
b
153
economics
2b
m
b
b
c
a
a
a
16
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