Bounded Rationality inTravel Behavior Modeling	
Takayuki Morikawa (Nagoya Univ.)
Toshiyuki Yamamoto (Nagoya Univ.)
Shinya Kurauchi (Ehime Univ.)
Hitomi Sato (Nagoya Univ.)

June 13, 2015
1

What is “Rationality”?	

1. Instrumental Rationality
2. Procedural Rationality
3. Expressive Rationality	

2

Instrumental Rationality	
• “Rational individuals” can 1) set the goals, 2) evaluate
the alternatives according to the goals, and 3) rank thealternatives by the preference order.
• Rationality is defined as the “instrument” to achieve thegoals.
• Since the preference rank is given by the order of“utility”, rational individuals are expressed as the utility
maximizers.
• It assumes that individuals 1) have all the attributes
values in the utility functions of all the available
alternatives, 2) know the probability distribution of theuncertain consequences, and 3) maximize the expectedutility.
3

Critiques to Instrumental Rationality	
• Many important decisions do not seem to use theinstrumental rationality.
–e.g., Follow traditional customs, other people’s decision,
fortune-tellers, etc.

• Social psychologists have shown many counterexamples in experimental environments.
–

Allais paradox, Ellsberg paradox, Framing effect, etc.

• Difficult to describe the information acquisition behavior.
–

When to stop obtain new information is very difficult to describe
by instrumental rationality because information is highly
heterogeneous.

4

Alternative Rationality: Procedural Rationality	• Acquisition and processing of information for decision
makings require human resources.
––

A chosen alternative may not be the optimum in terms ofachieving the goal, but may be the best decision if theinformation processing cost is considered.
“Satisfaction” may be more reasonable than optimization in thecontext of achieving the goals.

• “Bounded Rationality” (Simon, 1987) is a typical exampleof this category.
• “Following the social norm” may be categorized in thistype of rationality.

5Alternative Rationality: Expressive Rationality	
• “Choice” itself can be an objective rather than achieving
the goals.
• “Resolving cognitive dissonance” (Festinger, 1957) is atypical example of this category.
–An individual who holds conflicting attitudes and behaviors feels
uncomfortable and is motivated to resolve the dissonance bychanging either attitudes or behaviors.

6

Bounded Rationality vs. Instrumental Rationality	
Simon (1987) set up the following theoretical frameworks
in contrast with the instrumental rationality.
(1) The choice set generation process should be explicitly
considered rather than assuming the prespecified set.
(2) Heuristics should be considered to cope with theuncertainty of the consequences rather than assuming
the prespecified probability distribution.
(3) The principle of satisfaction should be used rather thanmaximization of expected utility.

7

Review of Decision-Making Strategies (1)	Let’s assume that every alternative is described by multiple
attributes.
(1) Additive Rule
The utility of an alternative is given by the weighted sum of
attribute values.

U n (i) = b1 X1n (i) + b2 X 2 n (i) + L + bK X Kn (i)This rule is usually employed in utility maximization models.

8

Review of Decision-Making Strategies (2)	(2) Rule of Maximizing Number of Attributes with Greatest
AttractivenessCompare an attribute one by one among alternatives and choose
the alternative with the greatest number of attributes that are most
attractive.

3 Wins	Alt.1	

X1n (1)X 2 n (1)

X 3n (1)X 4 n (1)

X 5n (1)

Alt.2	

X1n (2) X 2 n (2) X 3n (2) X 4 n (2) X 5n (2)2 Wins	Alt.1 will be chosen.	
9

Review of Decision-Making Strategies (3)	(3) Conjunctive Rule
The minimum requirement is assigned to each attribute and thealternatives that pass the requirements for all the attributes arechosen.

Alt.1	

X1n (1)X 2 n (1)

X 3n (1)X 4 n (1)

X 5n (1)

Alt.2	

X1n (2) X 2 n (2) X 3n (2) X 4 n (2) X 5n (2)Alt.3	

X1n (3) X 2n (3) X 3n (3) X 4n (3) X 5n (3)Red circled attributes satisfy the minimum requirement.	

Alt.2 will be chosen.	
10

Review of Decision-Making Strategies (4)	(4) Disjunctive Rule
The satisfactory level is assigned to each attribute and thealternatives that pass the satisfactory levels for any attributes arechosen.

Alt.1	

X1n (1)X 2 n (1)

X 3n (1)X 4 n (1)

X 5n (1)

Alt.2	

X1n (2) X 2 n (2) X 3n (2) X 4 n (2) X 5n (2)Alt.3	

X1n (3) X 2n (3) X 3n (3) X 4n (3) X 5n (3)Red circled attributes satisfy the satisfactory levels.	

Alt.2 and Alt.3 will be chosen.	
11

Review of Decision-Making Strategies (5)	(5) Lexicographic Rule
Assume that all the attributes can be sorted by the order ofimportance. The most important attribute is compared among all
the alternatives and the champion will be chosen. If somealternatives are tied, then the second most important attribute will
be compared, and so on.

Importance

1

2

3

4

5	

Alt.1	

X1n (1)X 2 n (1)

X 3n (1)X 4 n (1)

X 5n (1)

Alt.2	

X1n (2) X 2 n (2) X 3n (2) X 4 n (2) X 5n (2)Alt.3	

X1n (3) X 2n (3) X 3n (3) X 4n (3) X 5n (3)Alt.2 will bechosen.	

12

Review of Decision-Making Strategies (6)	(6) Elimination by Aspects (EBA)
Every attribute is screened by whether it has a certain aspect(e.g., “fare is less than 300 yen”, “can easily carry baggage”) andalternatives that don’t have the aspect are eliminated until the lastalternative remains.
The order of attributes screened is not fixed but the attribute ischosen according to the probability that is proportional to theimportance of attributes.

13

Compensatory and Non-Compensatory Rules	
• By the compensatory rules, low-scored attributes of analternative can be compensated by high-scoredattributes, and vice versa.
–

e.g., high price of a car is compensated by its luxuriousness.

• By the non-compensatory rules, low-scored attributes ofan alternative cannot be compensated by high-scoredattributes, and vice versa.
–

e.g., omnibus type of transport is never chosen by a certainclass of people even if the fare is very low.

• Rules (1) and (2) are compensatory while rules (3), (4),(5) and (6) are non-compensatory.

14

Choice Contexts and Decision-Making Strategies	
• Which strategy is used will depend on the significanceof the choice consequence and the magnitude of
information processing load.
• In choice contexts of small number of alternatives,compensatory rules tend to be used.
• When the number of alternatives is large, noncompensatory rules may be employed to reduce thenumber of alternatives that will be considered more
carefully, e.g., by compensatory rules. (Decision with
mixed strategies)–

e.g., in choosing the type and model of cars, a single attributesuch as size of the engine is focused on to reduce the size ofthe choice set.
15

Bounded Rationality and Random Utility Models	• The framework of random utility models (RUM):

U n (i) = Vn (i) + ε n (i)• The random term ε n (i ) represents the unknown factors
to the analyst. Those factors may include the decision
strategy that the decision maker actually took.
• In that sense, it might be said that RUM canapproximate the unknown decision strategies.
• But the additive form in the systematic part of the utility
may contain a too strong assumption.

16

A Modeling Framework for Bounded Rationality	
• A probabilistic choice model with latent classes:	

Pn (i) = ∑ Pn (i s)Qn ( s)s∈SPn (i )

: Probability that individual n chooses alternative i	

Pn (i s ) : Probability that individual n chooses alternative i giventhat n belongs to latent class s	

Qn ( s ): Probability that individual n belongs to latent class s	S: Set of latent classes	

17

Latent Choice Set Models	• Two-stage models with choice set formation (Manski 1977):	

Pn (i ) = ∑ Pn (i C )Qn (C )C∈GPn (i )

: Probability that individual n chooses alternative i	

Pn (i C ) : Probability that individual n chooses alternative i fromchoice set C	

Qn (C ) : Probability that individual n’s choice set is C	
G: The set of all the possible choice sets except null set	The choice model and choice set formation model
may have different decision-making strategies.	
18

Choice Set Formation Models	• Independent availability model (Swait & Ben-Akiva, 1987):{

Qn ( C ) = ∏ qn ( j )
j

d jC

(

1− d jC

1 − qn ( j ))}ConjunctiveRule	⎧ 1: if j ∈ C
d jC = ⎨⎩0 : otherwise

qn ( j ) : Probability that alternative j is included in the choice set	
• If the choice model can be expressed by a logit model:⎡⎤1⎢ exp(Vin )d jC
1−d jC ⎥
(
)
(
(
)
)
Pn (i ) =
q
j
1
−
q
j
∑
∏ n
n
⎥
1 − Qn (φ ) C∈Gn ⎢ ∑ exp(V jn ) j∈M n⎢⎣ j∈C
⎥⎦
19

{

}

Latent Classes for Different Decision-Making Rules	
• Classes may represent decision-making rules such as:	e.g., Logit model with linear-inattribute utility function	

Pn (i) = Pn (i compensatory)Qn (compensatory)+ Pn (i non-compensatory)Qn (non-compensatory)e.g., Semi-ordered
lexicographic model	
20

CASE STUDY #1	

21

Semi-ordered Lexicographic Rule	
Example: CAR vs. Dynamic Park & Ride (DP&R)

t：Travel Tme
c：Travel Cost
d：DistanceCAR
40 min.
200 yen-

DP&R
30 min.
1000 yen
Near

Importance1
2
3

Threshold
15 min.
500 yen.
Far- Evaluation is conducted in the attribute-by-attribute lexicographic
order.
- An alternative is rejected if the concerned attribute value of thealternative is inferior beyond the tolerable gap to the “best” alternative
Travel Time
(min.)

Travel Cost
(yen)
1000
Threshold
15min.

4540
30rejected

700

Threshold500yen

200
0

CAR

DP&R

0

CAR

DP&R

22

Model Formulation (1)Relative Evaluation of Attribute Value	
percentage deviated from the most desirable alternativemax ( X nkl ) − X nil~
k∈{i , j }Z nil =max ( X nkl )k∈{i , j }ExampleCar: 40min Rail: 30min
40 − 30~
Z car ,time == 0.3330
30 − 30~
Z rail ,time =
=0
30
23

Model Formulation (2)Threshold of Attributes	
probability of alternative i being rejected:~
qni (l ) = prob Z nil > τ nl[]

τ nl : log-normal distribution~⎛ ln Z nil − µl ⎞⎟⎟qni (l ) = Φ ⎜⎜σl⎝⎠f (τ )~
prob Z > τ

[

0

~
Z

]

τ
24

Model Formulation (3)Membership Function for Classification	

The hierarchy of attributes may vary across individuals
and is often unobservable for the analyst .
Probabilistic representation by Rank Logit Modele.g.）

Travel Time（t），Travel Cost（c），Distance to the Station（d）

Membership Function:

Ynl* = Γ l snl + ξ nl
Probability that Individual n’s First Ranked Attribute being Travel Time (t):Qn (t ) =exp(Γ t snt )∑ exp(Γ k snk )kProbability that Hierarchy of Attributes for Individual n being t, c, d:exp(Γ t snt )exp(Γ c snc )Qn (t ,c , d ) =⋅∑ exp(Γ k snk ) ∑ exp(Γ k snk )k∈{t ,c ,d }k∈{c ,d }25

Model Formulation (4)Choice Probability	Pn (i ) = Qn (t ,c ,d ){qni (t )qnj (t ) + qni (t )qnj (t )qni (c )qnj (c ) + qni (t )qnj (t )qni (c )qnj (c )qni (d )qnj (d )}+ Qn (t ,d ,c ){qni (t )qnj (t ) + qni (t )qnj (t )qni (d )qnj (d ) + qni (t )qnj (t )qni (d )qnj (d )qni (c )qnj (c )}+ Qn (c ,t ,d ){qni (c )qnj (c ) + qni (c )qnj (c )qni (t )qnj (t ) + qni (c )qnj (c )qni (t )qnj (t )qni (d )qnj (d )}+ Qn (c ,d ,t ){qni (c )qnj (c ) + qni (c )qnj (c )qni (d )qnj (d ) + qni (c )qnj (c )qni (d )qnj (d )qni (t )qnj (t )}+ Qn (d ,t ,a ){qni (d )qnj (d ) + qni (d )qnj (d )qni (t )qnj (t ) + qni (d )qnj (d )qni (t )qnj (t )qni (a )qnj (a )}+ Qn (d ,a ,t ){qni (d )qnj (d ) + qni (d )qnj (d )qni (a )qnj (a ) + qni (d )qnj (d )qni (a )qnj (a )qni (t )qnj (t )}+ qni (t )qnj (t )qni (c )qnj (c )qni (d )qnj (d )exp(Vni )exp(Vni ) + exp(Vnj )All Thresholds → 0 ： Non-compensatory Lexicographic Model→∞： Ordinary MNL Model

26

Model Performance（１）	
Distance: near, Parking: fully occupied

DP&R Share (%)

MNL Model

Proposed Model

50
40
30
20
10
0
0

200
400
600
DP&R - Car (yen)

800

1000

27

Model Performance（2）	

Distance: near, Parking: fully occupied

DP&R Share (%)

M NL M odel

Proposed M odel

80
60
40
20
0
0

5

10

15

20

25

30

Car-DP&R (min.)28

Findings from the Case Study	• Developed travel mode choice model including bothcompensatory and non-compensatory decision making
rules.
• Analyzed model performance and confirmed that theaggregate share dramatically changes around thethreshold values.

29More Psychological Approach	30

Prospect Theory (1) (Kahneman & Tversky, 1979)	
• Decision-making is assumed to have two stages:
value	

① Editing: cognitive process of information

Reference
Point	

risk aversive	consequence	risk prone	

Reference point may
shift under different
presentations	

31

Prospect Theory (2) (Kahneman & Tversky, 1979)	
② Evaluating: decision under subjective consequences andsubjective probability	

ation	
over-estim

subjective probability	

1.0	

0	

objective probability	

1.0	
32

CASE STUDY #2	

33

Mental Accounting Theory	
The total utility is composed of the “acquisition utility” andthe “transaction utility” (Thaler (1985) .
Acquisition Utility

U = AU ( p, − p ) + βTU (− p : − p*)Transaction Utility ：Perceived gain or loss in transaction
where

AU : AcquisitionUtility
TU : Transaction Utilityp : charged price of the goodp : value of the goodp* : refernce price of the goodβ : weight34

Reference Price (P*)

Reference Price: The price that thepurchaser believes to be fair.
We assume that the reference price fortransit ride is equal to the fare that theriders are paying.

35

Objective of the Study	
Analyze the effect of the Ride Point Program (RPP)(or Eco Point) in the context of discrete choice
travel behavior

Tested hypothesis:
The RPP is more efficient than the ordinary fare reduction
to promote ridership at the same operating cost.
Experiences from marketing research:
FFP or FSP is known as a powerful marketing tool. 	

36

Utility Change by the Two Policies	
Fare Reduction: Fare p → （p-Δp）	
Prior to implementation：	

U pr = AU ( p, − p)Right after impl.：	
U daf = AU ( p, − ( p − Δp)) + β d TU d (−( p − Δp) : − p*)
The reference price right after the implementation is the sameas the charged fare before the implementation.（p*=p）	

RPP: Fare p, Reward ΔpPrior to implementation：	

U pr = AU ( p, − p)Right after impl.：	
 U paf = AU ( p, − p) + β pTU p (−( p − Δp) : − p*)Assuming the reference price is the same as the chargedfare（p*=p）	
37

Time Dependent Utility	
Fare Reduction:

U daf 2 = AU ( p, − ( p − Δp)) + β d TU d (−( p − Δp) : − p*)
The reference price of FR converges intop-⊿p in the long run →TU=0

RPP:

U paf 2 = AU ( p, − p) + β pTU p (−( p − Δp) : − p*)
The reference price of RPP is unchanged （p*=p）	

Increase of TU
TU becomes 0 because
UU

p* becomes (p-⊿p)
U daf

U paf = U paf 2

U daf 2U

increase of TU

U pr

pr

increase of AU
implementation

time

38

implementationtimeEmpirical Study	RPP social experiments were conducted in
Nagoya to promote subway usage.
Data for the analysis
October, 2005
3000 households（2 questionnaires per household）	
 Citizens in Nagoya city
659 households, 948 individuals(response rate: 22.0 %）	
 39

Ranking Data on RPP	Rank the preference of the options
Type of policies
Option #1
Option #2

5% reduction
Fare reduction

Option #3
Option #4
Option #5
Option #6
Option #7
Most preferred（）	

Level of variables
10% reduction
20% reduction

Stored fare card 2,300 yen value for 2,000 yen
with premium
2,400 yen value for 2,000 yen
500 yen transit voucher per 100
pointsRide point
program
2nd

（

）	
 （

1,000 yen transit voucher per 100
points
3rd

4th

）	
 （

5th

）	
 （

6th

）	

（

Least preferred

）	

（

）	
40

Rating Data for RPPIntention to use public transportation to the city center
Most
preferred

2nd（option1）	
 （Most
preferred

（

）	

3rd

）	
 （

）	

Least
preferred

4th

（

4th

）	

（

）	

(option7)

5th

（

Least
preferred

6th

）	
 （

）	

（option4）	

1) I am already using by public
transportation, bicycle or walk2) I will use 	
3) I may use4) not sure5) I may not use6) I will not use

Using only current car users’ data（sample size: 144）	
Ranking data à Rank logit model
Rating data à Ordered-response logit model

41

Specification of Utility Function	
【Conventional model】

Amount of fare reduction

Part-worth of fare reduction
Part-worth of RPP

β c × ( p − Δp)
β c × ( p − Δp)
Amount of Reward【 Mental Accounting Theory model (MAT model)】× ( p − Δp) + β d × (Δp)β c × ( p ) + β p × (Δp )Part-worth fare reduction βPart-worth of RPP

c

TU

42

Estimation Results	
Estimates (t-statistic)
Variables

Conventional

MAT model

Travel time

-0.217 (-0.4)-0.449 (-0.8)

Travel cost (1,000 yen)

-11.5 (-9.4)-3.02(-2.5)

Dummy for fare reduction scheme

00Dummy for stored fare card with premium scheme

0.560(6.217)

0.081 (0.31)

Dummy for ride point program scheme

0.177 (2.24)

0.221(1.326)

Amount of fare reduction (1,000 yen)-

44.1 (17.6)

Amount of premium for stored fare card (1,000 yen)-

37.4 (7.8)

Amount of reward of ride point program(1,000 yen)-

63.4 (5.9)

AIC2093.1

1907.9ü The MAT model shows significantly better fit than theconventional one.
ü Parameters of TUs are positive, implying that individuals
seem to feel psychological gains.
ü Parameters of TUs are 12-20 times greater than the ‘travel43
cost’ parameter.

Utility Change with the Two Policies	
MAT model

Conventional model

2

RPP

1.8
1.6

Fare reduction

1.4
1.2

12
%
16
%
20
%

8%

4%

0%

1

rate

RPP
Fare
reduction

Stored fare card

12
%
16
%
20
%

Stored fare card

8%

2.2

4%

2.4

効用
Expected utility
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0

0%

Expected
utility
効用rate<Conventional model>
Preference for the three promotion schemes isdetermined by the alternative specific constants.
<MAT model>
RPP dominates the other two schemes for any reward
rate.
44

Predicted Probabilities of Transit Usage	
Fare Reduction

MAT

20%

20%

20%

10%

10%

10%

10%

0%

0%

0%

0%

0%

12
%
16
%
20
%

8%

0%

4%

I will use
I may not use

I may use
I will not use

0%

20%

20%

30%

16%

30%

12%

30%

30%

8%

40%

40%

4%

40%

40%

0%

50%

50%

12
%
16
%
20
%

50%

50%

8%

60%

60%

4%

60%

60%

12
%
16
%
20
%

Conventional

8%

MAT

4%

Conventional

RPP

Not sure・By the conventional model, public transportation usage
monotonically increases according to reduction rate.
・By the MAT model, the strong intention (“I will use”) sharply
increases for high reduction rates. ← more intuitive than 45
conventional model

Findings from the Case Study	
• Including the transaction utility may significantly
improve the goodness-of-fit of discrete choice models,
especially in the applications of usage promotions suchas price reduction and frequent user program.
• Magnitude of perceived gain represented by thetransaction utility may differ among the promotion
schemes.
• In our study, it is found that the RPP is most preferred forany rate of reward over fare reduction and stored farecard with premium. Since operating cost of the RPP islowest, RPP’s may be the most cost-effective promotion
scheme.
46

Thank you for your attention.	

47