reasoning-building process for transportation project ...docs.trb.org/prp/14-1784.pdf · 1...

Reasoning-Building Process for Transportation Project Evaluation 1

and Decision-Making: Use of Reasoning Map and Evidence Theory 2

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Paper 14-1784 7

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Nopadon Kronprasert, Ph.D. * 12

Research Associate 13

National Research Council 14

Federal Highway Administration 15

6300 Georgetown Pike, McLean, VA 22101, USA 16

Email: [email protected], Tel: +1 (202) 493-3214 17

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Antti P. Talvitie, Ph.D., Professor (em) 22

Aalto University, Finland 23

Rakentajanaukio 4, Pl 2100, Espoo, Finland 24

Email: [email protected] 25

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Submitted for review 31

Presentation at the 2014 TRB Annual Meeting and 32

Publication in Transportation Research Record 33

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Total Number of Words = 7489 words 39

(5739 words + 5 figures + 2 tables) 40

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November 2013 44

TRB 2014 Annual Meeting Paper revised from original submittal.

Reasoning-Building Process for Transportation Project Evaluation 1

and Decision-Making: Use of Reasoning Map and Evidence Theory 2

3

4

Abstract 5

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Policy-makers of today’s transportation investment projects engage in dialogues and debates in 8

which the reasonableness and clarity are of great value. In the traditional transportation systems 9

planning practices, different stakeholders reason and provide evidence in support of their 10

preferences, but these opinions are often conflicting and rarely consistent. This paper presents a 11

decision-aiding approach for finding a transportation alternative that best achieves the project’s 12

goals and also indicate the level of satisfaction of different stakeholders. The proposed approach 13

applies (i) a reasoning map to structure how experts and citizens perceive the alternatives for 14

achieving the project’s goals, and provides (ii) belief measures in evidence theory to what extent 15

the alternatives achieve the goals of different stakeholders. This method gives three kinds of 16

results. First, the degrees of goal achievement can be calculated for different stakeholders. 17

Second, the integrity of the reasoning and the quality of information are both evaluated based on 18

measures of uncertainty associated with this information. Finally, the critical reasoning links 19

that matter most significantly to goal achievement can be identified by means of sensitivity 20

analysis. The paper applies the proposed method to evaluate a Streetcar alternative against Bus 21

Rapid Transit alternative in a real-world transit alternatives analysis. The reasoning-building 22

process provides means for the planners and citizens to present their own logic and justifications. 23

This promotes focused discourse among different stakeholders and enriches the quality of the 24

planning and decision-making process. 25


Kronprasert, N. and Talvitie, A. P. TRB Paper 14-1784

1

1. INTRODUCTION 1 2

Planning and decision-making of transportation systems is a multidisciplinary process governed 3

by laws. In the U.S. SAFETEA-LU requires the consideration of a set of factors that reflect the 4

social benefits, costs and impacts. Policy-makers engage the public in planning process, which 5

both informs the public and reflects public purposes and needs through inclusion of stakeholder 6

input. This makes transportation planning and evaluation processes complex and require 7

reasonableness and clarity of judgment. 8

9

The transportation planning is a deliberative process of negotiation and consensus building that 10

is supported by rational analysis. (1, 2) Decision-making about a public transportation system is 11

not straightforward and requires negotiations. Often planning cannot advance because there is no 12

consensus with regard to the goals and expected outcomes of the project. 13

14

This study considers the planning of public transportation investment projects as a reasoning-15

building process to advance a desirable course of actions. A series of actions which achieve goals 16

give details of chained relations in a reasoning structure. The study approaches public 17

transportation decisions as decisions under uncertainty. Transportation analysts and planners 18

have incomplete knowledge or lack of information. 19

20

This study proposes a new goal-oriented transportation decision-aiding approach that models 21

decision systems in a logical manner and employs available even if uncertain knowledge and 22

inconsistent opinions in supporting decision-making. Section 2 comments briefly on the current 23

multi-criteria decision-making methods. Section 3 reasons the theoretical basis of the approach 24

to multi-criteria evaluation advocated in this paper. Section 4 details the practical steps for 25

applying the method and Section 5 gives an example application. Section 6 interprets the results 26

and discusses the intellectual merits of the approach. Section 7 concludes. 27

28

29

2. CURRENT PRACTICES AND THEIR ISSUES 30

31

Multi-criteria decision-making approaches have been applied for evaluating transportation 32

investment projects since 1970s (3). In a large-scale transportation decision problem, traditional 33

transportation planning and evaluation approaches are constructed with a decision tree structure 34

where the transportation system is decomposed into independent subsystems and the attributes of 35

a system are modeled in a hierarchical tree structure. 36

37

The tree structure has been favored by many planners and analysts because of its visualization of 38

the decision problem, and the simple mathematical operator used in the analyses. However, it 39

requires several simplifications and assumptions (4, 5). First, the tree-structure presents a 40

classification of attributes, but it does not present the dependent relationships between them and 41

their positive and negative effects. Second, the hierarchical structure cannot handle redundancy 42

of attributes when one attribute belongs to two categories. This redundancy is common and 43

always present in real-world problems. Third, the assignment of the values to the weights is 44

problematic. The weight can represent either an absolute value which the attribute contributes to 45

its class, or the importance of one attribute relative to another attribute in the same class. Within 46



2

a tree structure it is difficult to measure or compare the degree of contribution or the degree of 1

importance when two attributes are subjective, have different units, or are redundant. The linear 2

scoring method leaves room for “strategic inputs” in assigning the weights. The Analytical 3

Hierarchy Process (AHP) method gets around the weighting problem by pair-wise comparisons; 4

but, the issues of redundancy and interdependency remain. (6) 5

6

The traditional transportation system or project evaluation approaches do not have transparent, 7

sufficient and clearly reasoned justifications for preferring a specific transport alternative in 8

situations, which involve complicated chains of reasoning, uncertainty about information and 9

limited understanding. This is for three reasons: 10

11

First, there is insufficient knowledge about the relevant variables to build up chained reasons for 12

outcomes or goal attainment. Second, none of the traditional transport planning and evaluation 13

approaches structure the problem in such a way that the reasoning process can be modeled. They 14

simplify the problem, and are sometimes considered a “black box” where the inputs and the 15

relations between inputs and outputs are not fully described or are results of imagination. Third, 16

in reality, the goals and performance of alternatives are assessed and presented both in 17

quantitative and qualitative terms in a decision table format. In sum, without full knowledge and 18

information it is simply not possible to justify decisions using the traditional approaches. The 19

important question is how reliable are the values and judgments in the decision table and how 20

much they can be trusted. In the sequel, these values are called the measures of strength of 21

evidence for goals and performance. 22

23

Transport analysts and planners develop implicit reasoning chains when evaluating transport 24

alternatives; but, that reasoning is unstructured and undocumented. This causes difficulties in 25

understanding the bases of decision-making because there are no measures for inconsistency, 26

conflicts, and omissions without reference to the complexity of the problem. Therefore, in 27

practice, the evaluation and planning approaches are not enough for communicating decisions 28

because the (supposed) decision variables and criteria are not supported in a fact-based manner. 29

30

This paper views evaluation of transportation alternatives as a complex reasoning process, which 31

consists of various elements of both transportation and non-transportation nature and involves 32

diverse groups of stakeholders. 33

34

35

3. CONCEPTS OF REASONING-BUILDING PROCESS 36

37

A transportation decision problem consists of three components: objectively defined 38

transportation alternatives (supply side); the demand side comprising behavioral and 39

socioeconomic factors; and subjectively defined goals and objectives of the project (7). How to 40

explain the inter-relationships between these three is very challenging. The study proposes a 41

reasoning-building process and applies the following two concepts in reasoning process. 42

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3

3.1 Mapping Structure for Reasoning Process 1

2

A reasoning map is constructed for evaluating the alternatives. It consists of boxes connected 3

with links, which present the chain of reasoning of a collection of propositions and describe the 4

presumed cause-and-effect relationships among them (8-10). For evaluating transportation 5

alternatives, the reasoning map connects the set of transportation system characteristics to the 6

project’s goals and the relationships between the two are described by a series of performances 7

and impacts as shown in Figure 1. The reasoning map is useful in decision analysis because it is 8

easy to explain and is applicable in brainstorming and clarifying issues and uncertainties. 9

10

In Figure 1, the variables (boxes) are classified into four categories. Decision variables (Di) 11

present the physical and operational characteristics of transportation alternatives such as right-of-12

way, vehicles, propulsion system, stations, and control and management systems. Exogenous 13

factors (Ei) present attributes that are not part of the alternatives but affect the system 14

performances, such as predicted travel demand, and land use characteristics (transit oriented 15

development, TOD, can be made part of the Di’s). Consequences (Ci) present the expected 16

performances and impacts of transportation system, such as level of service, accessibility, air 17

pollution emission. Goals (Gi) boxes present the goals of the transportation project. 18

19 DECISION

VARIABLESCONSEQUENCES AND

EXOGENOUS FACTORSGOALS

D1

D2

D3

D4

D5

E1 C7

C1

G1

G2

G3

G4

C2

C4

C8

C5

C3

E2 C6 C9

C10

20 FIGURE 1 Structure of Reasoning Map 21

22

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3.2 Mathematical Formalisms for Reasoning 24

25

3.2.1 Representing Knowledge and Belief Distributions 26

27

Using the reasoning map, two knowledge representations are needed from (expert) opinions and 28

data sources. The first is knowledge about the inputs (decision variables and exogenous factors 29

in Figure 1), and the second is knowledge about the causal relations (links in Figure 1.) 30

31

Knowledge about inputs and relations is presented by the belief value (or the strength of 32

evidence). The initial values of the truth of the inputs and the relations are subjective and 33

expressed by stakeholders or predicted by the analysts. In evidence theory the belief value, m, is 34



4

expressed by a value between 0 and 1 (11). It presents the belief distribution across the states of 1

outcome (or the degree that each state of outcome is supported.) The belief distributions of the 2

input X and causal relation X→Y is expressed: 3

4

1XX

i

i

Xm (1) 5

1YY

ji

j

YXm (2) 6

7

where Xi and Yj are the possible states of outcome of sets X and Y, respectively. m(Xi) is the 8

belief value (or the strength of evidence) of the state Xi of set X. The causal relation m(Xi→Yj) is 9

the belief value that the state Yj of set Y will be the outcome given that the input X is Xi. 10

Equations (1) and (2) respectively imply the exhaustion of belief values of all states of outcome 11

in input X and all states of outcome in output Y given the input X, that is, they must sum up to 1. 12

13

For the input “X is X1”, the knowledge is specified by the belief value m(X1). For example, if 14

belief value of the premise “the service headway of Bus Rapid Transit is short” is 0.80, then 15

m(Short) = 0.80, or that “the operating speed of Light Rail is high” is 0.60, then m(High) = 0.60. 16

17

For the relation “If X is X1, then Y is Y1,” knowledge is specified by attaching the belief value 18

associated with causal relation XY, m(X1→Y1). For example, a belief value for causality “if the 19

population density along the transit line is high, then transit ridership is high” is 0.75. 20

21

The proposed method is an extension of the traditional Bayesian reasoning method (12). 22

However, the belief value in evidence theory is not the same as the probability value in 23

probability theory. Uniqueness of the belief value in evidence theory is its ability to specify 24

ignorance or “I don’t know (IDK)”. This is common in transportation planning when 25

stakeholders or analysts are not sure whether the outcome is X1 or not X1. Knowledge as “I don’t 26

know (IDK)” is conserved in the proposed approach. 27

28

3.2.2 Mechanism for Aggregating Opinions 29

30

Given multiple stakeholders in the planning process, knowledge from different experts (or 31

stakeholder groups) is combined by using Dempster’s rule of combination (DRC). DRC is an 32

aggregate operator in evidence theory used for combining two belief distributions (13, 14). Let 33

m1(X) and m2(X) be the belief distributions of a variable X from two experts where the outcomes 34

of X can be specific or non-specific, e.g. Low, Medium, High, or “I don’t know”. 35

36

Equation (3) combines the belief distributions of X from two experts (or stakeholder groups), m1 37

and m2. 38

39

VUVU

pVUVU

XXXX

VU

XXXXX

VU

iXmXm

XmXm

Xm

|,

21

|,

21

1 (3) 40

41



5

In Equation (3), the numerator is the sum of the product of the belief values that supports set X 1

assigned by (two) experts. The denominator is a normalizing factor which is the sum of the 2

product of the belief values associated with all the possible combinations of knowledge that are 3

not in conflict. In other words, it excludes the conflicting outcomes in the calculation. (13-14) 4

5

When two opinions support each other, the aggregation results in the higher belief value of the 6

given outcome. For example, if two stakeholders, say “Experts” 1 and 2, both say “the 7

population density will be High” with the belief value, m(High) = 0.80 for both and m(IDK) = 8

0.20 for both, then after combining the two opinions the new belief value for m(High) = 0.96 9

(and m(IDK) = 0.04.). Thus, with (new) consistent evidence, the belief value of m(High) 10

increased (or strengthened). 11

12

When two opinions are conflicting, the aggregation results in the compromising belief value 13

between the two. For example, if two “Experts” are in conflict––for “Expert 1” m1(High) = 0.80 14

(and m1(IDK) = 0.20)” and for “Expert 2” m2(Low) = 0.70 (and m2(IDK) = 0.30)”, then after 15

combining the two opinions the new belief values are: m(High) = 0.54, m(Low) = 0.32, and 16

m(IDK) = 0.14. Thus with (new) conflicting evidence, the belief value in “High population 17

density” and that in “Low population density” are both smaller than their original belief values. 18

19

When the “I don’t know” opinion (or weak opinion) is present, the aggregation favors the 20

“Expert” that has the stronger belief. For example, if “Expert 1” has strong belief that “the 21

population density will be High with m1(High) = 0.80 (and m1(IDK) = 0.20)” and “Expert 2” has 22

“I don’t know” opinion, m2(IDK) = 1.00, then after combining two opinions the new belief value 23

becomes: m(High) = 0.80 (and m(IDK) = 0.20). Thus when the weak and strong opinions are 24

combined, the stronger opinions would dominate the decision. 25

26

These mechanisms are intuitive and true in decision-making process. When new evidence 27

arrives, the analysts usually recognize whether it supports or opposes the current beliefs and 28

instead of retaining the ambiguity there is a learning process to update knowledge (or belief 29

value); and as a result, the “IDK” opinion vanishes is diminished. 30

31

32

3.2.3 Mechanism for Inferring the Belief Values in the Reasoning Process 33

34

Given knowledge about an input X and a causal relation X→Y, the belief value of an outcome Y 35

is calculated as follows. 36

37

XX

jiij

i

YXmXmYm (4) 38

39

where Xi and Yj are all the possible states of the input X and the outcome Y. Using this method 40

for inference, the belief value (m) can be propagated to other variables (consequences/outcomes) 41

along the reasoning chains. More details on the belief propagation process can be found in 42

Dubois and Prade (1988) and Kronpraseert and Kikuchi (2011) (15, 16). 43

44

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6

3.2.4 Mechanism for Measuring Uncertainty 1

2

Uncertainty is the lack of knowledge (or ambiguity associated with information used). 3

Measuring uncertainty helps identify information needs in the reasoning process. The amount of 4

uncertainty is quantified by two measures: non-specificity measure and discord measure. These 5

measures quantify the “bits” of information needed to find the outcome or make the decision in 6

the binary problem. For instance, it needs 1 bit of information to specify the outcome when 7

tossing a coin (Head or Tail). 8

9

Non-specificity, N(m), refers to uncertainty due to imprecise knowledge. N(m) increases when 10

the belief value of “I don’t know” increases and the belief values on the specific states decreases. 11

The discord measure, D(m), refers to uncertainty due to conflicting opinions. D(m) increases 12

when the belief values of two or more states are even. 13

14

The calculation and derivation of these two measures are found in evidence theory Klir and 15

Wierman (1999) and Klir (2006) (13, 14). 16

17

AA

ii

ii

AAmAmN 2log (5) 18

AA AA j

ji

ji

ii jA

AAAmAmAmD 2log (6) 19

20

where |Ai| and |AiAj| are respectively the size of the outcome set Ai and the size of intersection 21

between outcome sets Ai and Aj. log2|Ai| is the bits of information needed to find out the solution 22

to the binary problem. 23

24

N(m) and D(m) have a maximum value of the logarithm base 2 of the number of outcomes. For 25

example, consider three outcomes: “Low,” “Medium,” and “High.” If there is total lack of 26

knowledge about the outcomes m(IDK) = 1, then Non-specificity is at maximum, N(m) = log2(3) 27

= 1.585, but because there is unanimity about it, Discord D(m) = 0. If the opinions supporting 28

the three outcomes are in conflict (i.e. 0.333 each), then Discord D(m) = log2(3) and Non-29

specificity N(m) = 0. Note that the total uncertainty measure is equal to N(m) + D(m). 30

31

Table 1 (Columns No.1 to No.5) shows the increase of non-specificity measure with respect to 32

different patterns of belief distribution. The non-specificity measure gets the lowest value when 33

all the belief values point to single specific outcome (Column No.1), while the non-specificity 34

measure gets the highest value in the case of complete ignorance or “I don’t know.” In this case, 35

all the belief values are assigned to every outcome, m(IDK) = 1 (Column No.5). 36

37

Table 1 (Columns No.6 to No.10) shows the increase of discord measure with respect to different 38

patterns of belief distribution. The discord measure receives the lowest value when all the belief 39

values point to only one specific outcome (Column No.6). The discord measure receives the 40

highest value when the belief values is uniformly distributed over the outcomes, m(X1) = m(X2) = 41

m(X3) = 0.333 (Column No.10). 42

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7

TABLE 1 Effect of Belief Distribution Patterns on Non-specificity and Discord Measures 1

Outcome of

Population density

Belief

Value

Examples of Different Belief Distribution Patterns

No.1 No.2 No.3 No.4 No.5 No.6 No.7 No.8 No.9 No.10

Low (X1) m(X1) 1 0.8 0.5 0.25 0 1 0.80 0.60 0.5 0.333

Medium (X2) m(X2) 0 0 0.25 0.25 0 0 0.20 0.40 0.25 0.333

High (X3) m(X3) 0 0 0 0 0 0 0 0 0.25 0.333 I don’t know (Low

or Medium or High)

m(IDK) 0 0.2 0.25 0.5 1 0 0 0 0 0

Non-specificity measure 0.000 0.317 0.396 0.792 1.585 0.000 0.000 0.000 0.000 0.000

Discord measure 0.000 0.385 0.785 0.632 0.000 0.000 0.722 0.971 1.500 1.585

Total uncertainty measure 0.000 0.702 1.181 1.424 1.585 0.000 0.722 0.971 1.500 1.585

2

3

3.2.5 Numerical Example 4

5

This section illustrates a numerical example of the three mathematical mechanisms presented in 6

the last three sections. The first is the inference process which propagates the belief values from 7

premises to consequences/outcomes. The second is the aggregation of knowledge of different 8

opinions. And the third is the measuring of uncertainty of knowledge. These three mechanisms 9

are described using numerical examples. 10

11

Consider two reasoning chains supporting economic development by a Streetcar alternative as 12

shown in Figure 2. One argues that Transit Oriented Development (X) will encourage investment 13

in the corridor (Z). Another argues that permanence of transit system (Y) will increase investment 14

in the corridor (Z). The reasoning chains connect between X and Z and between Y and Z. Each 15

attribute has two states of opinions: “Agree” and “Disagree,” and “I don’t know” state is added 16

for non-specific opinions. Knowledge (or belief values) about the two inputs m(X) and m(Y), and 17

knowledge of the two causal relations, m(X→Y) and m(X→Z), are shown in Figure 2. The belief 18

values about the outcome “Investment in the Corridor,” m(Z), are calculated as follows. 19

20

Using inference method, the degrees of truth of input, m(X), are combined with the degrees of 21

truth of the relation X→Y, m(X→Y) using matrix multiplication. Let X1, X2, and (X1X2) are 22

“Agree,” “Disagree,” and “I don’t know” for “Transit-Oriented Development,” respectively. Z1, 23

Z2, and (Z1Z2) are “Agree,” “Disagree,” and “I don’t know” about “Investment in the 24

Corridor,” respectively. The belief value of the outcome Z from the first reasoning chain m(I)

(Z), 25

for TOD, are calculated as follows (Figure 2) 26

27

52.0||| 212112211111

)( XXmXXZmXmXZmXmXZmZm I 28

12.0||| 212122221122

)( XXmXXZmXmXZmXmXZmZm I 29

36.0|| 212121112111|2121

)( XXmXXZZmXmXZZmXmXZZmZZm I 30

31

Similarly, the belief values of the “Investment in the Corridor” from the second chain m(II)

(Z) for 32

“Permanence of Transit Service” are: 33

34

35



8

68.0||| 212112211111

)( YYmYYZmYmYZmYmYZmZm II 1

13.0||| 212121121122

)( YYmYYZmYmYZmYmYZmZm II 2

19.0||| 2121212221112121

)( YYmYYZZmYmYZZmYmYZZmZZm II 3

4

Using Dempster’s Rule of Combination, the belief values of the outcome Z (“Investment in the 5

Corridor”) from two reasoning chains, m(I)

(Z) and m(II)

(Z), are aggregated (see the grey table in 6

Figure 2). The combined belief value m(Zi)––“Agree,” “Disagree,” “IDK”––is calculated as 7

shown below: 8

9

82.0

09.006.01

25.010.035.0

1

or or

1

)(

2

)(

2

)(

1

)(

1

)(

21

)(

21

)(

1

)(

1

)(

1

)(

1

ZmZmZmZm

ZmZZmZZmZmZmZmZm

IIIIII

IIIIIIIII

10

10.0

09.006.01

05.002.002.0

1

or or

1

)(

2

)(

2

)(

1

)(

2

)(

21

)(

21

)(

2

)(

2

)(

2

)(

2

ZmZmZmZm

ZmZZmZZmZmZmZmZm

IIIIII

IIIIIIIII

11

08.0

19.006.01

07.0

1 1

)(

2

)(

2

)(

1

)(

21

)(

21

)(

21

ZmZmZmZm

ZZmZZmZZm

IIIIII

III

12

13

Using the evidence theory, the non-specificity N and discord D measures associated with the 14

combined belief distributions of the outcome Z (“Investment in the Corridor”) are 15

16

080.0080.000log 2 ZZ

ii

ii

ZZmZmN 17

462.0000.0284.0178.0log 2

ZZ ZZ j

ji

ji

ii jZ

ZZZmZmZmD 18

19

These N(m(Z)) and D(m(Z)) values for Z add up to total uncertainty of 0.542 (0.080+0.462), 20

whereas the maximum uncertainty of outcome Z is log2(2) = 1.000. These values imply that the 21

opinions about the outcome Z are quite specific––N(m(Z)) is small. However, there is discord 22

about whether there would be “investment along corridor” or not––D(m(Z)) is moderate. 23

24

25 FIGURE 2 Example of the calculation process 26

27

28



9

4. STEPS OF REASONING-BUILDING PROCESS 1 2

The steps in the proposed reasoning process for evaluating transportation alternatives are the 3

following. 4

5

Step 1: Construct the reasoning maps to present how the proposed alternatives would 6

influence the achievement of goals of the project. 7

Step 2: Assign the belief values to individual premises and causal relations by eliciting 8

“Expert” opinions. 9

Step 3: Execute the model by calculating (i) the degree of achievement of each goal; (ii) 10

measuring the integrity of the reasoning process; and (iii) identifying critical 11

reasoning chains. 12

13

4.1 Construction of Reasoning Maps and Elicitation of Knowledge 14

15

Two steps are needed to construct the reasoning map. First, the transportation project’s goals 16

(G), the collection of variables that describe the characteristics of the systems (D) and the 17

forecast travel conditions (E) are identified in the planning process. The goals (end nodes G in a 18

reasoning map) reflect the purposes of the proposed (transit) projects. The definition of the 19

alternatives and the project description define the variables (starting nodes D and E) in the 20

reasoning map. 21

22

Second, the reasoning chains that determine the causalities are developed by bridging the 23

relationships between the alternatives and the project’s goals. The chains of reasoning are 24

developed using performance measures and arguments about alternatives (documented in the 25

planning process). They can be input-output relations, cause-and-effect relations, or inferences 26

for particular actions. The reasoning maps are scrutinized by experts and informed by public 27

input before further analysis. 28

29

Once the reasoning chains are developed, knowledge (or evidence) about every premise and 30

every causal relation in the reasoning chains are elicited from experts and planners and citizen 31

groups. These “informants” assign belief values to every state in premise (D and E) and every 32

state in relation shown in Figure 1. 33

34

Belief in an outcome for which two reasoning chains contribute can also be aggregated using the 35

DRC. This rule can be used for combining two belief distributions and two or more reasoning 36

chains (points of view). It builds up the belief values (or eliminate the degree of ignorance or “I 37

don’t know”) of stakeholders when supporting pieces of evidence are combined. 38

39

4.2 Model Execution 40

41

Once knowledge about every input to transportation alternatives and every relation in the 42

reasoning map has been elicited, the following calculation process is performed to evaluate the 43

transportation alternatives. 44

45



10

The transportation alternatives are evaluated based on the belief values for achieving the 1

specified goals. 2

The integrity of the reasoning process is evaluated based on the measures of uncertainty, 3

non-specificity, and discord associated with available information. 4

The critical reasoning chains that significantly influence the outcome are determined 5

based on the sensitivity analysis. 6

7

4.2.1 Determination of the Degree of Achievement of Individual Goals 8

9

Using the inference process shown in Equation (4), the belief values (or truth values), m, are 10

propagated from the input to the consequences/outcomes all the way to the individual goals. 11

12

Once the likelihoods for achieving the individual goals, m(Gi), are calculated, Belief (Bel) and 13

Plausibility (Pl) measures can also be calculated, which indicate the conservative and optimistic 14

measures of achieving the goals. 15

16

These two measures are derived from the belief distributions. Bel(Gi), is measured by summing 17

all the consistent evidence pointing to goal Gi. Pl(Gi) is the weight of non-conflicting evidence 18

toward goal Gi, obtained by summing the non-conflicting belief values for outcome Gi. 19

20

ipp GGG

pi GmGBel|

)()( and

ipp GGG

pi GmGPl|

)()( (7) 21

22

4.2.2 Measure of Integrity of Reasoning Process 23

24

Measuring uncertainty of information and knowledge helps identify information needs in the 25

reasoning chains and promotes focused discourse in the decision-making process. In this step, 26

the amount of information-based uncertainty in a reasoning chain is quantified using the non-27

specificity and discord measures previously described. They measure the quality of knowledge 28

and information given to the transport analyst. 29

30

4.2.3 Identification of Critical Reasoning Chains 31

32

Identifying the strong and weak reasoning chains of the process is necessary to justify the 33

validity of reasoning. This helps decision-makers determine which characteristics of alternatives 34

affect the decision most, and provide information on how to improve the alternatives in order to 35

improve goal achievement. 36

37

Given the belief distributions attached to each attribute in a reasoning map, one can determine 38

the strength and weakness of the reasoning chains; in other words, one can determine whether a 39

reasoning chain is more influential (or less uncertain) than the other chains. 40

41

To identify the critical chain in the reasoning map involves finding the variable that most 42

influence the degree of goal achievement. This sensitivity analysis is done by comparing the 43

degree of goal achievement when a particular variable is removed from the map with all the 44

variables in the reasoning map (the base case). 45



11

1

The higher the difference between the degrees of goal achievement, the more that variable 2

affects goal achievement. The determination of critical reasoning chains is conducted backward 3

(from the goal node to the decision nodes) by comparing the importance measures among its 4

preceding nodes and selecting that preceding node, which has the highest difference. 5

6

7

5. APPLICATION OF REASONING PROCESS TO TRANSPORTATION PLANNING 8

9

The proposed methodology to the Alternatives Analysis process was applied in a case study in an 10

evolving public transportation investment project in Northern Virginia. The Streetcar alternative 11

is evaluated and compared to the Bus Rapid Transit (BRT) alternative with respect to five goals 12

of the project––mobility, economic development, livability and sustainability, multimodal 13

transport system, and safety (16). 14

15

The reasoning map represents opinions of experts from transit and regional planning entities and 16

allowing “I don’t know”; ideally citizen views would also be collected. The reasoning map was 17

first drawn up by ten transport experts. The belief values, which represent the confidence of 18

opinions associated with each causal link, were assigned next. The mechanism for propagating 19

the belief values along the chains was applied, and the degree of belief for achieving the goals 20

was obtained. Finally, a measure of uncertainty associated with each variable and goal was 21

calculated to assess the quality of information and the reasons for selecting the preferred 22

alternative. 23

24

The study presents the model results as follows. First, the reasoning map configuration is shown. 25

Second, the degrees of goal achievement and their uncertainty measures are discussed. Finally, 26

the critical reasons supporting the goals are determined. 27

28

5.1 Reasoning Maps for Goal Achievement 29 30

The reasoning map developed is composed of 91 variables (22 decision variables, 2 exogenous 31

variables, 62 consequences/outcomes, and 5 goals.) For each variable (proposition), two 32

possible states of outcomes exist: “Agree” and “Disagree.” The “I don’t know” state is added to 33

imply non-specific opinion. 34

35

Figures 3 and 4 are examples of the reasoning map for the goal of “Improved Mobility” and 36

“Economic Development.” The reasoning maps for the remaining goals are not shown here. The 37

boxes on the left column present the decision variables of the transit technology, and the boxes 38

on the right column show the goals of the project. The intermediate boxes which connect 39

between decision variables and goals are a series of interrelated consequences and performances. 40

41

In the analyses, some variables in one map may be connected to the reasoning maps for the other 42

goals. For example, “Increase in transit riders” is related to ‘Improved Mobility’ (Goal 1) and 43

‘Economic Development’ (Goal 2). To simplify the presentation these connections are not 44

shown. 45

46



12

1

Improved

Mobility

Better Quality

Service

Increased Transit

Line Capacity

‘Higher’ Vehicle

Capacity

Increased

Transit Ridership

Attraction to

Transit Users

‘Longer’ Transit

Line Alignment

‘Rail-Based’

Support

‘Better’ Aesthetic

Appearance

‘Better’ Security

Technology

Increased Transit

Mode Share

‘Fixed’ Guideway Difficulty to

Pass Obstacles

Improved Transit

Frequency

Improved

Travel Time

‘Frequent’ Service

‘Multi-door’

Transit Vehicles

‘Low-floor’

Transit Vehicles

‘User-friendly’

Stop Design

Ease of Vehicle

Boarding

‘Local and Super’

Stop Locations

‘Larger’ Service

Area near Stops

‘Mixed Traffic’

Right-of-Way

Increased Vehicle

Operating Speed

‘Off-board’

Fare Collection

Increased Vehicle

Accessibility

Increased Station

Accessibility

Improved

Ride Quality

Increased Person

Throughput

Improved

Transportation

Capacity

Serve More

Activity Centers

Alternate Mode

of Travel

Reduced Boarding/

Alighting Time

Improved Service for

Transit Dependents

* ** *

**

2 3

FIGURE 3 Reasoning map for achieving Mobility Goal 4

5

6

Economic

Development

Possibility of

Investment along

the Corridor

Opportunity for

Transit-Oriented

Development

Adaptable to

Increased Ridership

Supporting

Population and

Employment Growth

Consistency with

County’s Economic

Development Initiatives

‘Higher’ Vehicle

Capacity

Increased

Transit Ridership

‘Consistent’

Planned Transit

Service

‘Fixed’ Guideway Permanence of

Transit Service

Focused

Development

along the Corridor

Serve More

Activity Centers

Opportunity

for Land

Redevelopment

Local Economic

Impacts

Connectivity to Jobs

and Educational

Opportunities

Increased

Property Values

Opportunity to Shape

Future Growth

‘Larger’ Service

Area near Stops

Increased Tax

Revenues

‘Longer’ Transit

Line Alignment

**

*

7 8

FIGURE 4 Reasoning map for achieving Economic Development Goal 9

10

11

12



13

5.2 Degrees of Goal Achievement and Uncertainty Measures 1 2

Two ‘Build’ alternatives are compared: Streetcar and Bus Rapid Transit alternatives. The belief 3

values that the Streetcar alternative achieves the goals of the project relative to the Bus Rapid 4

Transit alternative are evaluated. 5

6

Table 2 presents the degrees of goal achievement and their associated uncertainty measures of 7

the Streetcar alternative relative to the BRT alternative. There is agreement among the experts 8

that the Streetcar alternative supports most of the goals of the corridor project at high degrees of 9

achievement: 0.803-0.953 for mobility, 0.911-0.982 for economic development, 0.949-0.999 for 10

livability and sustainability. The exception is for multi-modal transport system, for which the 11

agreement is low (0.149-0.352). Achieving “Safe environment” is about the same (no difference 12

between two alternatives). The lower values of the degrees of achievement of individual goals 13

represent the conservative values (Bel) and the upper values represent the optimistic values (Pl), 14

the sum of belief values attached to “Agree” and “IDK.” 15

16

The high degree of consensus among the planners was not shared by the affected interest along 17

the project corridor. In the public meetings there was a distinct division: the older people (say 45 18

and over) favored the BRT while the younger favored the Streetcar. There were some young 19

renters in the meeting in whose opinion Streetcar (and TOD meant) “transit oriented 20

displacement” and for whom the economic development in the corridor would require moving 21

away from the city to a more affordable rent location. 22

23

TABLE 2 Belief and Uncertainty Measures of Goal Achievement (Streetcar vs. BRT) 24

Goals

Degrees of Goal Achievement Uncertainty Measures

Agree Disagree IDK

Non-

specificity Discord

Total

Uncertainty c

Improve Mobility 0.803 0.047 0.150 0.150 0.293 0.443

Encourage Economic Development 0.911 0.018 0.071 0.071 0.148 0.219

Promote Livability and Sustainability 0.949 0.001 0.050 0.050 0.041 0.091

Support Multi-modal Transport 0.149 0.648 a 0.203 0.203 0.567 0.770

Improve Safe Environment 0.012 0.961 b 0.027 0.027 0.099 0.126 a It is not believed among experts that Streetcar would support multi-modal transport compared to the BRT. 25 b It is not believed that Streetcar would provide safer environment than BRT. The safety of both Streetcar and BRT 26 are believed to be about the same. 27 c The maximum uncertainty of opinions associated with individual goal is log2(2) = 1.000 as there are two possible 28 outcomes: “Agree” and “Disagree.” 29 30

31

6. DISCUSSION 32

33

The proposed method may give the impression of complexity and laboriousness not worth the 34

value of the results. Anyone who has developed the data and calculations of a benefit-cost 35

analysis or has applied the AHP or the Bayesian method knows that impression is debatable or 36

even moot. It also needs to be kept in mind that this was the first application of the method and 37

improvements are possible. Two key issues arise from this study: how to use the proposed 38

approach in a real transport planning process, and how to interpret or benchmark its results. 39



14

1

The proposed approach has practical value in two respects. First, it quantitatively measures the 2

degree that the selected alternative achieves individual goals. This enables the affected interest to 3

understand and assess the strength not only of the reasoning process, but also of the planning 4

process and the alternatives considered. Because it incorporates the notion of “I don’t know” in 5

the calculation of the ‘truth’, both the conservative and optimistic views of the degree of goal 6

achievement are obtained. 7

8

The reasoning map and the associated belief values of each variable and their interrelationships 9

help identify the critical links that made the most important contributions to the truth and the 10

degree of achievement of the goals. Once the critical nodes and links are identified, the planners 11

can pinpoint the relationships which should be studied more to improve the strength of the 12

reasoning process. 13

14

6.1 Effects of “I Don’t’ Know” Opinions 15 16

Figure 5 shows the effects of the “I don’t know” opinion on the achievement of individual goals 17

measured by Belief (Bel) and Plausibility (Pl) measures. The sensitivity of “I don’t know” 18

opinion is tested by increasing the belief value of “I don’t know,” m(IDK), for all input variables 19

from 0 to 1 with an increment of 0.1, and proportionally decreasing the belief values of other 20

outcomes. When the “Experts” are very certain about their opinions, m(IDK) = 0, then the Belief 21

(Bel) and Plausibility (Pl) measures are equal. When “I don’t know” increases the difference 22

between Bel and Pl measures also increase rapidly. The Bel value decreases since evidence is 23

less certain. The Pl value increases because it represents “optimism” about the outcome (“if you 24

don’t know, then everything is possible”). The Bel measure is a conservative one (“if you don’t 25

know, then it is unlikely that the possible happens”). The difference between the two measures 26

indicates the degree of uncertainty about goal achievement. 27

28

29

30 31

(a) Belief (Bel) Measure (b) Plausibility (Pl) Measure 32

33

FIGURE 5 Effects of ignorance “IDK” on Belief and Plausibility of goal achievement 34

35

36



15

6.2 Critical Reasons 1 2

A sensitivity analysis was performed to identify the critical link(s) that most influence the 3

support of the Streetcar alternative. The critical chains contain the variables that highly support 4

the belief of achieving a goal. The critical reasoning chain that influenced the most the 5

achievement of Goal 1 are marked by (*) in Figures 3 and 4. Should there be much uncertainty 6

in achieving a goal by a particular alternative; the critical chain would indicate where more 7

resources should be employed to increase knowledge and to reduce the uncertainty or ambiguity. 8

9

In Figure 4, showing the ‘Mobility’ goal, Streetcar receives higher achievement than BRT 10

because the streetcars’ ride is smoother with higher riding quality than of buses, which may be 11

sensitive to pavement irregularities and traffic interruptions. Streetcar is also believed to be more 12

attractive to residents, commuters, and visitors. The number of transit users would increase, and 13

Streetcar would increase the capacity of the corridor and carry more transit passengers. 14

15

In Figure 5, showing the ‘Economic Development’ goal, Streetcar would be better than BRT. It 16

is believed that a fixed rail infrastructure is a permanent and long-term transit investment. It 17

would become a corridor landmark and community resource. It would bring more private 18

investment and would encourage more economic activities along the corridor. 19

20

21

7. CONCLUSIONS 22

23

The principal advantages of the proposed reasoning-building process are: (i) potential to model 24

the planners’ and stakeholders’ reasoning process in the evaluation of transportation alternatives; 25

(ii) flexibility to handle different opinions which may be incomplete, uninformed or informed, or 26

conflicting elicited from multiple actors; (iii) capability to measure uncertainty associated with 27

information or knowledge to focus debates and improve analyses; and (iv) documented paper 28

trail and record about the reasoning process leading to the recommendation for the selection of 29

an alternative. All of these are useful for later studies and analyses about anticipated or predicted 30

outcomes and will improve the scientific knowledge-base on how decisions are reasoned. The 31

proposed approach clarifies transportation decision-making processes where multiple experts or 32

actors are involved, and knowledge of individual experts is fragmented and opinions among 33

them may be conflicting. 34

35

The possible drawbacks of the proposed approach are two-fold. First, the reasoning map can be 36

manipulated by the analysts/planners. This manipulation is mitigated by the greater transparency 37

of the process than in the traditional approaches in which the analysts/planners’ reasoning is not 38

revealed in a reasoning map. It may be an advantage to the planners to know the stakeholders’ 39

evaluations and have an opportunity to understand the concerns of stakeholders and their 40

reasoning. It also is possible to customize the map to reflect the stakeholders’ reasoning path. 41

This is an important issue. The advantage of the reasoning process is the possibility to separate 42

plan development from plan evaluation based on the reasoning process. The planner can then 43

legitimately use the reasoning map in planning by studying its weak links. 44

45



16

Second, the mechanism to calculate the degree of goal achievement is susceptible to ‘group 1

think’. This indeed may have been the case in the case study project. The underlying concept of 2

the proposed mechanism leads to believing the stronger opinions and suspecting the weaker 3

opinions. The stronger opinions dominate the calculations. This seems to be true in any decision-4

making process. Therefore, for the method to be constructive, it is important that “strong beliefs” 5

are close to the “truth” or at least frank. The other side of this issue is that opinions of the 6

stakeholders need not be combined and the strong voice need not necessarily dominate, but even 7

the weak voice can be heard. 8

9

It is desirable in applying the proposed reasoning-building process that several groups of 10

stakeholders, possibly representing different views and values, are involved in planning work. 11

The success of the proposed approach depends on the agreement on the reasoning maps and the 12

integrity of knowledge used on assigning belief values on those maps. During the planning 13

process, the reasoning map should be reviewed by several groups of stakeholders for 14

reasonableness, comprehensiveness, clarity, and economy (parsimony) in carrying out the 15

evaluation. The experts and participating citizens should speak out honestly and genuinely about 16

their judgments and openly admit their understanding and degree of uncertainty in their opinions. 17

18

The reasoning-building process developed in the paper assists transportation planners to evaluate 19

alternatives, to reason about the alternatives, and to measure the validity of reasoning in the 20

evaluation. The decision model was created using the reasoning map structure and the 21

evaluation developed using the evidence theory. 22

23

The following two observations are central and important in the context of this application. 24

Detailed information about characteristics of the alternatives was available and considered, and 25

professionally worked through by experts before their interviews and in drawing up the 26

reasoning map. Significant consequences, which contribute to the goals of the project, were 27

discussed and anticipated. They are reflected in the reasoning map and show the underlying 28

thinking of the consulted experts. It is likely that in a real-world application a smaller reasoning 29

map would evolve over time and would not only be justified for planning purposes, but would 30

also clarify the decision situation. 31

32

The credibility of the proposed approach does not, however, depend only on the assignment of 33

beliefs on the various elements of the plans. Although the experts and the participating citizens 34

should be genuine and honest about their judgments and openly discuss about their degrees of “I 35

don’t know,” there is value simply in drawing up the reasoning map about the plans and discuss 36

and clarify the relationships among the plan elements. 37

38

This is important. The method can be applied partially by developing the reasoning map first. 39

The mathematical parts can be added later if desired. In fact, conceivably, such a need for some 40

quantification would arise spontaneously in response to curiosity about the degree of rationality 41

of the reasoning underpinning the plan proposals. In the citizen participation meetings attended, 42

not influenced by this paper or its authors, the participants were indeed divided into voluntary 43

groups and asked to draw diagrams for the presumed relationships in affected planning variables 44

and issues. The observed difficulty of the task was that the groups, which gathered around the 45

four or five tables with maps and papers, were heterogeneous and did not represent a cohesive 46



17

interest group or neighborhood. The groups also had limited time to accomplish their task. A 1

more structured approach, perhaps evolved over several public meetings would likely result in a 2

more useful reasoning map. When applied in several planning projects, experiential knowledge 3

thus gathered would support the learning curve to apply the method. The mathematical processes 4

applied and shown in this paper are not a requirement. They can come part of the applications 5

later. Thus, the method would not increase the cost or duration of planning, but clarify it and 6

make it more focused. There also could be savings. 7

8

The proposed approach is a useful and illuminating method for transportation planning purposes 9

in which stakeholders can review the experts’ and decision makers’ judgments and evaluation as 10

a process. The method can promote focused discourse among the transportation planners and 11

citizens because it reveals the degree of beliefs and uncertainty, and how much trust is placed on 12

a proposed alternative to achieve the goals it is intended to serve or achieve. 13

14

The method, which bears similarity on Forrester’s systems dynamics (18), is useful in decision 15

analyses because it is easy to understand and is applicable in brainstorming and compromising. It 16

is forward-looking and not restricted to using quantitative models or regressions models on past 17

data and behavior—which can be both its strength and Achilles’ heel. 18

19

20

ACKNOWLEDGEMENT 21 22

The authors would like to recognize the late Professor Shinya Kikuchi from Virginia Tech for his 23

significant contribution to this paper. Professor Kikuchi who died in December 2012 was one of 24

the authors of the first draft and main contributor to the ideas in the paper. 25

26

27

REFERENCES 28

29

1. Kanafani A., Khattak, A. and Dahlgren J. A Planning Methodology for Intelligent Urban 30

Transportation Systems, Transportation Research Part C, Vol. 2, No. 4, 1994, pp. 197-215. 31

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the Face of Bounded Rationality and Unbounded Uncertainty. Transportation Research Part 33

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3. Urban Mass Transportation Administration. Procedures and Technical Methods for Transit 35

Project Planning. Publication UMTA-UGM-20-91-1, Washington, D.C., 1990. 36

4. Rittel, H., and Weber, M. Dilemma in the General Theory of Planning. Policy Sci., Vol. 4, 37

1973, pp. 155-169. 38

5. Khisty, C. J. Can Wicked Problems Be Tackled Through Abductive Inference? Journal of 39

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Inc.., New Jersey, 2005. 45

8. Halpern, J. Y. Reasoning about Uncertainty. MIT Press, London, 2003. 46



18

9. Schwartz, M., Merkhofer, M., and Upton, R. Innovative Approach to Multiple-criteria 1

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37-50. 12

12. Dempster, A. P. A Generalization of Bayesian Inference (with discussion). Journal of Royal 13

Statistics Society, Vol. 30, No. 2, 1968, pp. 205-247. 14

13. Klir, G. J. and Wierman, M. J. Uncertainty-Based Information: Elements of Generalized 15

Information Theory, Physica-Verlag, Helidelberg, 1999. 16

14. Klir, G. J. Uncertainty and Information: Foundations of Generalized Information Theory, 17

John Wiley & Sons, Inc., New Jersey, 2006. 18

15. Dubois, D. and Prade, H. Representation and Combination of Uncertainty with Belief 19

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244-264. 21

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Vulnerability and Risk Analysis and Management International Conference. ASCE, 24

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17. Pike Transit Initiative. Columbia Pike Transit Alternatives Analysis: Final Report. 2005. 26

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