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Spatial Cognition & ComputationAn Interdisciplinary JournalPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t775653698

Impact of Regionalization and Detour on Ad-hoc PathChoiceHartwig H. Hochmair a; Simon J. Büchner b; Christoph Hölscher ba Geomatics Program, University of Florida, Ft. Lauderdale, Florida, USAb Center for Cognitive Science, University of Freiburg, Germany

Online Publication Date: 01 July 2008

To cite this Article: Hochmair, Hartwig H., Büchner, Simon J. and Hölscher,Christoph (2008) 'Impact of Regionalization and Detour on Ad-hoc Path Choice',Spatial Cognition & Computation, 8:3, 167 — 192

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Spatial Cognition & Computation, 8:167–192, 2008

Copyright © Taylor & Francis Group, LLC

ISSN: 1387-5868 print/1542-7633 online

DOI: 10.1080/13875860701866446

Impact of Regionalization and Detour on

Ad-hoc Path Choice

Hartwig H. Hochmair,1 Simon J. Büchner,2 and Christoph Hölscher2

1Geomatics Program, University of Florida, Ft. Lauderdale, Florida, USA2Center for Cognitive Science, University of Freiburg, Germany

Abstract: Regionalization has been found to impact human route planning, both

when the planning is based on a previously learned environment encoded in memory

and when maps are used. This paper presents an experiment in a virtual desktop

environment and examines how the length of the path in the start region or goal

region impacts ad-hoc route choice, i.e., in situations where the decision is made

right after perceiving the decision situation. More specifically, this research aims at

quantifying the trade-off value between short travel distances and leaving the start as

well as reaching the goal region quicker, respectively.

Keywords: path choice, regionalized environment, preferential behavior, trade-off

surface

1. INTRODUCTION

Although finding the shortest path is one of the most prominent route selec-

tion criteria in route planning (Golledge, 1995), previous experiments have

revealed asymmetries in human route selection behavior (Christenfeld, 1995;

Stern & Leiser, 1987). Amongst other things, asymmetries can be caused

by heuristics or rules-of-thumb when planning routes (Bailenson, Shum, &

Uttal, 1998), or by a distortion in cognitive maps when making a decision

based on a memorized environment. This paper analyzes how the portion

of the path running in the start or the goal region affects route choice. In

a desktop experiment, participants state their preference between two path

options shown in a series of 3D scenes on a computer screen. This paper

deliberately does not investigate effects of memorization of the environment

and its potential distortions but instead examines the impact of regionalization

on ad-hoc path choice from perceived decision situations.

Correspondence concerning this article should be addressed to Hartwig H.

Hochmair, University of Florida, IFAS, 3205 College Avenue, Fort Lauderdale, FL

33314, USA. E-mail: [email protected]

167

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168 H. H. Hochmair, S. J. Büchner, and C. Hölscher

1.1. Route Planning: Impact of Regions and Route Geometry

A recent study (Büchner, Hölscher, & Strube, 2007) found that people grouped

objects located in a building either by the building level or by staircases they

were located in. This kind of “natural” regionalization was also relevant for

path choice behavior. A study in a Virtual Environment by Wiener and Mallot

(2003) analyzes regionalization in memory structures after a learning task.

In their Hierarchical Planning hypothesis the authors suggest that humans

plan routes using different levels of the hierarchical representation of space.

In this strategy, the navigator plans a route for fast access to the goal region,

independent of where exactly the goal is within that region. The experimen-

tal findings supported this hypothesis, while contradicting the Persistence

hypothesis.

This hypothesis suggests that regions are explicitly represented in spatial

memory, and that subjects prefer to stay in their current region as long as

possible, delaying region transitions. When navigating symmetric routes, this

would also implicitly result in a preference for routes that cross fewer region

boundaries. Earlier findings show that distance estimations across barriers

or region boundaries are exaggerated as compared to distances not crossing

barriers (Thorndyke, 1981). Similarly, routes in a crowded area are estimated

longer than those in a less crowded area (Byrne, 1979), which can be ascribed

to the clutter effect. Bailenson et al. (1998) studied the role of regionalization

for human route planning using maps. The results confirmed the formulated

road climbing model, which states that instead of actually calculating the

globally shortest route between start and goal, people will attempt to leave

the region containing the start as quickly as possible using the longest and

straightest road out.

The impact of route straightness of the initial segments of routes was

specifically examined in subsequent work (Bailenson, Shum, & Uttal, 2000)

which formulated the Initial Segment Strategy (ISS). In this heuristics de-

cisions are disproportionally based on the straightness of the initial route

segment. The authors also found that navigators focused on route choice

within a given region and followed the selected route until they reached the

next region. This way, adding regions changed people’s perception of what

constitutes an initially straight route segment. Bovy and Stern (1990) showed

that preferred roads were particularly attractive at the beginning of a route,

stressing the importance of initial segments of a route in route choice.

Leaving aside the impact of regionalization, simplicity of routes (in terms

of angular measurement), and small deviation of the traveler’s orientation

from the direction to the destination are further competing route selection

criteria. A strategy that relies solely on the latter criterion is also referred

to as Least-Angle strategy (Hochmair & Frank, 2002). In experiments with

a virtual desktop environment where participants could only see the two

outgoing street segments at an intersection and a distal destination, because

all intermediate streets were blocked from the participants’ view by buildings,

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Regionalization and Human Route Planning 169

participants considered both the deviation angle of an outgoing street from

the direction to the destination as well as the length of its initial segment in

decision making (Hochmair & Karlsson, 2005).

The decision behavior could best be described as choosing the minimum

triangle path. Such path minimizes the total length of the (perceived) initial

street segment and the fictive segment running from the endpoint of the initial

segment to the distal target. In an experiment using a Virtual Environment

described by Dalton (2001), people were instructed to “walk” to the opposite

corner in the virtual world by the most direct route possible. Results revealed

that subjects were choosing the straightest possible routes as opposed to the

more meandering routes, which supports a hypothesis by Hillier (1997) that

people tend to follow the longest line of sight that approximates their heading.

1.2. Research Questions

As has been demonstrated in other studies (Bailenson et al., 1998; Wiener

& Mallot, 2003), both leaving the start region quickly and reaching the goal

region quickly are desirable criteria in route selection besides shortest path

and other criteria. Using a virtual desktop environment our research will

investigate the following related research questions:

Question 1: Which of the two criteria is more important: Leaving the start

region as quickly as possible or reaching the goal region as quickly as

possible?

Question 2: Given that both route alternatives reach the goal region after

the same distance: Which detour is the decision maker willing to take

in order to leave the start region earlier on that longer route? In other

words: What is the trade-off between route length in the start region and

total route length?

Question 3: Given that all path alternatives leave the start region after the same

distance: Which detour is the decision maker willing to take in order to

reach the goal region earlier on that longer route? In other words: What

is the trade-off between route length in the goal region and total route

length?

Further we will examine the following:

� the interrelation between the preferential difference between routes in-

cluded in a decision situation and subject response time for decision making� the interrelation between the preferential difference between routes in-

cluded in a decision situation and decision consistency� estimation of relative lengths in the virtual environment, and the impact of

regionalization on estimated distances

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1.3. Structure of the Paper

The remainder of the paper is structured as follows. Section 2 describes the

experiment setup and the testing procedures, followed by an analysis of the

results regarding questions 1–3 in section 3. Further results are presented in

section 4, which is followed by a discussion and conclusions in section 5.

2. ROUTE SELECTION BEHAVIOR: EXPERIMENT SETUP

In order to obtain results that are closer to “real world” situations than printed

maps, we used a desktop virtual 3D environment to present intersections to

the participants. The 3D environment is not as schematized and abstract as

2D maps and it provides depth cues, such as perspective. It resembles a

vista space perspective rather than an abstract representation in figural space

(Montello, 1993). In real situations this kind of view may occur not quite

often, but it is a view that people are regularly exposed to in the area of

Freiburg, in the Black Forest villages. A variety of scenes were designed

to be able to answer questions 1–3 as stated before, and to obtain distance

estimations. This section describes the design criteria for the scenes and the

testing procedures.

2.1. Participants

Thirty participants (15 female) between the ages of 16 and 42 years (Mean D

25.1, SD D 5.0) were recruited through postings on the Freiburg campus

and e-mailing lists. Most of them were students from a variety of subjects,

including one student in Geoscience. Participants were paid or received course

credit for participation.

2.2. Material and Design

Each scene showed a landscape from an egocentrically situated overview

perspective, i.e., the participants saw the scene from a slightly elevated

position. Participants were located at a fork with two paths both leading

to the goal, a tower (Figure 1).

One or more of the following parameters varied between the two paths

in a scene as in more detail described further below: Detour, portion of path

in start region, and portion of path in goal region. In order to exclude the

potential impact of other variables on the observed preferential behavior, paths

were kept identical regarding following criteria: Each visualized path crossed

two region boundaries, contained exactly one intersection (besides the one at

the start point), and made two turns. The regions subdivided both paths into

approximately three equal portions, where regions show asymmetries with

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Figure 1. Screenshot of a scene in the 3D environment as seen by the participants.

respect to the vertical central axis (see Figure 2), which allowed us to elicit

preferential behavior and trade-offs.

They were arbitrarily colored polygons with sharp boundaries so that they

were easily discriminable. They were selected independently of hierarchical

models or the built elements of the virtual city whatsoever. The length of

Figure 2. Counting the portion of a path in the start and the goal region (design for

answering question 2).

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the initial leg and its deviation from the target direction was identical for

each path. This eliminated the potential impacts of the Least-Angle Strategy

or the Initial Segment Strategy. Furthermore, trees and houses were added to

the scene in order to make it look more realistic and to provide participants

with a scale. Trees and houses were identical along all paths visualized, i.e.,

mirrored along the vertical line in the center of the scene, so that they did not

bias participants’ decision behavior. The viewpoint and the distance to the

target were kept constant for all combinations. The number of longer paths

over all scenes, i.e., paths with larger detours, was balanced between left and

right for each participant.

Detour (d) in the designed paths varied between 0% (shortest path), 10%,

35%, and 50%. The portion of a path running in the start region (s) and goal

region (g) varied between 10%, 20%, 30%, 40%, and 60%. Figure 2 shows

how the path portions are counted. In this example, the left path has a start

region of 20%, whereas the right path has a start region of 40%. The amount

in the goal region is counted from the intersection in the middle starting with

50%. This is because for questions 1 and 3 the point of entry in the goal

region is of higher interest than the actual length traversed inside the goal

region.

Thus, in Figure 2 both paths would be counted as having the same

portion of goal region, namely 30%, although strictly speaking, the left path

runs slightly longer in the goal region. To keep the length for each of the

four 10% steps behind the middle turn points approximately equal between

the right and left path, only the first segment after the middle turn is used for

measuring the number of 10% steps. This way, the actual length differences

between routes, which can be mostly ascribed to the last (horizontal) segment

leading to G, does not impact the measure of when the goal region is reached.

Thus, route length and the latter measure can be changed quasi independently

in different scenes of the experiment setup.

With regard to the first question, i.e., whether leaving the start region

quickly or entering the goal region quickly is more important, an asymmetric

scene was designed as shown in Figure 3a. Participants considering leaving

the start region quickly as more important would give preference to the left

path, whereas participants assigning higher importance to reaching the goal

region quickly would prefer the right path. Subjects who consider both criteria

as equally important or are insensitive to regionalization would be indifferent

to both paths.

Question 2 examines the trade-off between a short route distance and

a short start region. A trade-off is also referred to as marginal rate of sub-

stitution of attribute X for Y at a given point (xi ; yi ) (Keeny & Raiffa,

1993). Presuming that X and Y are desirable attributes, the marginal rate of

substitution describes, if Y is increased by a certain number of units, how

much does X have to decrease in order for the decision maker to remain

indifferent. Scenes related to question 2 have one path that is longer but has

a shorter start region, whereas the other path is shorter but runs longer in

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Figure 3. Samples of designs for answering question 1 (a) and question 3 (b).

the start region. Region-sensitive participants are expected to be more often

indifferent to both paths, or even to prefer the longer path, compared to strict

“shortest path takers.” A sample scene related to this question is shown in

Figure 2.

Question 3 examines the trade-off between short distance against quick

entrance in the goal region. Scenes related to this question have one path

that is longer but enters the goal region quicker, whereas the second path is

shorter but enters the goal region later. Again, region-sensitive participants

are expected to be more often indifferent to both paths, or to prefer the

longer path, compared to strict “shortest path takers.” A sample scene for

this question is shown in Figure 3b.

With regard to question 2 and 3, the combination of the four attribute

values for detour (0%, 10%, 35%, 50%) and the 5 attribute values for

regionalization (10%, 20%, 30%, 40%, 60%) lead to 20 path designs for

each question. The goal of the study is to find a preference ranking of all

20 paths, which would reveal the relative importance of route length and

portion within the start region or the goal region. As the number of 190

possible path combinations .20 � .20 � 1/=2/ is too large to be evaluated

by participants, a series of 21 pre-testings were carried out. The results of

these led to the exclusion of some combinations that provided redundant

information concerning the observed preference structure, but also led to

the addition of others to refine preference elicitation. Finally 64 scenes for

question 2, and 55 scenes for question 3 remained. In addition to this, three

scenes from the 64 scenes, and three scenes from the 55 scenes were shown

5 times and shuffled randomly into the sequence of scenes. This was done to

assess participants’ decision consistency in section 4.1.

The 3D scenes were designed with GtKRadiant 1.5.0, courtesy of Id

Software Inc., and displayed using the Irrlicht-engine SDK, version 0.4.

GtKRadiant is an editor used to design 3D maps containing different objects,

for instance, houses and streets. The Irrlicht-engine is used to import these

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maps and enable a user to move around in the environment like in a computer

game. The pivoting and moving functions were, however, deactivated for this

experiment, and the participants were presented with static scenes. The scenes

were presented on a desktop PC with a 1900 monitor and a regular keyboard.

The F-key and the J-key were marked with arrows to the left and the right,

respectively. The B-button was marked with a dot denoting the button for

“indifferent.”

2.3. Procedure

Participants were seated in front of the screen and instructed to indicate which

one of the two paths they would choose when trying to reach the tower (G)

as fast as possible. Participants had to indicate their preference by using the

prepared keys on the keyboard showing arrows to the left and the right. In

case they had no preference they were instructed to press the button showing

a dot (prepared B-button). The time to complete a trial was not limited though

participants were instructed to respond spontaneously.

Each participant completed 10 training trials with scenes that were not

used in the actual experiment but similar in structure. A total of 120 different

scenes were used in the main part, with one scene for question 1, 64 scenes

for question 2, and 55 scenes for question 3. All scenes were presented in

a random sequence which was created individually for each participant. Be-

tween two scenes a blank screen was shown, otherwise the changes between

scenes (path lengths and region boundaries) would have captured too much

of the participants’ attention. After each third of the trials participants were

allowed to take a break.

Afterwards participants were given a distance estimation task. They

were shown another 18 scenes that were not used in the main part of the

experiment, but were similar in structure. They were then asked to judge

which of the two paths was longer and to estimate how much longer it was

(in %). Participants were told to consider the shorter of the two paths as the

reference line and were asked to estimate the length of the longer path in

relation to the shorter path. We chose to ask for percentages in contrast to

absolute distances, because pilot testing yielded that participants had serious

difficulties to give an even rough estimate of the absolute distance.

The 18 scenes consisted of 3 sets of 6 scenes each (all 6 combinations

of 0%, 10%, 35%, and 50% detour). Set 1 had no regionalization at all. Set

2 had a constant goal region of 20% on both sides with a start region of 10%

and 60%, on the left and right side, respectively. Set 3 had a constant start

region of 20% on both sides with a goal region of 10% and 60%, on the

left and right side, respectively. All 18 scenes were presented in a different

randomized order for each participant. Although we did not expect an impact

on the length estimation of whether the longer path was the left or the right

one, longer paths were balanced between left and right in all scenes.

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The entire experiment took about 25 minutes.

3. RESULTS FOR QUESTIONS 1–3

This section analyzes the relative importance of start and goal region in the

decision making process, which is followed by a description of the conver-

sion from participants’ binary preference statements, as obtained from the

experiment, into preference values for the different paths. These preference

values are then used to visualize participants’ preferential behavior in contour

maps.

3.1. Question 1: Impact of Start and Goal Region

This analysis included the responses to the scene in Figure 3a from all 30

participants and the 21 candidates from the pre-tests. Pre-test results could

be included because only binary preference statements between shown paths,

but no rankings of paths were needed to answer question 1. A random

choice between the three alternatives would result in an equal distribution

among the three options. This is clearly not the case. A �2-test yielded a

�2-value of 6.12, p < 0:05. However, the results in Figure 4 show that

among the 51 participants, more than half of them (51%) indicated some

preference. Reaching the goal region quickly was found to be slightly more

important than leaving the start region quickly, but differences were not

significant (�2D 0:62, p > 0:43). The results suggest that there are two

groups of participants, those who are sensitive to regions and those who

are not. However, strictly speaking, the “indifferent” group may also contain

participants that are region-sensitive, for whom short start region and long

goal region are equally important.

Figure 4. Importance of short start region versus long goal region.

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3.2. Ranking the Choice Alternatives for Questions 2 and 3

For an assessment of the trade-offs, the preference ratings for the 20 different

paths used for questions 2 and 3 needed to be found. In a first step, the

responses in the log file were sorted for each participant regarding the question

the scene was referring to. Next, responses for repeated scenes were removed

for this analysis. For each participant a set of 64 (question 2) and 55 (question

3) binary constraints .�; �; �/ remained between the paired street segments.

The binary relation ‘�’ means preference for the left path, ‘�’ preference

for the right path, and ‘�’ denotes the decision maker’s indifference to the

two options. From the binary constraints a final sorting of the 20 paths

that reflects the decision maker’s preferential structure was derived, with the

highest preferential number being assigned to the most preferred path.

Formally, this sorting task corresponds to a constraint satisfaction prob-

lem (CSP). Each CSP involves a set of variables (in our case 20 path

variables), a domain of potential values for each variable (i.e., an integer

number between 1 and 20 denoting the preference value), and a set of

constraints, specifying which combinations of values are acceptable (e.g.,

64 binary constraints). A perfect solution specifies a value to each variable

that does not violate any of the constraints. A pair of values that violates a

constraint is called inconsistency. In an overconstrained CSP no valid value

for all variables can be found, and the CSP must be weakened, for example,

by removing constraints. For all participants, the sets of 64 (55) binary

constraints recorded during the study contained inconsistencies. Figure 5

visualizes an example for a small subset of the complete domain for question

2 that consists of three constraints that cannot be completely solved. The

example is taken from a participant’s binary preference statements. The

numbers in each variable expresses detour in percent (d) and percentage

of path in start region (s).

Partial constraint satisfaction problems (PCSP) (Freuder & Wallace,

1992) involve finding values for a subset of variables that satisfy a subset of

the constraints, which yields a partial solution. A metric evaluates the differ-

ence between a perfect solution of a CSP and a partial solution. A metric can,

among others, be expressed by the number of inconsistencies to be removed

for finding a partial solution, by assigning arbitrary weights to constraints,

or by introducing priorities. Using algorithms that maximize the number of

Figure 5. An overconstrained constraint satisfaction problem.

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satisfied constraints (such as branch and bound or backjumping) may yield

unnatural results that do not reflect the decision maker’s preferences, as no

semantics is involved in the weakening process. Formalizing more complex

metrics that distinguish between hard and soft constraints (Moratz & Freksa,

1998; Rudová & Murray, 2002) is also questionable if the participant’s

preferential behavior is not known in advance. Therefore we decided to

remove inconsistencies from each set of binary relations manually until the

weakened CSP could be solved with a constraint satisfaction algorithm in

Prolog (Poole et al., 1998). In the weakening process we tried to incorporate

the following (conflicting) rules:

(1) Keep the number of removed binary constraints small.

(2) Remove constraints which violate the principle that the shorter path is

preferred if all other parameters are equal.

(3) Keep a balance between removing constraints that support a region-

sensitive ranking and constraints that support a shortest-path based rank-

ing.

We use the overconstrained CSP in Figure 5 to further explain rules (2) and

(3). The binary relation ‘�’ to the lower left indicates that, with start regions

of 60% for both routes, the person prefers the shorter route (0% detour) over

the longer route (10% detour). This is the preferential behavior one can expect

as the shorter route will be the faster one. If, however, the longer route was

preferred, and this caused an overconstrained CSP, the corresponding binary

relation was removed, according to rule (2). Such behavior means that the

person could not identify the longer route as such.

The binary relation ‘�’ to the right shows that the decision maker prefers

the shorter route (10% detour) with a longer start region (60%) over a longer

route (35% detour) with a shorter start region (20%). Such behavior indicates

that the decision maker either does not consider the size of the start region

at all (which means that he or she is a “shortest route taker”), or that the

amount by which the route would leave the start region earlier (20% vs. 60%)

is not enough to give up the advantage of the shorter route (35% vs. 60%

detour). If such constraint is removed from the CSP, the overall preference

structure for this participant will be inclined towards a region-sensitive person

that would be willing to give up the shortest path in lieu of leaving the start

region earlier.

The binary constraint ‘�’ on top indicates that the decision maker prefers

the longer route (35% detour) with a short start region (20%) over the

shorter route (0% detour) with a larger start region (60%). A person with this

preference behavior is region-sensitive, and removing such binary constraint

from the CSP will yield a preference structure that is inclined towards a strict

shortest path taker.

Thus, to satisfy rule (3), we balanced the number of removed constraints

that shift a decision maker’s preference profile towards region-sensitivity and

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the number of removed constraints that shift a decision maker’s preference

profile towards shortest path taking. Similar considerations were made for

the CSP for question 3.

On average, 8.2 (for question 2) and 7.6 (for question 3) constraints

were removed per participant. After removing inconsistencies, the algorithm

in Prolog yielded a partially ordered ranking of (distance, start region) and

(distance, goal region) combinations for the 20 paths of each question for

each participant.

3.3. Identifying Groups of Decision Makers through Clustering

The pattern of preferential responses to scenes revealed a varying inclination

of participants to trade-off the shorter path against a shorter start region

(question 2), or a longer goal region (question 3), respectively. These find-

ings suggest a classification of participants into two groups: The first group

would be region-sensitive and not always prefer the shortest path, whereas

the second group would mostly choose the shortest path independent of

regionalization. In order to verify the existence of such groups, we analyzed

separately responses related to question 2 (i.e., scenes with equal portion in

goal region) and question 3 (i.e., scenes with equal portion in start region). To

test participants’ inclination towards region-sensitivity, we used scenes which

included paths of different lengths. Consider as an example the first scene in

Table 1 related to question 2.

If the decision maker prefers the shortest route although that route has a

longer portion in the start region (�), this indicates that the decision maker

is not particularly region-sensitive. More specifically, the decision maker is

not willing to “pay” a detour of 35% to leave the start region quicker (i.e.,

after 10% instead of 40%). We assign such a situation where a trade-off is

not reached, letter (a). Indifference (�) between both routes indicates that the

decision maker is willing to accept a 35% detour, and a shorter distance is

traded off against a shorter start region. We call this case (b). When preferring

the right path (�), the decision maker is willing to “pay” even a longer

detour than 35% in order to decrease the portion in the start region from

40% to 10%, which indicates high region-sensitivity. This is option (c). As

mentioned before, the use of the longer path was balanced between left and

right throughout all scenes for each participant. Thus the left and right paths

characterized in Table 1 were randomly switched for other participants. For

Table 1. Scenes with paths of different lengths used for clustering

Left path Right path

Question 2 0% detour, 40% in start region 35% detour, 10% in start region

Question 3 0% detour, 10% in goal region 35% detour, 40% in goal region

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the purpose of comprehensible presentation, we will here only refer to one

of the combinations.

A similar distinction can be made for the second scene in Table 1, which

is related to question 3: Preference for the left option means no or only a small

willingness of the decision maker to substitute a shorter route with a quicker

arrival in the goal region (a). On the contrary, indifference (b) or preference

for the right option (c) demonstrates the decision maker’s willingness to “pay”

the quicker reaching the goal region with a detour of 35% (case b) or more

(case c).

Participants’ responses were classified into the categories a, b, c, and the

portion of counts for each category within the total number of responses was

calculated (Table 2).

To identify a potential grouping of the 30 participants, we applied a

hierarchical cluster analysis on the values in the (a)-columns (Ward method

with Squared Euclidean distance measure), which clusters participants after

their aversion to trade-off a shorter path against one of the two regionalization

effects. Figure 6 shows the dendrograms for responses to question 2. The

dataset used for Figure 6a is based on responses from all participants and

identifies two outliers (participants #30, 31), who were more sensitive to

regionalization than the other participants. When excluding these two partic-

ipants, a two-cluster solution is found (Figure 6b). Participants in the upper

cluster show smaller (a)-values in Table 2 (first column), whereas members

of the bottom cluster could be classified as “shortest-path takers” who are

not or only little affected by regionalization in their decision behavior.

Figure 7 shows the dendrogram for the clustering of (a)-values for ques-

tion 3 (column 4, Table 2) which suggests a two-cluster solution. The bottom

cluster includes 6 participants that are particularly sensitive to regionalization.

Reaching the target region early is a crucial part of these participants’ decision

behavior. Five out of these 6 participants were also identified as region-

sensitive in question 2.

Dendrograms do not provide a unique, best solution to clustering, but

rather a visual mean to interpret distances between clusters which can give

Table 2. Responses indicating that a trade-off has not been reached (a), that a

trade-off has been reached (b), or that the detour has been overcompensated by

quickly leaving the start region or quickly reaching the goal region (c)

Question 2 Question 3

Participant a b c a b c

#1 .71 .24 .05 .63 .21 .16

#2 .93 .07 .00 .80 .15 .05

#3 .22 .00 .78 .82 .00 .18

... ... ...

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Figure 6. Question 2: Clustering of trade-off aversion for all users (a), except for

two outliers (b).

clues to identify the best solution. The structure of dendrograms changes

with different cluster methods and distance measures used. To validate the

results of cluster analysis we tested other clustering methods and distance

measurements for both data sets. Whereas, for example, the Between-groups

linkage method or the Centroid method also yield a two cluster solution with

the same number of cluster members as in Figure 7, the Furthest neighbor

methods suggests seven members in the second cluster instead. Thus the two

clusters shown in Figure 6 and Figure 7 can vary in the number of members.

However, we found that, despite some variations, the distinction between two

clusters could be observed in various other clustering methods as well, and

that the variation in member number was small.

3.4. Question 2: Trade-off between Short Start Region and Detour

For each participant the ranked preference values for paths, which were found

through Prolog, were normalized between 1 (least preferred path) and 20

(most preferred path). The number 20 was chosen because of the 20 different

paths used in the scenes for each question, and theoretically 20 different

ranking levels for the 20 paths were possible. However, due to indifferences

stated between various paths, a smaller number of preference values (ranking

levels) was observed for all participants. More specifically, for question 2,

an average of 9.6 different ranking levels were observed for the group more

inclined to regionalization, whereas an average of 7.2. different ranking levels

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Figure 7. Question 3: Clustering of combined preference measure for all users.

were found for the “shortest-path takers.” The smaller value for the latter

group may be explained by the fact that only four different path lengths

were provided, and path length was the crucial criterion for this group. For

question 3, the corresponding numbers are 8.3 (regionalization group) and

7.8 (shortest path takers).

For question 2, participants were grouped according to their region sensi-

tivity as found in the first cluster analysis (Figure 6). Although the preference

values provide only ordinal information and not ratio, we make the simplified

assumption that preferential differences between adjacent preference values

are equal, and that routes with a preference value of 1 are equally disliked

among participants, so that the average of preferential values for the 20 paths

among the grouped participants can be used to identify a preferential pattern

for that group.

Figure 8 shows an isoline map, where mean preference values are plotted

against the independent variables “% in start region” and “Detour [%]” using

linear interpolation. The contour lines represent indifference curves. This

means that all paths with their parameter combinations (% in start region,

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Figure 8. Question 2: Indifference curves for (a) participants inclined to consider

regionalization, and (b) “shortest path takers.”

detour) which lie on the same contour line share the same preference value.

Figure 8a refers to the cluster of participants identified to be region-sensitive

in scenes for question 2. As can be seen from the pattern of indifference

lines, participants tend to accept longer detours if the start region is left

quicker. The average trade-off is roughly about 20% detour for a drop from

a 60% to a 10% portion in the start region. Figure 8b shows the same plot

for participants that were identified as shortest path takers. As opposed to the

first group, average preference values decrease uniformly with a decreasing

path distance, and regionalization does not seem to affect the preferential

behavior.

3.5. Question 3: Trade-off between Long Goal Region and Detour

For this task, ranked preference values of paths from scenes related to ques-

tion 3 were used as input data, and normalized between 1 and 20. Again,

participants were grouped into region-sensitive decision makers and shortest

path takers, following the results of the cluster analysis for question 3 (see

Figure 7). As before, the average of preferential values for the 20 paths over

the groups of participants was calculated.

Figure 9 shows the isoline map, where mean preference values are plotted

against the independent variables “% in goal region” and “Detour [%]”. The

left figure clearly indicates a group of participants who accept a longer path

if it reaches the goal region quicker. The average participant of that group

is willing to “pay” an increase from a 10% to a 60% portion in the goal

region, i.e., the ability to reach the goal region quicker, with a detour of

roughly 20%. The observed decision behavior for the second group reveals

a general indifference towards regionalization, where a small anomaly in

the preferential pattern can be observed at a detour of about 20%. Such

anomaly may have been caused by a gap in the design of the scenes, so that

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Figure 9. Question 3: Indifference curves for participants inclined to consider

regionalization (a), and “shortest path takers” (b).

the true preference value of a path could not be captured correctly but was

underestimated in the ranking.

4. FURTHER ANALYSIS

4.1. Decision Consistency

Participants’ judgments are primarily based on independent variables (region-

alization, distance). Potential inconsistencies in the obtained decisions may be

explained in two ways. Firstly, the decision making can be modeled through

a deterministic utility and a probabilistic decision process (Luce, 1959). This

means that, even if participants would be shown the exact same decision

situation again, they might decide differently. Secondly, random utility models

(Ben-Akiva & Bierlaire, 1999) consider the individuals’ decision rules as

deterministic, and motivate the uncertainty from the limited capability of the

analyst to observe and capture all the dimensions of the choice process, due

to its complexity.

Independent of the model used to explain inconsistencies in decision

making, we hypothesize that for scenes with two similarly preferable paths,

the choice behavior will lean towards a random decision (i.e., provide low

repetition reliability), whereas for scenes with paths that are clearly discern-

able in terms of their assigned preference value, the choice behavior will be

more consistent. To investigate the participants’ reliability in their preferential

judgments, a total of six scenes, i.e., three related to question 2, and three

related to question 3, were selected and in a random order shown five times

within the sequence of the remaining 120 scenes.

This process was done within the computerized randomization of scenes

for the main experiment. Three of the six repeated scenes were selected

with a varying amount of start region and a constant amount of goal region

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(related to question 2), whereas the remaining three repeated scenes were

selected with a constant amount of start region but a varying amount of goal

region (related to question 3). Each of the three related scenes revealed in

the pre-testing a different amount of preferential difference (deltaPreference)

between both paths. In order to avoid the potential impact of a right-left

bias, repeated scenes were not balanced between left and right for individual

participants.

The five preference statements made for each repeated scene were mapped

to integer numbers as follows: � ! 1, � ! �1, � ! 0. Variability v for

each scene and each participant was calculated as the absolute difference

between the most often stated choice (�1 or 0 or 1) and the remaining

choice statements. The highest possible v occurs with a preference statement

containing the numbers 1, 1, 0, �1, �1. For this case, v D 5 (through

1 � .1 � 0/ C 2 � .1 � .�1/), which denotes high inconsistency in the

participant’s preferential behavior. On the other end of the range, a statement

of 1, 1, 1, 1, 1 or �1, �1, �1, �1, �1 or 0, 0, 0, 0, 0 gives v D 0, which

shows perfect consistency in the participant’s decision behavior. The last of

the three cases shows that the user is consistently indifferent to two paths,

which may occur for scenes where both paths have the same length and vary

only in the regionalization, and the decision maker is a shortest path taker.

As preferences for paths vary between participants, the preferential dif-

ference for repeated scenes were looked up from the individual ranking results

for each participant, and then plotted against the computed variability. In the

plot (Figure 10), variabilities were normalized to a range between 0% and

100%, where 100% corresponds to v D 5.

Two scatter plots plot preferential difference of paths in a scene against

choice variability for the three repeated scenes related to question 2 (Fig-

ure 10a) and question 3 (Figure 10b). The plots visualize how the consistency

in preferential statements vary with preferential differences between two

routes. Variability ranges between 0% and 80%, thus no participant revealed

Figure 10. Choice variability for repeated scenes.

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the most inconsistent behavior possible with any of the six scenes chosen.

As expected, choice variability decreases with a larger preferential difference

between the two paths in a scene. For the first set of scenes (Figure 10a)

the correlation was not found to be significant (Pearson correlation: �0.048,

p > 0:65), whereas for repeated scenes of question 3 (Figure 10b), the

correlation was significant (Pearson correlation: �0.292, p < 0:01).

4.2. Decision Times

We hypothesize that decisions are made quicker in scenes that have a clear

favorite than in scenes where decision alternatives have a similar preference

value. To test this hypothesis, the difference in preferential values between

the left and right path option was looked up for all evaluated scenes for all

participants. These preferential differences were then compared to response

times logged during the experiment. As separate rankings were created for

scenes related to question 2 and 3, two plots are found (Figure 11a, 11b). In

the plots, outliers were determined by the eye, and it seemed appropriate to

remove response times larger than 10 seconds. This makes seven removed

data points for question 2 and seven for question 3. For both sets of scenes,

a small negative significant correlation between rank difference and decision

time could be observed, which confirms our hypothesis (question 2: Pearson

correlation: �0.131, p D 0:000; question 3: Pearson correlation: �0.108,

p D 0:000).

4.3. Estimated Distances

For the analysis of the distance estimations the ratio between the longer path

length and the shorter path length was calculated and multiplied by 100, i.e.,

expressed in percent. Ratios were calculated for real and estimated distances

Figure 11. Response times against difference in preferential values of choice alter-

natives (after removal of outliers).

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and compared afterwards. For example, a scene with path lengths of 150%

and 135% (i.e., 50% detour and 35% detour, respectively, compared to the

path length without detour) yields a distance ratio of 111%, i.e., the longer

path is 111% of the shorter path.

In general distances were underestimated, which is consistent with previ-

ous findings (Willemsen & Gooch, 2002; Witmer & Kline, 1998). The overall

correlation between the real and estimated distances was significant (Pearson

r D 0:47, p < 0:001).

We were interested if region-sensitive and region-insensitive people would

estimate path lengths differently. If the region-insensitive people indeed focus

strictly on the path length, they should be better in distance estimation as they

dedicate more attention to the pure distance than to other sources.

The difference between real distance and estimated distance was cal-

culated for each trial yielding the error in distance estimations (Figure 12).

Participants were grouped as either region-sensitive or region-insensitive and

considered as region-sensitive when they were in the region-sensitive cluster

in both cluster analyses (for question 2 and 3; N D 5). An ANOVA with

factors region-sensitivity (with groups region-sensitive and region-insensitive

as found in the cluster analysis) and real distance was conducted with distance

estimation error as the dependent variable. The ANOVA yielded a main effect

of region-sensitivity, F.1; 726/ D 46:53, p < 0:001, and a main effect of real

distance, F.5; 726/ D 19:83, p < 0:001. The interaction was not significant.

The estimation error was higher for region-sensitive participants (Mean D

19%) than region-insensitive (Mean D 14%). This means that region-sensitive

people were more error prone and inclined to underestimate distances than

region-insensitive people.

Figure 12. Distance estimation error as a function of real distance.

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A separate analysis of the estimation of regionalized and non-regionalized

paths showed that region-sensitive participants made equally large estimation

errors in regionalized and nonregionalized scenes.

5. DISCUSSION AND CONCLUSIONS

The scope of this experiment was to explore the importance of the start and

goal region for path choices, and to determine the detour people are willing

to take in order to leave the start or reach the goal region quickly.

With respect to research question 1 we found that half of the participants

were indifferent towards two paths that were equally long and only differed in

the size of the start and goal region. The other half showed a slight preference

for reaching the goal region first, and the smallest group of participants gave

preference for a short start region. These results suggest that only some people

are sensitive to boundaries that divide an environment into different regions.

The cluster analysis that was conducted for research questions 2 and

3 suggests that there are two groups of people who choose their paths by

different criteria. The shortest path criterion is the most frequently applied

criterion for path choices (Golledge, 1995) and is compatible with the prin-

ciple of rational behavior (Anderson, 1993). Nevertheless we find a group of

people that doesn’t follow this principle strictly but takes other factors (such

as regionalization) into account when choosing a path, even when being

asked to select the fastest route to a goal. The size of this group varies

between 20% and 50% depending on where the larger region is located.

This contextual effect may be subject to further investigation, now that we

established a baseline of distance estimates for this setting. However, it is

clear that there are individual differences between people with respect to the

impact of regionalization on ad-hoc path choice.

The design of the experiment is suited to test ad-hoc decision behavior

and a view, where the participants could see both the route alternatives and

the regions in full. This kind of view rarely occurs in places without hills.

However, we created a situation in which the person has an overview over an

area comparable to physical vista space in contrast to a symbolic represen-

tation as in maps. Nevertheless the symbolic nature of virtual environments

in general is comparable to maps. Although the impact of regionalization

is probably the highest in such a situation when people see the full space

constantly, a regionalized mental representation alone can affect path choice

(Büchner et al., 2007).

Independent of the regionalization and hierarchical structuring of regions

in memory, a wayfinder may consider reaching the highest hierarchical street

level, such as highways, as soon as possible in multi-hierarchical networks in

order to reach the goal quickly (Timpf et al., 1992). The trade-off rates found

in our experiment are expected to be different from the real world case, or

when maps are used. Revealed preference surveys (Hunt & Abraham, 2007)

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are a possible approach to elicit trade-off values for route planning in the real

world.

Whereas previous research predominantly examined the impact of re-

gionalization on route choice in memorized environments, the presented

experiment revealed the role of regionalization in ad-hoc choice. Another

difference is that previous research tested primarily the impact of absence

or presence of region boundaries and start or goal regions on path choice,

whereas this experiment examined the impact of the size of start and goal

region on route choice. Results showed that one group, the strict shortest path

takers, ignore the size of regions of the environment and focuses solely on

the length of the paths. The other group is influenced by these regions and

is more willing to choose paths that are longer in favor of leaving the start

or reaching the goal region quickly. The trade-off surfaces found in sections

3.4 and 3.5 refer to designed distances and not to perceived distances.

The consistency analysis yielded that the variability in participants’ de-

cisions varied with the preferential difference between the two paths shown

in a scene. Decisions tended to be slightly more consistent when the pref-

erential difference between the two included paths was higher. Similarly,

decision times for scenes with a higher preferential difference between the

two included paths were lower than for scenes with a smaller preferential

difference. An analysis of estimated distances confirmed previous results,

namely that estimated distances are underestimated in Virtual Environments.

Region-sensitive participants were found to underestimate distances more

than strict shortest path takers. That is, shortest path takers are better distance

estimators. There may be different reasons for this observation. One might

be that participants who are shortest path takers allocate more attention to the

task in general and thus are able to estimate distances more accurately and

choose the shortest path spontaneously without being distracted by region-

alization. Alternatively, people who have problems with providing accurate

estimations of distance, be it for perceptual or other cognitive reasons, may

(unconsciously) compensate for their relative deficit by concentrating on

alternative cognitive strategies, i.e., region-based path-choice heuristics. This,

however, is largely speculative at this point and must be subject to future

research.

One possible area of application of the presented study is the simulation

of pedestrian traffic flows and modeling of evacuation heuristics (Løvås, 1998;

Hoogendoorn & Bovy, 2004). The results suggest that in addition to common

criteria included as disutilities in the modeling of pedestrian route choice,

such as distance, proximity of obstacles, and number of sharp turns, the

regionalization of the building should be considered as a determining factor

as well.

As there was no difference in distance estimation between regionalized

and non-regionalized environments, regionalization was not found to impact

estimated path lengths in this study. Thus, the impact of barriers or region

boundaries on estimated distances as observed in the real world (Thorndyke,

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1981), could not be observed in this experiment. Therefore it may be possible

that in virtual environments the impact of boundaries and cluttered routes

are generally smaller than in the real world or even neglectable. To our

knowledge, no empirical studies exist on this topic, which could be done in

future work.

Another aspect of future work is to assess the factors that determine if

a person strictly follows the principle of rational choice or takes regionaliza-

tion into account. One potential method to assess individual differences in

route choice behavior are psychometric tests of spatial ability and preference

(Evans, 1980). Spatial abilities tests provide the best standardized means

to assess inter-individual differences in spatial cognition. Hegarty, Montello,

Richardson, Ishikawa, & Lovelace (2006) have recently published a large

study on the relationship of different factors of spatial abilities and corre-

sponding measures from the literature. They mainly differentiate between

small-scale and large-scale spatial abilities. Small-scale spatial abilities tests

are sensitive to the cognitive processes of encoding and memorizing spatial

arrangements in figural or room-level scale, and very prominently to mental

rotation which also yields distinct gender differences. In the current experi-

ment the participants were neither required to memorize a spatial setting nor

to perform any mental rotation of the spatial setting. Thus the small-scale tests

of spatial ability would probably not be sensitive for the tasks in the current

experiment. In large-scale tests, memory for layouts at the environmental

scale is an important factor. So is the ability to update the locations of oneself

and other objects in the environment. Self-report tests like the SBSOD scale

(Hegarty, Richardson, Montello, Lovelace, & Subbiah, 2002) also capture

abilities in this direction. Again, in the current experiment participants were

not required to perform either of these tasks. The complete scene is immedi-

ately visible and no spatial updating or memorization is needed. In fact, the

tasks are situated at the vista-space scale, since all relevant information is

directly visible (unlike the environment-space scale). Allen, Kirasic, Dobson,

Long, & Beck (1999, as reviewed by Hegarty et al., 2006) have used a

spatial abilities test on the vista scale that might be a moderator of small-

and large-scale abilities. Their test requires perspective taking on the vista-

space scale. Yet again, the current tasks require no change of perspective, and

the participants do not need to make any mental transformation of that sort.

To summarize, route-planning on environment-scale tasks should clearly be

sensitive to spatial abilities tests, as well as to general measures of working

memory capacity. Yet the current tasks concentrate on a specific case of

route-choices that require no planning from memory, as they are entirely in

vista space. To the authors’ knowledge there are no spatial ability tests that

assess this topic specifically, so in order to relate individual spatial abilities

to route judgments an adequate test needed to be constructed.

Another area of interest for future work is to further clarify, in real

world experiments, how start and goal regions impact route choice in indoor-

navigation tasks, specifically when change of floors is involved.

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ACKNOWLEDGMENTS

This research has been partly conducted in the framework of the R6-

[SpaceGuide] project within the Transregional Collaborative Spatial Cogni-

tion Research Center (SFB/TR8) funded by the German Research Foundation

(DFG). We thank Christopher Kalff and Henrike Sprenger for their support

with data collection, and Johannes Otepka for his help in customizing the

Irrlicht-engine.

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