sovmaterikoistyo

Aalto University
School of Science





Tuomas Lahtinen
Path dependency in the Even Swaps process










Mat-2.4108 Independent Research Project in Applied Mathematics
27.08.2012

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Contents
1. INTRODUCTION.................................................................................................................................... 3
2. THE EVEN SWAPS METHOD.................................................................................................................. 4
2.1. DOMINANCE AND IRRELEVANCE........................................................................................................................5
2.2. MAKING THE EVEN SWAPS ...............................................................................................................................6
2.3. THEORETICAL PREMISES OF THE EVEN SWAPS.....................................................................................................8
3. THE SMART-SWAPS DECISION SUPPORT SYSTEM................................................................................. 9
4. POSSIBLE SOURCES OF PATH DEPENDENCY IN EVEN SWAPS.............................................................. 12
4.1. INCONSISTENCY OF TRADE-OFFS BETWEEN CONSEQUENCES................................................................................12
4.2. THE EVEN SWAPS PROCESS RELATED CAUSES FOR PATH DEPENDENCY .................................................................14
5. DISCUSSION OF THE EXPERIMENTAL DESIGN ..................................................................................... 14
5.1. GENERAL FEATURES OF THE EXPERIMENT .........................................................................................................14
5.2. STATISTICS TO COMPARE OUTCOMES OF EVEN SWAPS PROCESS' ........................................................................16
5.3. EXAMINING THE SWAPS BY COMPARING TRADE-OFF RATIOS ..............................................................................18
6. RESULTS FROM PRELIMINARY EXPERIMENTS..................................................................................... 20
6.1. GENERAL NOTIONS AND COMPARISON OF THE OUTCOMES.................................................................................20
6.2. EVIDENCE OF BIASES IN THE PRELIMINARY EXPERIMENTS....................................................................................22
7. CONCLUSIONS.................................................................................................................................... 25

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1. Introduction
Even Swaps (Hammond et al. 1998, 1999) is a multicriteria decision analysis method that
provides a framework for using trade-offs to compare alternatives. The goal is to select
the single, "best", alternative out of many. The alternatives are characterized by their
consequences with regard to several objectives. For example, a used car is represented in
terms of kilometers driven, price and car model, which describe its consequences with
regard to objectives "as few kilometers driven as possible", "as cheap as possible" and
"as preferred model as possible". Even swaps are trade-offs, where a consequence of an
alternative is changed (to better or worse) and compensated for by a change in another
consequence. For example, the price of a used-car-alternative is increased, and
compensated for by reduction of the kilometers driven. After the changes in two
consequences, the altered alternative should be equally preferred to the initial.

In the Even Swaps process, the decision maker (DM) carries out even swaps that replace
initial alternatives with the equally preferred, altered, alternatives. The swaps aim at
revealing the best alternative by creating dominances. An alternative x dominates an
alternative y, if x is better with regard to one objective, and at least as good as y with
regard to rest of the objectives. The even swap process should be carried out to a point
where only one alternative remains non-dominated. To the knowledge of the author, at
least six reported applications of the method exist in current academic literature (Kajanus
et al. 2001, Gregory and Wellman 2001, Wakshull 2002, Hurley and Andrews 2003, Luo
and Cheng 2006, Dereli and Altun 2012).

The Even Swaps process can be carried out in multiple ways: the DM decides which
swaps he wants to make and the order in which they are made. If the DM is rational, it
does not matter which swaps are made to carry out the process - if only one alternative is
non-dominated, it is the most preferred one. On the other hand, making the even swaps
truly even in terms of preferences can be a difficult task; random elements or systematic
biases affecting the swaps may play a role. As a consequence, the outcome of the Even
Swaps process might be affected by which swaps are selected and the order in which they

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are carried out, i.e., the path. I define the path dependency in the Even Swaps process to
mean a systematic relation between the path and the outcome.

In this work, I take a look at behavioral decision making literature (e.g. Samuelson and
Zeckhauser 1988, Tversky and Kahneman 1991, Delquie 1993) and apply the known
results to identify some of the possible sources of path dependency in the Even Swaps
process. Moreover, I discuss an experimental design to investigate the phenomena and
report results from preliminary experiments. The aim is to later use similar design in a
real life experiment. The experiment will be carried out with the Smart-Swaps software
(Hamalainen et al. 2003) which is based on the Smart-Swaps decision support system
(Mustajoki and Hamalainen 2005, 2007) that aids the DM in going trough the Even
Swaps process.

2. The Even Swaps method
The Even Swaps method is introduced alongside the decision making process PrOACT
(Problem, Objectives, Alternatives, Consequences and Trade-offs) by Hammond et al. in
their book Smart Choices (1999). In this work, I take problem, objectives, alternatives
and consequences as given and concentrate on the trade-offs part, more specifically, the
Even Swaps process.

In the beginning point of the Even Swaps process, the DM has several alternatives, which
are described by several consequences that measure the alternatives' success towards the
given objectives. These elements are presented in a consequences table. Here, I will
introduce the method with an illustrative example adopted from the Harvard Business
Review article by Hammond et al. (1998). The example considers a case where a
computer scientist, Alan Miller, is deciding upon a new office location. Miller's
consequences table is presented as table 1. Commute in minutes measures Miller's
commuting time, customer access measures the percentage of current customers within
travel radius of an hour, office services measures the amount of services in the office
building (e.g. copy and fax machines) and the two last objectives are self explanatory.

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Table 1. Miller's initial consequences table

Alternatives



Objectives
Parkway Lombard Baranov Montana Pierpoint
Commute in minutes
45
25
20
25
30
Customer access (%)
50
80
70
85
75
Office services
Good
Okay
None
Good
None
Office size (square feet)
800
700
500
950
700
Monthly cost ($)
1850
1700
1500
1900
1750

2.1. Dominance and irrelevance
An alternative x dominates alternative y, if x is better with regard to one objective, and at
least as good as y with regard to the rest of the objectives. In the example case, the
Lombard office dominates the Pierpoint office, as it is better or equal with regard to each
objective. Looking at table 1, it can also be seen that Montana is better or equal to
Parkway in each but the last objective: monthly cost. In the case that an alternative is
very close to dominating another alternative, a concept of practical dominance can be
used. Here, since Montana is clearly better in several alternatives and only slightly worse
in one, Parkway can be eliminated as practically dominated. After these dominations, the
consequences table reduces to table 2, where the dominated and practically dominated
alternatives are removed.

Table 2. Miller's consequences table after eliminating Parkway and Pierpoint.

Alternatives

Objectives
Lombard Baranov Montana
Commute in minutes
25
20
25
Customer access (%)
80
70
85
Office services
Okay
None
Good
Office size (square feet)
700
500
950
Monthly cost ($)
1700
1500
1900


An objective is irrelevant if all the alternatives have the same consequence with regard to
it. In table 2 none of the objectives are irrelevant. On the other hand, if Baranov's
commute time was 25, the commute time would be an irrelevant objective. Making

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objectives irrelevant is a sound goal in determining which even swaps to begin with,
because, as a consequence the alternatives will differ in fewer objectives and creating
dominances becomes easier. However, the irrelevant objectives should not be removed
from the consequences table without further considerations. For more detailed discussion
about this topic, see section 2.3 Theoretical premises of the Even Swaps.

2.2. Making the even swaps
An even swap consists of switching an alternative's consequence in two objectives. First
one consequence is changed with a certain amount and then compensated for by a change
in another consequence of the same alternative. After the swap the altered alternative
should be equally preferred to the initial one. Therefore, the altered alternative can
replace the initial in the consequences table.

Before deciding on the amounts of the changes, the DM needs to choose what he wants to
swap. When choosing a swap, the DM should seek for possibility of dominances and
irrelevances. At the end, the goal is to dominate all but one alternative. Then again, some
trade-offs are easier to make than others. For example, if the swap is between two
discrete scales, it might be impossible to find an even trade-off. Or it might be hard to
compare quantitative and qualitative scales. In their article Hammond et al. (1999)
suggest making the easier swaps first.

In our example, a good swap to start with, could be making "commute in minutes" an
irrelevant objective. This is done in the illustration of Hammond et al. (1999) as follows:
Alan Miller will make a swap in the alternative Baranov such that "commute in minutes"
is increased from 20 to 25 minutes and it is compensated for by a change in customer
access from 70% to X%. After consideration, Miller decides X to be 78 which results in
the following consequences table (table 3). The irrelevant objective is highlighted with
yellow color.

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Table 3. Miller's consequences table after a swap in Baranov.

Alternatives

Objectives
Lombard Baranov Montana
Commute in minutes
25
25
25
Customer access (%)
80
78
85
Office services
Okay
None
Good
Office size (square feet)
700
500
950
Monthly cost ($)
1700
1500
1900

Next in the illustration of Hammond et al. (1999), Alan Miller decides to make office
services irrelevant. This is done by switching both Baranov's and Montana's office
services to Okay, compensated for by switches in the alternatives' monthly cost. The
result is presented in table 4.

Table 4. Miller's consequence table after Baranov is dominated.

Alternatives

Objectives
Lombard Baranov Montana
Commute in minutes
25
25
25
Customer access (%)
80
78
85
Office services
Okay
Okay
Okay
Office size (square feet)
700
500
950
Monthly cost ($)
1700
1700
1800

After the swap Baranov is dominated by Lombard. In table 4 the dominated alternative is
marked with red and can be ignored. The remaining alternatives, Montana and Lombard,
differ in three objectives. Lombard is better only with regard to monthly cost. In the
example of Hammond et al., the Office size is next made irrelevant. Alan Miller makes a
swap in alternative Lombard, where a change in size from 700 to 950 square feet is
compensated for by a change in monthly cost from 1700 to 1950 dollars. The change
results in following consequence table (table 5), in which Montana dominates Lombard.
Montana is therefore left as the only non-dominated alternative and a decision
recommendation for Alan Miller.

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Table 5. Miller's final consequences table.

Alternatives
Objectives
Lombard Montana
Commute in minutes
25
25
Customer access (%)
80
85
Office services
Okay
Okay
Office size (square feet)
950
950
Monthly cost ($)
1950
1800

2.3. Theoretical premises of the Even Swaps
From theoretical perspective, the method does not require many assumptions about the
DM's preferences if objectives are not allowed to be eliminated from the consequences
table. For the use of dominance it is implicitly assumed that for each objective, the
possible consequences can be arranged in a preference order, which is not dependant on
the alternative's consequences with regard to the other objectives. For example, bigger
office is always better, regardless of the other consequences. Often the assumption is
natural, but is not fulfilled in all cases. For example, when dining at a restaurant, the
preference between white and red whine is dependent on the choice of food.

Moreover, the method is based on the transitive preference relation that allows the DM to
replace an original alternative with a virtual one in the consequences table. For example,
if original alternatives x and y are equally preferred to virtual alternatives x' and y', then
preference of x' over y' implies that x is preferred to y.

The role of irrelevances is controversial. In the original paper of Hammond et al. (1999),
it is said that irrelevant objectives can be eliminated (p.7). In the papers of Mustajoki and
Hamalainen (2005, 2007), it is said that irrelevant objectives can be eliminated, but in the
Smart-Swaps software (Hamalainen et al. 2003) the user can decide to eliminate or not
eliminate the irrelevant alternatives. Clearly in some occasions, the DM should not be
allowed to eliminate the irrelevant objective. For example, in deciding which apartment
to choose, a change in the apartment's size is more valuable, if the building is new, than
if it is old. In other words, in new building gaining a square meter is more valuable than

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in old building. Therefore, when making an even swap, for example between size and
cost, the age is relevant. As a conclusion, the decision maker should be instructed to
always consider all the consequences of an alternative, when making a swap in two of
them.

Discussion about the assumptions behind eliminating objectives has been omitted in most
published papers about the Even Swaps (Hammond et al. 1998, 1999, Gregory et al.
2001, 2012, Mustajoki and Hamalainen 2005, 2007, Wachowicz 2010, Elahi and Yu
2012). Neglecting the implications of removing objectives may affect the outcome of the
Even Swaps process. The issue should be noted in an academic publication, as especially
people with no decision analysis education may not notice the mistake. The Even Swaps
method has been proposed, for example in making healthcare decisions (Dolan 2010).

Theoretically, the elimination of irrelevant objectives could be justified, if changes in
consequences with regard to remaining objectives are difference independent (for
definition, see e.g. Dyer and Sarin 1979) of the eliminated objective. That is, the values
of changes in remaining objectives are not dependent of consequence with regard to the
eliminated objective.

3. The Smart-Swaps decision support system
The Smart-Swaps software (Hamalainen et al. 2003) is designed to support the Even
Swaps process. First the user is instructed to create the consequences table, after which he
can proceed to the trade-offs section. The trade-offs tab of Smart-Swaps software is
presented in figure 1.

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Figure 1. The trade-offs windows of Smart-Swaps software.

In Smart-Swaps, the even swap in alternative A is made such that a consequence in A is
switched to same level as it is for alternative X. The switch is compensated for by a
change in another consequence of the alternative A.
1. Select A and X, and the consequence of A you want to change to the level of X's
2. Decide another consequence of A, to compensate for the change
3. Decide on the amount of compensation

In the figure 2, the consequence in objective "Malli" (model) in alternative Alfa is
changed to the same level as the consequence is for Gamma. This change is compensated
for by an increase in Alfa's consequence level with regard to objective "Ajokilometrit"
(kilometers driven)

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