INTEREST-BASED PREFERENCE REASONING

Wietske Visser, Koen V. Hindriks and Catholijn M. Jonker

Man-Machine Interaction Group, Delft University of Technology, Delft, The Netherlands

Keywords:

Qualitative preferences, Underlying interests, Argumentation.

Abstract:

In the context of practical reasoning, such as decision making and negotiation, it is necessary to model pref-

erences over possible outcomes. Such preferences usually depend on multiple criteria. We argue that the

criteria by which outcomes are evaluated should be the satisfaction of a person’s underlying interests: the

more an outcome satisﬁes his interests, the more preferred it is. Underlying interests can explain and eliminate

conditional preferences. Also, modelling interests will create a better model of human preferences, and can

lead to better, more creative deals in negotiation. We present an argumentation framework for reasoning about

interest-based preferences. We take a qualitative approach and provide the means to derive both ceteris paribus

and lexicographic preferences.

1 INTRODUCTION

We present an approach to qualitative, multi-criteria

preferences that takes underlying interests explicitly

into account. Reasoning about interest-based prefer-

ences is relevant in decision making, negotiation, and

other types of practical reasoning. Since our long-

term goal is the development of a negotiation support

system, the motivations and examples in this paper

are mainly taken from the context of negotiation, but

the main ideas apply equally well in other contexts.

The goal of a negotiation support system is to help

a human negotiator reach a better deal in negotiation.

The quality of a deal is determined for a large part by

the user’s personal preferences. A deal generally con-

sists of multiple issues. For example, when applying

for a new job, some issues are the position, the salary,

and the possibility to work part-time. For a complete

deal, negotiators have to agree on the value for every

issue. The satisfaction of a negotiator with a possible

outcome depends on his preferences.

Since the number of possible outcomes is typ-

ically very large (exponential in the number of is-

sues), it is not feasible to have the user express his

preferences over all possible outcomes directly. It

is common to compute or derive preferences over

possible outcomes from preferences over the possi-

ble values of issues and a weighing or importance

ordering of the issues. One of the best-known ap-

proaches is multi-criteria utility theory (Keeney and

Raiffa, 1993), a quantitative approach where prefer-

ences are expressed by numeric utilities. Since such

quantities are hard for humans to provide, qualitative

approaches have been proposed too, e.g. (Brewka,

2004). Our approach is also of a qualitative nature.

In this paper we argue that issues alone are not

enough to derive outcome preferences. Instead, we

will focus on modelling underlying interests and their

relation to issues. There are several reasons for taking

interests into account. First, underlying interests can

explain and eliminate conditional preferences. Con-

sider the following example. If it rains, I prefer to

take my umbrella, but if it doesn’t, I prefer not to take

it. This is a conditional preference; my preference

over taking my umbrella depends on the circumstance

of rain. Underlying interests can explain such condi-

tional preferences: I prefer to take my umbrella when

it rains because I do not want to get wet, and I pre-

fer not to take it when it’s dry because I don’t want

to carry things unnecessarily. If we take such inter-

ests as criteria on which to base preference, we can

eliminate conditional preferences entirely. We will

get back to this in more detail later. Second, interest-

based negotiation is said to lead to better outcomes

than position-based negotiation (Keeney, 1992; Rah-

wan et al., 2007). By understanding one’s own and

the other party’s reasons behind a position and dis-

cussing these interests, people are more likely to ﬁnd

more creative options in a negotiation and by that

reach a mutually acceptable agreement more easily. A

well-known example is that of the two sisters negoti-

ating about the division of an orange. They both want

79

Visser W., V. Hindriks K. and M. Jonker C..

INTEREST-BASED PREFERENCE REASONING.

DOI: 10.5220/0003141300790088

In Proceedings of the 3rd International Conference on Agents and Artiﬁcial Intelligence (ICAART-2011), pages 79-88

ISBN: 978-989-8425-40-9

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

the orange, and end up splitting it in half. Had they

known each other’s underlying interests, they would

have reached a better deal: one sister only needed the

peel to make a cake and would gladly have let the

other sister have all of the ﬂesh for her juice. Third,

thinking about underlying interests is a very natural,

human thing to do. Interests are what really matters

to people, they are what drive them in their decisions

and opinions. Taking underlying interests explicitly

into account will result in a better model of human

preferences. Such a model is also suited for explana-

tion of the reasoning and advice of a support system.

This last point brings us to the motivation for us-

ing argumentation to reason about interest-based pref-

erences. Reasoning by means of arguments is a very

human type of reasoning. People often base their de-

cisions on (mental) lists of arguments in favour of and

against certain decisions. Therefore argumentation is

suitable for explanation of a system’s reasoning to a

human user. Another advantage of argumentation is

that it is a kind of defeasible reasoning. It is able to

reason with incomplete, uncertain and contradictory

information. Finally, argumentation can be used to

(try to) persuade the opponent during negotiation (but

this is outside the scope of this paper).

The paper is organised as follows. In Section 2

we introduce and discuss the most important con-

cepts that we will use throughout the paper. Then,

in Section 3, we give an overview of existing ap-

proaches to preferences and underlying interests. We

give some more details about qualitative multi-criteria

preferences in Section 4. In Section 5 we motivate

the explicit modelling of underlying interests, illus-

trated with examples. Our own approach is presented

in Section 6. Finally, Section 7 concludes the paper.

2 CONCEPTS

Before we go on, we will clarify some important con-

cepts that we will use. In negotiation, issues are the

matters which are under negotiation. An issue is a

concrete, negotiable aspect such as monthly salary or

number of holidays. Every issue has a set or range

of possible values. The value of an issue in a given

instance can be objectively determined (e.g. e2400,

30 days). Issues and their possible values typically

depend on the domain. Besides the issues under ne-

gotiation, there may be other properties of a deal that

inﬂuence preferences. For example, the location of

the company that you are applying to work for can be

very important, because it determines the duration of

your daily commute, but it is hardly negotiable. Still,

such properties are important in negotiation. If, for

example, you already got an offer from another com-

pany near your home, you will only consider offers

that are better taking the location into account.

A possible outcome or possible deal has a spec-

iﬁed value for every issue. All bids made during a

negotiation are possible outcomes. For example, a

possible outcome could be a job contract for the posi-

tion of programmer, with a salary of e3000 gross per

month, with 25 holidays, for the duration of one year

with the possibility of extension. Any other assign-

ment to the issues would constitute a different out-

come. It is the user’s preferences over such possible

outcomes that we are interested in.

With criteria we mean the features on which a

preference between outcomes is based. It is common

to base preferences directly on the negotiated issues;

in that case the issues are the criteria. In this paper we

argue that not issues, but underlying interests should

be used as criteria.

Many terms are used for what we consider to be

underlying interests, such as fundamental objectives,

values, concerns, goals and desires. In our view, an

interest can be any kind of motivation that leads to a

preference. Essentially, a preference depends on how

well your interests are met in the outcomes to be com-

pared. The degree to which interests are met is in-

ﬂuenced by the issues, but there is not necessarily a

one-to-one relation between issues and interests. For

example, an applicant with childcare responsibilities

will have the interest that the children are taken care

of after school. This interest can be met by various

different issues, for example part-time work, the pos-

sibility to work from home, a salary that will cover

childcare expenses, etc. One issue may also con-

tribute to multiple interests. Many issues that deal

with money do so, because the interests different peo-

ple have for using the money will be diverse.

3 RELATED WORK

Existing literature about preferences is abundant and

very diverse. In this section we brieﬂy discuss the ap-

proaches that are most closely related to our interests.

Interest-based negotiation is discussed in (Rah-

wan et al., 2007). However, this approach has a par-

ticular view on negotiation as an allocation of indi-

visible and non-sharable resources. The resources are

needed to carry out plans to reach certain goals. Even

though the goals can be seen as underlying interests, it

is hard to model e.g. negotiation about a job contract

as an allocation of resources. Salary might be an allo-

cation of money, but other issues, like position or start

date, cannot be translated as easily into resources.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

80

Argumentation about preferences has been stud-

ied extensively in the context of decision making

(Amgoud et al., 2005; Amgoud and Prade, 2009;

Ouerdane et al., 2008; Ouerdane et al., 2010). The

aim of decision making is to choose an action to per-

form. The quality of an action is determined by how

well its consequences satisfy certain criteria. For ex-

ample, (Amgoud et al., 2005) present an approach in

which arguments of various strengths in favour of and

against a decision are compared. However, it is a two-

step process in which argumentation is used only for

epistemic reasoning. In our approach, we combine

reasoning about preferences and knowledge in a sin-

gle argumentation framework.

Within the context of argumentation, an approach

that is related to underlying interests is value-based

argumentation (Bench-Capon, 2003; Bench-Capon

and Atkinson, 2009). Values are used in the sense

of ‘fundamental social or personal goods that are de-

sirable in themselves’ (Bench-Capon and Atkinson,

2009), and are used as the basis for persuasive argu-

ment in practical reasoning. In value-based argumen-

tation, arguments are associated with values that they

promote. Values are ordered according to importance

to a particular audience. An argument only defeats

another argument if it attacks it and the value pro-

moted by the attacked argument is not more impor-

tant than the value promoted by the attacker. We will

illustrate this with a little example. Consider two job

offers a and b. a offers a higher salary, but b offers

a better position. We can construct two mutually at-

tacking preference arguments, A: ‘I prefer job offer a

over job offer b because it has a higher salary’, and B:

‘I prefer job offer b over job offer a because it has a

better position’. In Dung-style argumentation frame-

works (Dung, 1995), there is no way to choose be-

tween two mutually attacking arguments (unless one

is defended and the other is not). In value-based argu-

mentation, we could say that preferring a over b pro-

motes the value of wealth (w), and preferring b over

a promotes the value of status (s), and e.g. wealth is

considered more important than status. In this case A

defeats B, but not the other way around.

In this framework, every argument is associated

with only one value, while in many cases there are

multiple values or interests at stake. (Kaci and van der

Torre, 2008) deﬁne so-called value-speciﬁcation ar-

gumentation frameworks, in which arguments can

support multiple values, and preference statements

about values can be given. However, the preference

between arguments is not derived from the preference

between the values promoted by the arguments. Be-

sides, there is no guarantee that a value-speciﬁcation

argumentation framework is consistent, i.e., some sets

of preference statements do not correspond to a pref-

erence ordering on arguments.

In value-based argumentation, we cannot argue

about what values are promoted by the arguments

or the ordering of values; this mapping and order-

ing are supposed to be given. But these might well

be the conclusion of reasoning, and might be defea-

sible. Therefore, it would be natural to include this

information at the object level. (van der Weide et al.,

2009) describe some argument schemes regarding the

inﬂuence of certain perspectives on values. However,

for the aggregation of multiple values, they assume a

given order on sets of values, whereas we want to de-

rive such an order from an order on individual values.

4 QUALITATIVE

MULTI-CRITERIA

PREFERENCES

Regardless of whether we take issues or interests as

criteria, we need to be able to model multiple criteria.

In any realistic setting, preferences are determined

by multiple criteria and the interplay between them.

Therefore we shortly introduce two well-known ap-

proaches to multi-criteria preferences which we will

use in our framework.

One approach is ceteris paribus (‘all else being

equal’) comparison. One outcome is preferred to an-

other ceteris paribus, if it is better on some criteria and

the same on all other criteria. This approach has been

widely used since (von Wright, 1963). Also (Well-

man and Doyle, 1991) derive preferences from sets

of goals in a ceteris paribus way. In (Boutilier et al.,

2004), ceteris paribus comparison is combined with

conditional preferences in a graphical preference lan-

guage called CP-nets. The preference order resulting

from ceteris paribus comparison is not complete; an

outcome satisfying criterion G but not H cannot be

compared to an outcome satisfying H but not G.

Another well-known approach is the lexico-

graphic preference ordering (see e.g. (Brewka, 2004),

where it is denoted #). Here, preferences over out-

comes are based on a set of relevant criteria, which are

ranked according to their importance. The importance

ranking of criteria is deﬁned by a total preorder ,

which yields a stratiﬁcation of the set of criteria into

importance levels. Each importance level consists of

criteria that are equally important. The lexicographic

preference ordering ﬁrst considers the highest impor-

tance level. If some outcome satisﬁes more criteria on

that level than another, then the ﬁrst is preferred over

the second. If two outcomes satisfy the same num-

INTEREST-BASED PREFERENCE REASONING

81

Table 1: Satisfaction of issues and interests.

a. Issues b. Interests

high high full-

salary position time

a 3 3 3

b 3 3 7

c 3 7 3

d 3 7 7

e 7 3 3

f 7 3 7

g 7 7 3

h 7 7 7

family

wealth status time

a 3 3 7

b 3 3 3

c 3 3 7

d 3 3 3

e 7 3 7

f 7 3 3

g 7 7 7

h 7 7 3

ber of criteria on this level, the next importance level

is considered, and so on. Two outcomes are equally

preferred if they satisfy the same number of criteria

on every level.

We use a slightly more abstract deﬁnition of pref-

erence that covers both ceteris paribus and lexico-

graphic preferences. Let C be a set of binary criteria,

ordered according to importance by a preorder . If

P Q and not Q P, we say that P is strictly more

important than Q and write P Q. If P Q and

Q P, we say that P is equally important as Q and

write P ≈ Q. C can be divided into equivalence classes

induced by ≈, which we call importance levels. An

importance level L is said to be more important than

L

0

iff the criteria in L are more important than the cri-

teria in L

0

. Let O be a set of outcomes, and sat a

function that maps outcomes a ∈ O to sets of criteria

C

a

∈ 2

C

. If P ∈ sat(a), we say that a satisﬁes P.

Deﬁnition 1. (Preference). An outcome a is strictly

preferred to another outcome b if it satisﬁes more cri-

teria on some importance level L, and for any impor-

tance level L

0

on which b satisﬁes more criteria than

a, there is a more important level on which a satisﬁes

more criteria than b. An outcome a is equally pre-

ferred as another outcome b if both satisfy the same

number of criteria on every importance level.

The least speciﬁc importance order possible is the

identity relation, in which case the importance lev-

els are all singletons and no importance level is more

important than any other. In this case, the preference

deﬁnition is equivalent to ceteris paribus preference

(if a is preferred to b ceteris paribus, there are no cri-

teria that b satisﬁes but a does not). If the importance

order is a total preorder, the deﬁnition is equivalent

to lexicographic preference. In general, the more in-

formation about the relative importance of interests

is known, the more preferences can be derived. We

note that lexicographic preferences subsume ceteris

paribus preferences in the sense that if one outcome

is preferred to another ceteris paribus, it is also pre-

b,d

g

he

fa,c

e,f

c,d

g,ha,b

a) For Mark. b) For Jones.

Figure 1: Ceteris paribus preference orderings (arrows point

towards more preferred outcomes).

ferred lexicographically, regardless of the importance

ordering on criteria.

5 MODELLING INTERESTS

We will illustrate the ideas presented in this paper by

means of an example. Mark has applied for a job at a

company called Jones. After the ﬁrst interview, they

are ready to discuss the terms of employment. There

are three issues on the table: the salary, the position,

and whether the job is full-time or part-time. All pos-

sible outcomes are listed in Table 1a. After some

thought, Mark has determined that the interests that

are at stake for him are wealth, status, and time with

his family. A high position will give status. A high

salary will provide both wealth and status. A part-

time job will give him time to spend with his family.

Table 1b shows which interests each of the outcomes

satisﬁes.

All information is encoded in a knowledge base,

which consists of three parts.

• Facts about the properties of the outcomes to be

compared. When comparing offers in negotiation,

these may be the values for each issue, or any

other relevant properties. Facts are supposed to

be objectively determined.

• A set of interests of a negotiator. Underlying in-

terests are personal and subjective, although they

can sometimes be assumed by default. Interests

may vary according to importance. If no impor-

tance ordering is given, the ceteris paribus princi-

ple can be used to derive preferences. The more

information about the relative importance of in-

terests is known, the more preferences can be de-

rived. If there is a total preorder of interests ac-

cording to importance, a complete preference or-

dering over possible outcomes can be derived us-

ing the lexicographic principle.

• Rules relating issues and other outcome proper-

ties to interests. These rules can be very sub-

jective, e.g. some people consider themselves

very wealthy if they earn e3000 gross salary per

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

82

Table 2: Outcomes in the evening dress example.

a. Issues b. Interests

jacket pants shirt

i b b w

j b b r

k b w w

l b w r

m w b w

n w b r

o w w w

p w w r

good

combi-

nation

i 7

j 3

k 3

l 7

m 3

n 7

o 7

p 3

month, while for others this may be a pittance.

Even so, there can still be default rules that apply

in general, e.g. that a high salary promotes wealth

for the employee. The relation between issues and

interests does not have to be one-to-one. There

may be multiple issues that can satisfy an inter-

est, some issues may satisfy multiple interests at

once, or a combination of issues may be needed

to fulﬁll an interest. As is common in defeasible

reasoning, there may be exceptions to rules. For

example, one might say that a high position en-

sures status in general, but this effect is cancelled

out if the job is badly paid.

With the inference scheme of defeasible modus

ponens (see scheme 1 in Table 4), arguments can be

constructed that derive statements about what inter-

ests are satisﬁed by possible outcomes, based on their

issue values and the rules relating issues to interests.

The conclusions from these arguments are summa-

rized in Table 1b. If we compare the possible out-

comes ceteris paribus, we can construct a partial pref-

erence order for Mark, with b and d being the most

preferred options, and g the least preferred (see Fig-

ure 1a). This preference order is not complete. To

determine Mark’s preference between a and c on the

one hand and f on the other hand, we need to know

whether wealth or family time is more important to

him. If wealth is more important, Mark will prefer a

or c. If family time is more important, he will prefer

f . Similarly, to determine a preference between e and

h, we need to know whether status or family time is

more important.

The company Jones has two major interests: it

needs a manager and it has to cut back on expenses.

These interests relate directly (one-to-one) to high po-

sition and low salary. The ceteris paribus preference

ordering for Jones is displayed in Figure 1b.

i

p

nl

mk

j

o

i

pnl

mk

j

o

p

i

nl

mk

j

o

a) Preference graph

induced by CP-net.

b) Ceteris paribus or-

dering with interests.

c) Ceteris paribus or-

dering with interests,

good combination

most important.

Figure 2: Preference orderings (arrows point towards more

preferred outcomes).

The Added Value of Interests. It may seem that

using interests next to issues just introduces an extra

layer in reasoning. From the issues and the relations

between issues and interests, we derive the interests

that are met by outcomes, and from that we derive

preferences. Would it not be easier to derive the pref-

erences directly from the issues? We could just state

that Jones has the interests of high position and low

salary, optionally with an ordering between them, and

we would be able to derive Jones’ preferences from

that. This is because in this case there is a one-to-one

relation between interests and issues: every interest is

met by exactly one issue, and every (relevant) issue

meets exactly one interest.

There are good reasons, however, why this ap-

proach is not always a good solution. Consider for

example Mark’s preferences. A high salary satisﬁes

both wealth and status, and status can be satisﬁed by

either a high salary or a high position. Because of

this, the (partial) preference ordering we determined

for Mark cannot be deﬁned as a ceteris paribus order-

ing if the issues are taken as criteria. This is because

high position as criterion is dependent on high salary:

if the salary is not high, then high position is a distin-

guishing criterion, but if the salary is high, high po-

sition is not relevant anymore, since the only interest

that it serves, status, is already satisﬁed by high salary.

So with a ﬁxed set of issues as criteria, ceteris paribus

or lexicographic models cannot represent every pref-

erence order. In many cases, this can be solved intu-

itively by taking underlying interests into account.

There are other approaches to deal with this mat-

ter. Instead of assuming independence of the criteria,

one can also model conditional preferences, where

criteria may be dependent on other criteria. A well-

known approach to represent conditional preferences

is CP-nets (Boutilier et al., 2004), which is short for

conditional ceteris paribus preference networks. A

INTEREST-BASED PREFERENCE REASONING

83

CP-net is a graph where the nodes are variables (com-

parable to our notion of issues). Every node is anno-

tated with a conditional preference table, which lists

a user’s preferences over the possible values of that

variable. If such preferences are conditional (depen-

dent on other variables), each condition has a sepa-

rate entry in the table, and the variables that inﬂu-

ence the preference are parent nodes of this variable

in the graph. In (Boutilier et al., 2004), an example of

conditional preference is given regarding an evening

dress. A man unconditionally prefers black to white

as a colour for both the jacket and the pants. His pref-

erence between a white and a red shirt is conditioned

on the combination of jacket and pants. If they have

the same colour, he prefers a red shirt (for a white

shirt will make his outﬁt too colourless). If they are

of different colours, he prefers a white shirt (because

a red shirt will make his outﬁt too ﬂashy). The com-

plete assignments (outcomes in our terminology) are

listed in Table 2a. The preference graph induced by

the CP-net for this example is displayed in Figure 2a.

We propose to replace the variables the prefer-

ences over which are conditional with underlying

interests – the reason for the dependency. In the

evening dress example, the underlying interest is that

the colours of jacket, pants and shirt make a good

combination, which in this case is deﬁned by being

neither too colourless nor too ﬂashy. The satisfaction

of this interest by the different outcomes is listed in

Table 2b. The variables jacket and pants are uncondi-

tional, so they can remain as criteria. If we take jacket,

pants, and good combination as criteria, we can con-

struct the preference graph in Figure 2b, using the ce-

teris paribus principle. The difference with the prefer-

ences induced by the CP-net is that in the CP-net case,

outcome i is more preferred than k and m, and p is

less preferred than l and n, while in the interest-based

case they are incomparable. This is due to the fact

that in CP-nets, conditional preferences are implicitly

considered less important than the preferences on the

variables they depend on ((Boutilier et al., 2004), p.

145). In fact, if we would specify that both jacket

and pants are more important than a good combina-

tion, our preference ordering would be the same as in

Figure 2a. But the interest approach is more ﬂexible;

it is possible to specify any (partial) importance or-

dering on interests. For example, we could also state

that a good combination is more important than either

the jacket or the pants, which results in the preference

ordering in Figure 2c. In our opinion, there is no a pri-

ori reason to attach more importance to unconditional

variables as is done in the CP-net approach.

Table 3: The knowledge base for the example.

highsal(c) I

M

(wealth) highsal(x) ⇒ wealth(x)

¬highpos(c) I

M

(status) highsal(x) ⇒ status(x)

full-time(c) I

M

(family) highpos(x) ⇒ status(x)

¬highsal( f ) ¬full-time(x) ⇒ family(x)

highpos( f ) I

J

(manager) highpos(x) ⇒ manager(x)

¬full-time( f ) I

J

(cutback) ¬highsal(x) ⇒ cutback(x)

6 ARGUMENTATION

FRAMEWORK

In this section, we present an argumentation frame-

work (AF) for reasoning about qualitative, interest-

based preferences. An abstract AF in the sense of

Dung (Dung, 1995) is a pair hA, →i where A is a

set of arguments and → is a defeat relation (infor-

mally, a counterargument relation) among those ar-

guments. To deﬁne which arguments are justiﬁed, we

use Dung’s (Dung, 1995) preferred semantics.

Deﬁnition 2. (Preferred Semantics) . A preferred

extension of an AF hA, →i is a maximal (w.r.t. ⊆) set

S ⊆ A such that: ∀A, B ∈ S : A 6→ B and ∀A ∈ S: if B →

A then ∃C ∈ S : C → B. An argument is credulously

(sceptically) justiﬁed w.r.t. preferred semantics if it is

in some (all) preferred extension(s).

Informally, a preferred extension is a coherent point

of view that can be defended against all its attack-

ers. In case of contradictory information, there will

be multiple preferred extensions, each advocating one

point of view. The contradictory conclusions will be

credulously, but not sceptically justiﬁed.

We instantiate an abstract AF by specifying the

structure of arguments and the defeat relation.

Arguments. Arguments are built from formulas of

a logical language, that are chained together using

inference steps. Every inference step consists of

premises and a conclusion. Inferences can be chained

by using the conclusion of one inference step as a

premise in the following step. Thus a tree of chained

inferences is created, which we use as the formal def-

inition of an argument (cf. e.g. (Vreeswijk, 1997)).

Deﬁnition 3. (Argument). An argument is a tree,

where the nodes are inferences, and an inference can

be connected to a parent node if its conclusion is a

premise of that node. Leaf nodes only have a con-

clusion (a formula from the knowledge base), and no

premises. A subtree of an argument is also called a

subargument. inf returns the last inference of an ar-

gument (the root node), and conc returns the conclu-

sion of an argument, which is the same as the conclu-

sion of the last inference.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

84

Table 4: Inference schemes.

1

L

1

, . . . , L

k

, ∼ L

l

, . . . , ∼ L

m

⇒ L

n

L

1

. . . L

k

∼ L

l

. . . ∼ L

m

L

n

DMP

2 ∼ L

asm(∼ L)

5

P

1

(a) . . . P

n

(a) P

1

≈

α

. . . ≈

α

P

n

I

α

(P

1

) . . . I

α

(P

n

)

sat(a, [P

1

]

α

, n)

count(a, [P

1

]

α

, {P

1

, . . . , P

n

})

3

L

asm(∼ L) is inapplicable

asm(∼ L)uc

6

P

1

(a) . . . P

n

(a) P

1

≈

α

. . . ≈

α

P

n

I

α

(P

1

) . . . I

α

(P

n

)

count(a, [P

1

]

α

, S ⊂ {P

1

, . . . , P

n

}) is inapplicable

count(a, [P

1

]

α

, S)uc

4 sat(a, [P]

α

, 0)

count(a, [P]

α

, ∅)

7

sat(a, [P]

α

, n) sat(b, [P

0

]

α

, m) P ≈

α

P

0

n > m

pref

α

(a, b)

preﬁnf(a, b, [P]

α

)

8

sat(a, [Q]

α

, n) sat(b, [Q

0

]

α

, m) Q ≈

α

Q

0

α

P n < m

preﬁnf(a, b, [P]

α

) is inapplicable

preﬁnf(a, b, [P]

α

)uc

9

sat(a, [P]

α

, n) sat(b, [P

0

]

α

, m) P ≈

α

P

0

n = m

eqpref

α

(a, b)

eqpreﬁnf(a, b, [P]

α

)

10

sat(a, [Q]

α

, n) sat(b, [Q

0

]

α

, m) Q ≈

α

Q

0

n 6= m

eqpreﬁnf(a, b, [P]

α

) is inapplicable

eqpreﬁnf(a, b, [P]

α

)uc

Deﬁnition 4. (Language). Let P be a set of predicate

names with typical elements P,Q; O a set of outcome

names with typical elements a, b; α an audience; and

n a non-negative integer. The input language L

KB

and

full language L are deﬁned as follows.

ϕ ∈ L

KB

::= L | I

α

(P) | P

α

Q | P ≈

α

Q |

L

1

, . . . , L

k

, ∼ L

l

, . . . , ∼ L

m

⇒ L

n

where L

i

= P(a) or ¬P(a).

ψ ∈ L ::= ϕ ∈ L

KB

| ∼ L | sat(a, [P]

α

, n) |

pref

α

(a, b) | eqpref

α

(a, b)

We make a distinction between an input and full lan-

guage. A knowledge base, which is the input for an

argumentation framework, is speciﬁed in the input

language. The input language allows us to express

facts about the criteria that outcomes (do not) satisfy,

statements about interests of an audience and their im-

portance ordering, and defeasible rules. The knowl-

edge base for the job contract example (the facts re-

stricted to outcomes c and f ) is displayed in Table 3.

Other formulas of the language that are not part of the

input language, e.g. expressing a preference between

two outcomes, can be derived from a knowledge base

using inference steps that build up an argument (such

formulas are not allowed in a knowledge base because

they might contradict derived statements).

Inferences. Table 4 shows the inference schemes

that are used. The ﬁrst inference scheme is called

defeasible modus ponens. It allows to infer conclu-

sions from defeasible rules. The next two inference

rules deﬁne the meaning of the weak negation ∼. Ac-

cording to inference rule 2, a formula ∼ ϕ can always

be inferred, but such an argument will be defeated by

an undercutter built with inference rule 3 if ϕ is the

case. Inference schemes 4 and 5 are used to count the

number of interests of equal importance (according to

audience α) as some interest P

1

that outcome a sat-

isﬁes. This type of inference is inspired by accrual

(Prakken, 2005), which combines multiple arguments

with the same conclusion into one accrued argument

for the same conclusion. Although our application

is different, we use a similar mechanism. Inference

scheme 4 can be used when an outcome satisﬁes no

interests. It is possible to construct an argument that

does not count all interests that are satisﬁed, a so-

called non-maximal count. But we want all interests

to be counted, otherwise we would conclude incor-

rect preferences. To ensure that only maximal counts

are used, we provide an inference scheme to construct

arguments that undercut non-maximal counts (infer-

ence scheme 6). An argument of this type says that

any count which is not maximal is not applicable. In-

ference scheme 7 says that an outcome a is preferred

over an outcome b if the number of interests of a cer-

tain importance level that a satisﬁes is higher than the

number of interests on that same level that b satisﬁes.

Inference scheme 8 undercuts scheme 7 if there is a

more important level than that of P on which a and b

do not satisfy the same number of interests. Finally,

inference schemes 9 and 10 do the same as 7 and 8,

but for equal preference.

Defeat. The most common type of defeat is re-

buttal. An argument rebuts another argument if its

conclusion contradicts conclusion of the other ar-

gument. Conclusions contradict each other if one

is the negation of the other, or if they are prefer-

INTEREST-BASED PREFERENCE REASONING

85

Table 5: Example arguments.

A:

highsal(c) highsal(x) ⇒ wealth(x)

wealth(c) I

M

(wealth)

sat(c, [wealth]

M

, 1) sat( f , [wealth]

M

, 0) wealth ≈

M

wealth 1 > 0

pref

M

(c, f )

α

B:

¬full-time( f ) ¬full-time(x) ⇒ family(x)

family( f ) I

M

(family)

sat( f , [family]

M

, 1) sat(c, [family]

M

, 0) family ≈

M

family 1 > 0

pref

M

( f , c)

β

C:

highsal(c) highsal(x) ⇒ wealth(x)

wealth(c) I

M

(wealth)

sat(c, [wealth]

M

, 1) sat( f , [wealth]

M

, 0) wealth

M

family 1 6= 0

β is inapplicable

D:

¬full-time( f ) ¬full-time(x) ⇒ family(x)

family( f ) I

M

(family)

sat( f , [family]

M

, 1) sat(c, [family]

M

, 0) family

M

wealth 1 6= 0

α is inapplicable

ence or importance statements that are incompatible

(e.g. pref

α

(a, b) and pref

α

(b, a), or pref

α

(a, b) and

eqpref

α

(a, b)). Defeat by rebuttal is mutual. Another

type of defeat is undercut. An undercutter is an ar-

gument for the inapplicability of an inference used in

another argument. Undercut works only one way. De-

feat is deﬁned recursively, which means that rebuttal

can attack an argument on all its premises and (inter-

mediate) conclusions, and undercut can attack it on

all its inferences.

Deﬁnition 5. (Defeat) . An argument A defeats an

argument B (A → B) if conc(A) and conc(B) are con-

tradictory (rebuttal), or conc(A) =‘inf(B) is inappli-

cable’ (undercut), or A defeats a subargument of B.

Let us return to the example. With the informa-

tion from the knowledge base, the arguments A and

B in Table 5 can be formed. A advocates a preference

for c, based on the interest wealth. B advocates a pref-

erence for f , based on the interest family. Without an

ordering on these interests, no decision between these

arguments can be made. But if wealth

M

family is

known, argument C can be made, which undercuts B.

Similarly, with family

M

wealth, argument D can be

made, which undercuts A.

Validity. If some conditions in the input knowledge

base (KB) hold, it can be shown that the proposed

argumentation framework models ceteris paribus and

lexicographic preference. In the following, we con-

sider a single audience and leave out the subscript α.

Condition 1. Let C be a set of interests to be used as

criteria, with importance order .

(1) For all P, ‘I(P)’ is in KB iff P ∈ C.

(2) For all P ∈ C, a, ‘P(a)’ is a conclusion of a scep-

tically justiﬁed argument iff a satisﬁes P.

(3) The relative importance among interests is

(a) a total preorder,

(b) the identity relation,

and for all P, Q ∈ C, ‘P Q’ is in KB iff P Q, and

‘P ≈ Q’ is in KB iff P ≈ Q.

Theorem 1. (i) If conditions 1.1, 1.2 and 1.3a hold,

then pref(a, b) (resp. eqpref(a, b)) is a sceptically jus-

tiﬁed conclusion of the argumentation framework iff

a is strictly (resp. equally) preferred over b according

to the lexicographic preference ordering.

(ii) If conditions 1.1, 1.2 and 1.3b hold, then pref(a,b)

(resp. eqpref(a,b)) is a sceptically justiﬁed conclu-

sion of the argumentation framework iff a is strictly

(resp. equally) preferred over b according to the ce-

teris paribus preference ordering.

Proof. We prove the theorem for strict preference.

The same line of argument can be followed for equal

preference.

(i) ⇐: Suppose a is strictly lexicographically pre-

ferred over b. This means that there is an impor-

tance level on which a satisﬁes more interests (say,

P

1

, . . . , P

n

) than b (say, P

0

1

, . . . , P

0

m

, n > m), and on all

more important levels, a and b satisfy an equal num-

ber of interests. In this case, we can construct the fol-

lowing arguments, where the ﬁrst two arguments are

subarguments of the third (note that these arguments

can also be built if m is equal to 0, by using the empty

set count).

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

86

P

1

(a) . . . P

n

(a) I(P

1

) . . . I(P

n

) P

1

≈ . . . ≈ P

n

sat(a, [P

1

], n)

P

0

1

(b) . . . P

0

m

(b) I(P

0

1

) . . . I(P

0

m

) P

0

1

≈ . . . ≈ P

0

m

sat(b, [P

0

1

], m)

sat(a, [P

1

], n) sat(b, [P

0

1

], m) P

1

≈ P

0

1

n > m

pref(a, b)

We will now try to defeat this argument. Premises of

the type P(a) are justiﬁed by condition 1.2. Premises

of the type I(P) and P

1

≈ P

2

cannot be defeated (con-

ditions 1.1 and 1.3a). There are three inferences we

can try to undercut (the last inference of the argument

and the last inferences of two subarguments). For the

ﬁrst count, this can only be done if there is another

P

j

such that I(P

j

) and P

j

≈ P and P

j

6∈ {P

1

, . . . , P

n

}

and P

j

(a) is the case. However, P

1

. . . P

n

encompass

all interests that a satisﬁes on this level, so count un-

dercut is not possible. The same argument holds for

the other count. At this point it is useful to note that

these two counts are the only ones that are undefeated.

Any lesser count will be undercut by the count under-

cutter that takes all of P

1

. . . P

n

(resp. P

0

1

. . . P

0

m

) into

account. Such an undercutter has no defeaters, so any

non-maximal count is not justiﬁed. The undercutter

of preﬁnf(a, b, [P

1

]) is based on two counts. We have

seen that any non-maximal count will be undercut. If

the maximal counts are used, we have n = m for un-

dercutter arguments that use Q P, since we have

that on all more important levels than [P

1

], a and b

satisfy an equal number of interests. So the under-

cutter inference rule cannot be applied since n 6= m is

not true. For that reason, a rebutting argument with

conclusion pref(b, a) will not be justiﬁed. This means

that for every possible type of defeat, either the defeat

is inapplicable or the defeater is itself defeated by un-

defeated arguments. This means that the argument is

sceptically justiﬁed.

⇒: Suppose that a is not strictly lexicographically

preferred over b. This means that for all impor-

tance levels [P], either a does not satisfy more in-

terests than b on that level, or there exists a more

important level where b satisﬁes more interests than

a. This means that any argument with conclusion

pref(a, b) (which has to be of the form above) is ei-

ther undercut by count(b, [P], S)uc because it uses a

non-maximal count, or by preﬁnf(a, b, [P])uc because

there is a more important level where a preference for

b over a can be derived. This means that any such

argument will not be sceptically justiﬁed.

(ii) ⇐: Suppose a is strictly ceteris paribus preferred

over b. This means that there is (at least) one interest,

let us say P, that a satisﬁes and b does not, and there

are no interests that b satisﬁes and a does not. In this

case, we can construct the following argument.

P(a) I(P)

sat(a, [P], 1) sat(b, [P], 0) P ≈ P 1 > 0

pref(a, b)

Premise P(a) is justiﬁed by condition 1.2. Premise

I(P) cannot be defeated (condition 1.1). Note

that, since there is no importance ordering speciﬁed,

counts can only include 0 or 1 interest(s). So the ﬁrst

count cannot be undercut, because there are no other

interests that are equally important as P (condition

1.3b). The second count cannot be undercut because

b does not satisfy P. Since there are no interests that b

satisﬁes but a does not, the last inference can only be

undercut by an undercutter that uses a non-maximal

count and so will be undercut itself.

⇒: Suppose a is not strictly ceteris paribus preferred

over b. This means that either there is no interest that

a satisﬁes but b does not, or there is some interest that

b satisﬁes and a does not. In the ﬁrst case, the only ar-

guments that derive a preference for a over b have to

use non-maximal counts and hence are undercut. In

the second case, any argument that derives a prefer-

ence for a over b is rebut by the following argument,

Q(b) I(Q)

sat(b, [Q], 1) sat(a, [Q], 0) Q ≈ Q 1 > 0

pref(b, a)

and is not sceptically justiﬁed.

7 CONCLUSIONS

In this paper we have made a case for explicitly mod-

elling underlying interests when reasoning about pref-

erences in the context of practical reasoning. We have

presented an argumentation framework for reasoning

about qualitative interest-based preferences that mod-

els ceteris paribus and lexicographic preference.

In the current framework, we have only consid-

ered Boolean issues and interests. While this sufﬁces

to illustrate the main points discussed in this paper,

multi-valued scales would be more realistic. Such

an approach would open the way to modelling dif-

ferent degrees of (dis)satisfaction of an interest. For

example, (Amgoud et al., 2005) take into account the

level of satisfaction of goals on a bipolar scale. In

the Boolean case, the lexicographic preference order-

ing is based on counting the number of interests that

are satisﬁed by outcomes. This is no longer possi-

ble if multi-valued scales are used. In that case, we

INTEREST-BASED PREFERENCE REASONING

87

could count interests that are satisﬁed to a certain de-

gree (like e.g. (Amgoud et al., 2005)), or compare out-

comes in a pairwise fashion and count the number of

interests that one outcome satisﬁes to a higher degree

than another (like e.g. (Ouerdane et al., 2008; van der

Weide et al., 2009)).

Currently, we suppose that the interests and im-

portance ordering among them are given in a knowl-

edge base. We can make our framework more ﬂexible

by allowing such statements to be derived in a way

that is similar to the derivation of statements about

the satisfaction of interests.

We would also like to look into the interplay

between different issues promoting or demoting the

same interest. For example, a high salary and a high

position both lead to status, but together they may

lead to even more status. Or a low salary may pro-

mote cutback, but providing a lease car will demote

it. Do these effects cancel each other out? The prin-

ciples that play a role here are related to the questions

posed in the context of accrual of arguments (Prakken,

2005).

Since our long-term goal is the development of

an automated negotiation support system, we plan

to look into negotiation strategies that are based on

qualitative, interest-based preferences as described

here, as opposed to utility-based approaches cur-

rently in use. For the same reason, we plan to im-

plement the argumentation framework for reasoning

about interest-based preferences that we have pre-

sented here. Another interesting question in this con-

text is how interest-based preferences can be elicited

from a human user.

ACKNOWLEDGEMENTS

We thank Henry Prakken for useful comments on ear-

lier drafts of this paper. This research is supported by

the Dutch Technology Foundation STW, applied sci-

ence division of NWO and the Technology Program

of the Ministry of Economic Affairs. It is part of the

Pocket Negotiator project with grant number VICI-

project 08075.

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