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An argumentation-based approach to multiple

criteria decision

Leila AmgoudJean-Francois BonnefonHenri Prade

Institut de Recherche en Informatique de Toulouse (IRIT)

118, route de Narbonne,

31062 Toulouse Cedex 4 France

{amgoud, bonnefon, prade}@irit.fr

Abstract. The paper presents a first tentative work that investigates

the interest and the questions raised by the introduction of argumenta-

tion capabilities in multiple criteria decision-making. Emphasizing the

positive and the negative aspects of possible choices, by means of ar-

guments in favor or against them is valuable to the user of a decision-

support system. In agreement with the symbolic character of arguments,

the proposed approach remains qualitative in nature and uses a bipolar

scale for the assessment of criteria. The paper formalises a multicriteria

decision problem within a logical argumentation system. An illustrative

example is provided. Various decision principles are considered, whose

psychological validity is assessed by an experimental study.

Keywords: Argumentation; multiple-criteria decision, qualitative scales.

1Introduction

Humans use arguments for supporting claims e.g. [5] or decisions. Indeed, they

explain past choices or evaluate potential choices by means of arguments. Each

potential choice has usually pros and cons of various strengths. Adopting such

an approach in a decision support system would have some obvious benefits. On

one hand, not only would the user be provided with a “good” choice, but also

with the reasons underlying this recommendation, in a format that is easy to

grasp. On the other hand, argumentation-based decision making is more akin

with the way humans deliberate and finally make a choice. Indeed, the idea of

basing decisions on arguments pro and cons is very old and was already some-

what formally stated by Benjamin Franklin [10] more than two hundreds years

ago.

Until recently, there has been almost no attempt at formalizing this idea if

we except works by Fox and Parsons [9], Fox and Das [8], Bonnet and Geffner

[3] and by Amgoud and Prade [2] in decision under uncertainty. This paper

focuses on multiple criteria decision making. In what follows, for each criterion,

one assumes that we have a bipolar univariate ordered scale which enables us

to distinguish between positive values (giving birth to arguments pro a choice

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x) and negative values (giving birth to arguments cons a choice x). Such a scale

has a neutral point, or more generally a neutral area that separates positive and

negative values. The lower bound of the scale stands for total dissatisfaction and

the upper bound for total satisfaction; the closer to the upper bound the value

of criterion cifor choice x is, the stronger the value of ciis an argument in favor

of x; the closer to the lower bound the value of criterion cifor choice x is, the

stronger the value of ciis an argument against x.

In this paper, we propose an argumentation-based framework in which ar-

guments provide the pros and cons of decisions are built from knowledge bases,

which may be pervaded with uncertainty. Moreover, the arguments may not have

equal forces and this make it possible to compare pairs of arguments. The force

of an argument is evaluated in terms of three components: its certainty degree,

the importance of the criterion to which it refers, and the (dis)satisfaction level

of this criterion. Finally, decisions can be compared, using different principles,

on the basis of the strength of their relevant arguments (pros or cons).

The paper is organized as follows. Section 2 states a general framework for

argumentation-based decision, and various decision principles. This framework

is then instantiated in section 3. Lastly, section 4 reports on the psychological

validity of these decision principles.

2A general framework for multiple criteria decision

Solving a decision problem amounts to defining a pre-ordering, usually a com-

plete one, on a set X of possible choices (or decisions), on the basis of the different

consequences of each decision. Argumentation can be used for defining such a

pre-ordering. The basic idea is to construct arguments in favor of and against

each decision, to evaluate such arguments, and finally to apply some principle

for comparing the decisions on the basis of the arguments and their quality or

strengths. Thus, an argumentation-based decision process can be decomposed

into the following steps:

1. Constructing arguments in favor of /against each decision in X.

2. Evaluating the strength of each argument.

3. Comparing decisions on the basis of their arguments.

4. Defining a pre-ordering on X.

2.1Basic definitions

Formally, an argumentation-based decision framework is defined as follows:

Definition 1 (Argumentation-based decision framework). An argumentation-

based decision framework is a tuple <X, A, ?, ?Princ> where:

– X is a set of all possible decisions.

– A is a set of arguments.

– ? is a (partial or complete) pre-ordering on A.

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– ?Princ(for principle for comparing decisions), defines a (partial or complete)

pre-ordering on X, defined on the basis of arguments.

The output of the framework is a (complete or partial) pre-ordering ?Princ, on

X. x1?Princx2means that the decision x1is at least as preferred as the decision

x2w.r.t. the principle Princ.

Notation: Let A, B be two arguments of A. If ? is a pre-order, then A ? B

means that A is at least as ‘strong’ as B.

? and ≈ will denote respectively the strict ordering and the relation of equiva-

lence associated with the preference between arguments. Hence, A ? B means

that A is strictly preferred to B. A ≈ B means that A is preferred to B and B

is preferred to A.

Different definitions of ? or different definitions of ?Princ may lead to differ-

ent decision frameworks which may not return the same results.

Each decision may have arguments in its favor, and arguments against it. An ar-

gument in favor of a decision represents the good consequences of that decision.

In a multiple criteria context, this will represent the criteria which are positively

satisfied. On the contrary, an argument against a decision may highlight the

criteria which are insufficiently satisfied. Thus, in what follows, we define two

functions which return for a given set of arguments and a given decision, all the

arguments in favor of that decision and all the arguments against it.

Definition 2 (Arguments pros/cons). Let x ∈ X.

– ArgP(x) = the set of arguments in A which are in favor of x.

– ArgC(x) = the set of arguments in A which are against x.

2.2Some principles for comparing decisions

At the core of our framework is the use of a principle that allows for an argument-

based comparison of decisions. Below we present some intuitive principles Princ,

whose psychological validity is discussed in section 4. A simple principle consists

in counting the arguments in favor of each decision. The idea is to prefer the

decision which has more supporting arguments.

Definition 3 (Counting arguments pros: CAP). Let <X, A, ?, ?CAP>

be an argumentation based decision framework, and Let x1, x2∈ X.

x1 ?CAP x2 w.r.t CAP iff |ArgP(x1)| > |ArgP(x2)|, where |B| denotes the

cardinality of a given set B.

Likewise, one can also compare the decisions on the basis of the number of

arguments against them. A decision which has less arguments against it will be

preferred.

Definition 4 (Counting arguments cons: CAC). Let <X, A, ?, ?CAC>

be an argumentation based decision framework, and Let x1, x2∈ X.

x1?CAC x2w.r.t CAC iff |ArgC(x1)| < |ArgC(x2)|.

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Definitions 3 and 4 do not take into account the strengths of the arguments. In

what follows, we propose two principles based on the preference relation between

the arguments. The first one, that we call the promotion focus principle (Prom),

takes into account only the supporting arguments (i.e. the arguments PRO a

decision), and prefers a decision which has at least one supporting argument

which is preferred to (or stronger than) any supporting argument of the other

decision. Formally:

Definition 5 (Promotion focus). Let <X, A, ?, ?Prom> be an argumentation-

based decision framework, and Let x1, x2∈ X.

x1?Promx2w.r.t Prom iff ∃ A ∈ ArgP(x1) such that ∀ B ∈ ArgP(x2), A ?

B.

Note that the above relation may be found too restrictive, since when the

strongest arguments in favor of x1 and x2 have equivalent strengths (in the

sense of ≈), x1 and x2 cannot be compared. Clearly, this could be refined in

various ways by counting arguments of equal strength.

The second principle, that we call the prevention focus principle (Prev), consid-

ers only the arguments against decisions when comparing two decisions. With

such a principle, a decision will be preferred when all its cons are weaker than

at least one argument against the other decision. Formally:

Definition 6 (Prevention focus). Let <X, A, ?, ?Prev> be an argumenta-

tion based decision framework, and Let x1, x2∈ X.

x1?Prevx2w.r.t Prev iff ∃ B ∈ ArgC(x2) such that ∀ A ∈ ArgC(x1), B ? A.

Obviously, this is but a sample of the many principles that we may con-

sider. Human deciders may actually use more complicated principles, such as

for instance the following one. First, divide the set of all (positive or negative)

arguments into strong and weak ones. Then consider only the strong ones if any,

and apply the Prevention focus principle. In absence of any strong argument,

apply the Promotion focus principle. This combines risk-aversion in the realm

of extreme consequences, with risk-tolerance in the realm of mild consequences.

3 A specification of the general framework

In this section, we give some definitions of what might be an argument in favor

of a decision, an argument against a decision, of the strengths of arguments,

and of the preference relations between arguments. We will show also that our

framework capture different multiple criteria decision rules.

3.1Basic concepts

In what follows, L denotes a propositional language, ? stands for classical infer-

ence, and ≡ stands for logical equivalence. The decision maker is supposed to be

equipped with three bases built from L:

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1. a knowledge base K gathering the available information about the world.

2. a base C containing the different criteria.

3. a base G of preferences (expressed in terms of goals to be reached).

Beliefs in K may be more or less certain. In the multiple criteria context, this

opens the possibility of having uncertainty on the (dis)satisfaction of the criteria.

Such a base is supposed to be equipped with a total preordering ≥.

a ≥ b iff a is at least as certain as b.

For encoding it, we use the set of integers {0,1,...,n} as a linearly ordered

scale, where n stands for the highest level of certainty and ‘0’ corresponds to

the complete lack of information. This means that the base K is partitioned and

stratified into K1, ..., Kn(K = K1∪ ... ∪ Kn) such that formulas in Kihave

the same certainty level and are more certain than formulas in Kjwhere j < i.

Moreover, K0is not considered since it gathers formulas which are completely

not certain.

Similarly, criteria in C may not have equal importance. The base C is then also

partitioned and stratified into C1, ..., Cn(C = C1∪ ... ∪ Cn) such that all criteria

in Cihave the same importance level and are more important than criteria in Cj

where j < i. Moreover, C0is not considered since it gathers formulas which are

completely not important, and which are not at all criteria.

Each criterion can be translated into a set of consequences, which may not

be equally satisfactory. Thus, the consequences are associated with the satisfac-

tion level of the corresponding criterion. The criteria may be satisfied either in

a positive way (if the satisfaction degree is higher than the neutral point of the

considered scale) or in a negative way (if the satisfaction degree is lower than

the neutral point of the considered scale). For instance, consider the criterion

“closeness to the sea” for a house to let for vacations. If the distance is less than

1 km, the user may be fully satisfied, moderately satisfied if it’s between 1 and 2

km, slightly dissatisfied if it is between 2 and 3 km, and completely dissatisfied

if it is more than 3km from the sea. Thus, the set of consequences will be parti-

tioned into two subsets: a set of positive “goals” G+and a set of negative ones G−.

Since the goals may not be equally satisfactory, the base G+(resp. G−) is also

supposed to be stratified into G+= G+

where goals in G+

and are more important than goals in G+

Gi’s may be empty if there is no goal corresponding to this level of importance.

For the sake of simplicity, in all our examples, we only specify the strata which

are not empty. In the above example, taking n = 2, we have G+

G+

A goal gj

gj

1∪ ... ∪ G+

n(resp. G−= G−

1∪ ... ∪ G−

n)

i(resp. G−

i) correspond to the same level of (dis)satisfaction

j(resp. G−

j) where j < i. Note that some

2= {dist < 1km},

2= {3 < dist}.

1= {1 ≤ dist < 2km}, G−

1= {2 ≤ dist ≤ 3km} and G−

iis associated to a criterion ciby a propositional formula of the form

i→ cimeaning just that the goal gj

irefers to the evaluation of criterion ci. Such

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formulas will be added to Kn. More generally, one may think of goals involving

several criteria, e.g. dist ¡ 1km or price ≤ 500.

3.2Arguments pros and cons

An argument supporting a decision takes the form of an explanation. The idea

is that a decision has some justification if it leads to the satisfaction of some

criteria, taking into account the knowledge. Formally:

Definition 7 (Argument). An argument is a 4-tuple A = <S, x, g, c> s.t.

1) x ∈ X, 2) c ∈ C, 3) S ⊆ K, 4) Sxis consistent, 5) Sx? g, 6) g → c ∈ Kn,

and 7)S is minimal (for set inclusion) among the sets S satisfying the above

conditions.

S is the support of the argument, x is the conclusion of the argument, c is the

criterion which is evaluated for x and g represents the way in which c is satisfied

by x. Sxis the set S adding the information that x takes place.

A gathers all the arguments which can be built from the bases K, X and C.

Let’s now define the two functions which return the arguments in favor and

the arguments against a decision. Intuitively, an argument is in favor of a given

decision if that decision satisfies positively a criterion. In other terms, it satisfies

goals in G+. Formally:

Definition 8 (Arguments pros). Let x ∈ X.

ArgP(x) = {A =< S,x,g,c > ∈ A | ∃j ∈ {0,1,...,n} and g ∈ G+

Sat(A) = j is a function which returns the satisfaction degree of the criterion c

by the decision x.

j}.

An argument is against a decision if the decision satisfies insufficiently a given

criterion. In other terms, it satisfies goals in G−. Formally:

Definition 9 (Arguments cons). Let x ∈ X.

ArgC(x) = {A =< S,x,g,c > ∈ A | ∃j ∈ {0,1,...,n} and g ∈ G−

Dis(A) = j is a function which returns the dissatisfaction degree of the criterion

c by the decision x.

j}.

3.3The strengths of arguments

In [1], it has been argued that arguments may have forces of various strengths.

These forces allow an agent to compare different arguments in order to select

the ‘best’ ones, and consequently to select the best decisions.

Generally, the force of an argument can rely on the beliefs from which it is

constructed. In our work, the beliefs may be more or less certain. This allows us

to attach a certainty level to each argument. This certainty level corresponds to

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the smallest number of a stratum met by the support of that argument.

Moreover, the criteria may not have equal importance also. Since a criterion may

be satisfied with different grades, the corresponding goals may have (as already

explained) different (dis)satisfaction degree.

Thus, the the force of an argument depends on three components: the cer-

tainty level of the argument, the importance degree of the criterion, and the

(dis)satisfaction degree of that criterion. Formally:

Definition 10 (Force of an argument). Let A = <S, x, g, c> be an ar-

gument. The force of an argument A is a triple Force(A) = <α, β, λ> such

that:

α = min{j | 1 ≤ j ≤ n such that Sj?= ∅}, where Sjdenotes S ∩ Kj.

β = i such that c ∈ Ci.

λ = Sat(A) if A ∈ ArgP(x), and λ = Dis(A) if A ∈ ArgC(x).

3.4 Preference relations between arguments

An argumentation system should balance the levels of satisfaction of the criteria

with their relative importance. Indeed, for instance, a criterion cihighly satisfied

by x is not a strong argument in favor of x if cihas little importance. Conversely,

a poorly satisfied criterion for x is a strong argument against x only if the

criterion is really important. Moreover, in case of uncertain criteria evaluation,

one may have to discount arguments based on such evaluation. This is quite

similar with the situation in argument-based decision under uncertainty [2]. In

other terms, the force of an argument represents to what extent the decision will

satisfy the most important criteria.

This suggests the use of a conjunctive combination of the certainty level, the

satisfaction / dissatisfaction degree and the importance of the criterion. This

requires the commensurateness of the three scales.

Definition 11 (Conjunctive combination). Let A, B be two arguments with

Force(A) = <α, β, λ> and Force(B) = <α’, β’, λ’>.

A ? B iff min(α, β, λ) > min(α’, β’, λ’).

Example 1 Assume the following scale {0,1,2,3,4,5}. Let us consider two ar-

guments A and B whose forces are respectively (α,β,λ) = (5, 3, 2) and (α’, β’,

λ’) = (5, 1, 5). In this case the argument A is preferred to B since min(5, 3,

2) = 2, whereas min(5, 1, 5) = 1.

However, a simple conjunctive combination is open to discussion, since it gives

an equal weight to the certainty level, the satisfaction/dissatisfaction degree of

the criteria and to the importance of the criteria. Indeed, one may prefer an

argument that satisfies for sure an important criteria even rather poorly, than

an argument which satisfies very well a non-important criterion but with a weak

certainty level. This suggests the following preference relation:

Definition 12 (Semi conjunctive combination). Let A, B be two arguments

with Force(A) = <α, β, λ> and Force(B) = <α’, β’, λ’>. A ? B iff

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– α ≥ α’,

– min(β, λ) > min(β’, λ’).

This definition gives priority to the certainty of the information, but is less dis-

criminating than the previous one.

The above approach assumes the commensurateness of two or three scales,

namely the certainty scale, the importance scale, and the weighting scale. This

requirement is questionable in principle. If this hypothesis is not made, one can

still define a relation between arguments as follows:

Definition 13 (Strict combination). Let A, B be two arguments with Force(A)

= <α, β, λ> and Force(B) = <α’, β’, λ’>. A ? B iff:

– α ≥ α?, or

– α = α?and β > β?or,

– α = α?and β = β?and λ > λ?.

3.5Retrieving classical multiple criteria aggregations

In this section we assume that information in the base K is fully certain.

A simple approach in multiple criteria decision making amounts to evaluate each

x in X from a set C of m different criteria ciwith i = 1,...,m. For each ci, x

is then evaluated by an estimate ci(x), belonging to the evaluation scale used

for ci. Let 0 denotes the neutral point of the scale, supposed here to be bipolar

univariate.

When all criteria have the same level of importance, counting positive or

negative arguments obviously corresponds to the respective use of the following

evaluation functions for comparing decisions

?

where c?

0 and c??

i

c?

i(x) or

?

i

c??

i(x)

i(x) = 1 if ci(x) > 0 and c?

i(x) = 1 if ci(x) < 0.

i(x) = 0 if ci(x) < 0, and c??

i(x) = 0 if ci(x) >

Proposition 1. Let <X,A,?, ?CAP> be an argumentation-based system. Let

x1, x2∈ X.

When C = Cn, x1?CAP x2iff?

Proposition 2. Let <X,A,?, ?CAC> be an argumentation-based system. Let

x1, x2∈ X.

When C = Cn, x1?CAC x2iff?

When all criteria have the same level of importance, the promotion focus

principle amounts to use maxic?

0 if ci(x) < 0 as an evaluation function for comparing decisions.

Proposition 3. Let <X,A, Conjunctive combination, ?Prom> be an argumentation-

based system. Let x1, x2∈ X.

When C = Cn, x1?Promx2iff maxic?

ic?

i(x1) ≥?

ic?

i(x2).

ic??

i(x1) ≤?

i(x) with c?

ic??

i(x2).

i(x) = ci(x) if ci(x) > 0 and c?

i(x) =

i(x1) ≥ maxic?

i(x2).

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The prevention focus principle amounts to use minic??

ci(x) > 0 and c??

i(x) with c??

i(x) = 0 if

i(x) = −ci(x) if ci(x) < 0.

Proposition 4. Let <X,A, Conjunctive combination, ?Prev> be an argumentation-

based system. Let x1, x2∈ X.

When C = Cn, x1?Prevx2iff minic??

When each criterion ci(x) is associated with a level of importance wirang-

ing on the positive part of the criteria scale, the above c?

min(c?

i(x1) ≤ minic??

i(x2).

i(x) is changed into

i(x),wi) in the promotion case.

Proposition 5. Let <X,A, Conjunctive combination, ?Prom> be an argumentation-

based system. Let x1, x2∈ X.

x1?Promx2iff maximin(c?

i(x1),wi) ≥ maximin(c?

i(x2),wi).

Similar proposition holds for the prevention focus principle. Thus, weighted

disjunctions and conjunctions [7] are retrieved.

3.6 Example: Choosing a medical prescription

Imagine we have a set C of 4 criteria for choosing a medical prescription: Avail-

ability (c1), Reasonableness of the price (c2), Efficiency (c3), and Acceptability

for the patient (c4). We suppose that c1,c3are more important than c2,c4. Thus,

C = C2∪ C1with C2= {c1,c3}, C1= {c2,c4}.

These criteria are valued on the same qualitative bipolar univariate scale

{−2,−1,0,1,2} with neutral point 0. From a cognitive psychology point of

view, this corresponds to the distinction often made by humans between what is

strongly positive, weakly positive, neutral, weakly negative, or strongly negative.

Each criterion ci is associated with a set of 4 goals gj

denotes the fact of reaching levels 2,1,−1,−2 respectively. This gives birth to

the following goals bases:

G+= G+

G+

with G−

{e(x,c1) = −1,e(x,c2) = −1,e(x,c3) = −1,e(x,c4) = −1}.

Let X = {x1,x2} be a set of two potential decisions regarding the prescription

of drugs. Suppose that the three alternatives, x1 and x2 receive the following

evaluation vectors:

iwhere j = 2,1,−1,−2

2∪ G+

1with G+

2= {e(x,c1) = 2,e(x,c2) = 2,e(x,c3) = 2,e(x,c4) = 2},

1= {e(x,c1) = 1,e(x,c2) = 1,e(x,c3) = 1,e(x,c4) = 1}. G−= G−

2= {e(x,c1) = −2,e(x,c2) = −2,e(x,c3) = −2,e(x,c4) = −2}, G−

2∪ G−

1=

1

– e(x1) = (−1,1,2,0),

– e(x2) = (1,−1,1,1),

where the ith component of the vector corresponds to the value of the ith cri-

terion. This is encoded in K. All the information in K are assumed to be fully

certain.

K = {e(x1,c1) = −1, e(x1,c2) = 1, e(x1,c3) = 2, e(x1,c4) = 0, e(x2,c1) = 1,

e(x2,c2) = −1, e(x2,c3) = 1, e(x2,c4) = 1, (e(x,c) = y) → c}. Note that the

last formula in K is universally quantified.

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Let’s now define the pros and cons each decision.

A1= <{e(x1,c2) = 1},x1,e(x1,c2) = 1,c2>

A2= <{e(x1,c3) = 2},x1,e(x1,c3) = 2,c3>

A3= <{e(x1,c1) = −1},x1,e(x1,c1) = −1,c1>

A4= <{e(x1,c4) = 0},x1,e(x1,c4) = 0,c4>

A5= <{e(x2,c1) = 1},x2,e(x2,c1) = 1,c1>

A6= <{e(x2,c2) = −1},x2,e(x2,c2) = −1,c2>

A7= <{e(x2,c3) = 1},x2,e(x2,c3) = 1,c3>

A8= <{e(x2,c4) = 1},x2,e(x2,c4) = 1,c4>

ArgP(x1) = {A1,A2}, ArgC(x1) = {A3},

ArgP(x2) = {A5,A7,A8}, ArgC(x2) = {A6}.

If we consider an argumentation system in which decisions are compared w.r.t

the CAP principle, then x2? x1. However, if a CAC principle is used, the two

decisions are indifferent.

Now let’s consider an argumentation system in which a conjunctive combination

criterion is used to compare arguments and the Prom principle is used to com-

pare decisions. In that case, only arguments pros are considered.

Force(A1) = (2,1,1), Force(A2) = (2,2,2), Force(A5) = (2,2,1), Force(A7)

= (2,2,1), Force(A8) = (2,1,1). It is clear that A2? A5, A7, A8. Thus, x1is

preferred to x2.

In the case of the Prev principle, only arguments against the decisions are con-

sidered, namely A3and A6. Note that Force(A3) = (2,2,1) and Force(A6) =

(2,1,1). The two decisions are then indifferent using the conjunctive combina-

tion. The leximin refinement of the minimum in the conjunctive combination

rule leads to prefer A3to A6. Consequently, according to Prev principle x2will

be preferred to x1.

This example shows that various Princ may lead to different decisions in case of

alternatives hard to separate.

4Psychological validity of argumentation-based decision

principles

Bonnefon, Glasspool, McCloy, and Yule [4] have conducted an experimental

test of the psychological validity of the counting and Prom/Prev principles for

argumentation-based decision. They presented 138 participants with 1 to 3 ar-

guments in favor of some action, alongside with 1 to 3 arguments against the

action, and recorded both the decision (take the action, not take the action,

impossible to decide) and the confidence with which it was made. Since the de-

cision situation was simplified in that sense that the choice was between taking

a given action or not (plus the possibility of remaining undecided), counting ar-

guments pro and counting arguments con predicted similar decisions (because,

e.g., an argument for taking the action was also an argument against not taking

it). Likewise, and for the same reason, the Prom and Prev principles predicted

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similar decisions.

The originality of the design was in the way arguments were tailored participant

by participant so that the counting principle on the one hand and the Prom

and Prev principles on the other hand made different predictions with respect to

the participant’s decision: During a first experimental phase, participants rated

the force of 16 arguments for or against various decisions; a computer program

then built online the decision problems that were to be presented in the second

experimental phase (i.e., the decision phase proper). For example, the program

looked for a set of 1 argument pro and 3 arguments con such that the argument

pro was preferred to any of the 3 arguments con. With such a problem, a count-

ing principle would predict the participant to take the action, but a Prom/Prev

principle would predict the participant not to take the action.

Overall, 828 decisions were recorded, of which 21% were correctly predicted by

the counting principle, and 55% by the Prom/Prev principle. Quite strikingly,

the counting principle performed significantly below chance level (33%). The

55% hit rate of the Prom/Prev principle is far more satisfactory, its main prob-

lem being its inability to predict decisions made in situations that featured only

one argument pro and one argument con, of comparable forces. The measure

of the confidence with which decisions were made yielded another interesting

result: The decisions that matched the predictions of the Prom/Prev principles

were made with higher confidence than the decisions that did not, in a statisti-

cally significant way. This last result suggests that the Prom/Prev principle has

indeed some degree of psychological validity, as the decisions that conflict with

its predictions come with a feeling of doubt, as if they were judged atypical to

some extent.

The dataset also allowed for the test of the refined decision principle intro-

duced at the end of section 2.2. This principle fared well regarding both hit rate

and confidence attached to the decision. The overall hit rate was 64%, a signifi-

cant improvement over the 55% hit rate of the Prom/Prev principles. Moreover,

the confidence attached to the decisions predicted by the refined principle was

much higher (with a mean difference of more than two points on a 5-point scale)

than the confidence in decisions it did not predict.

5Conclusion

Some may wonder why bother about argumentation-based decision in multiple

criteria decision problems, since the aggregation functions that can be mimicked

in an argumentation-based approach would remain much simpler than sophisti-

cated aggregation functions such as a general Choquet integral. There are several

reasons however, for studying argumentation-based multiple criteria decision. A

first one is related to the fact that in some problems criteria are intrinsically qual-

itative, or even if they are numerical in nature they are qualitatively perceived

(as in the above example of the criterion ’being close to the sea’), and then it

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is useful to develop models which are close to the way people deal with decision

problems. Moreover, it is also nice to notice that the argumentation-based ap-

proach provides a unified setting where inference, or decision under uncertainty

can be handled as well. Besides, the logical setting of argumentation-based de-

cision enables to have the values of consequences of possible decisions assessed

through a non trivial inference process (in contrast with the above example)

from various pieces of knowledge, possibly pervaded with uncertainty, or even

partly inconsistent.

The paper has sketched a general method which enables us to compute and

justify preferred decision choices. We have shown that it is possible to design

a logical machinery which directly manipulates arguments with their strengths

and returns preferred decisions from them.

The approach can be extended in various directions. It is important to study

other decision principles which involve the strengths of arguments, and to com-

pare the corresponding decision systems to classical multiple criteria aggregation

processes. These principles should be also empirically validated through exper-

imental tests. Moreover, this study can be related to another research trend,

illustrated by a companion paper [6], on the axiomatization of particular qual-

itative decision principles in bipolar settings. Another extension of this work

consists of allowing for inconsistent knowledge or goal bases.

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