EFFICIENCY IN PERSUASION DIALOGUES

Katie Atkinson

, Priscilla Bench-Capon

and Trevor Bench-Capon

Department of Computer Science, University of Liverpool, Liverpool, U.K.

The Open University, Milton Keynes, U.K.

Keywords:

Dialogue, Persuasion, Argumentation.

Abstract:

Inquiry, Persuasion and Deliberation Dialogues are all designed to transfer information between agents so that

their beliefs and opinions may be revised in the light of the new information, and all make use of a similar

set of speech acts. These dialogues also have signiﬁcant differences. We deﬁne success conditions for some

different dialogue types in this family and note the pragmatic implications of the speech acts they employ.

Focusing on persuasion we consider how successful persuasion dialogues can be conducted efﬁciently, in

terms of minimising the expected transfer of information. We observe that a strategy for efﬁcient persuasion

can be developed by considering the pragmatic implications. We present results showing that our strategy is

an optimal strategy in a range of representative persuasion scenarios.

1 INTRODUCTION

The inﬂuential dialogue typology of Walton and

Krabbe (Walton and Krabbe, 1995) has been taken

as a basis for developing dialogue protocols for use

in agent systems by several authors. For example, see

(Black and Hunter, 2009) for inquiry dialogues; (Rah-

wan et al., 2003) for negotiation; (Prakken, 2006) for

persuasion; and (McBurney et al., 2007) for delib-

eration. It is, Walton and Krabbe argue, important

that the agents recognise the type of dialogue they are

participating in, since otherwise misunderstandings

arise, fallacies become possible and the conversation

may break down. None the less, the distinctions have

rarely been made precise, and confusion is increased

because inquiry, persuasion and deliberation all make

use of a similar set of speech acts. In this paper we

will give a precise characterisation of the distinctive

features of persuasion dialogues that show how these

features distinguish persuasion dialogues from delib-

eration and inquiry dialogues. Our analysis will draw

attention to the pragmatic meaning of utterances used

in persuasion dialogues, which give such dialogues

their particular character. Following this analysis, we

will focus further on persuasion, with a view to ob-

taining a clear speciﬁcation of, and an optimal strat-

egy for, persuasion. Our contribution is thus the anal-

ysis yielding the distinguishing features of persuasion

dialogues, as well as the optimal strategy we present

for a common class of persuasion dialogues.

One common situation in which both persuasion

and deliberation occur is when an agent must choose

between several options, each of which has several

features which can serve as reasons for and against the

choice, to which different agents will ascribe different

degrees of importance. When buying a car one person

will be most interested in safety, another in speed, an-

other in comfort. For cameras, some will require the

best quality, whereas others will value compactness or

a low price more highly. In such situations an agent

will often need to deal with a series of salespeople,

each trying to overturn the agent’s currently preferred

option, or to consider recommendations from other

agents. A very common example in AI conference pa-

pers is choosing a restaurant for lunch or an evening

dinner. Typically the individual agents will have only

incomplete and often ill-founded or outdated beliefs

about the local eateries, and so they will pool their

knowledge to get a more complete picture of the sit-

uation before deciding. Thus one agent may solicit

recommendations, and another agent may attempt to

persuade that agent of its own favourite venue. We

will use this as an illustration throughout this paper.

In (Walton and Krabbe, 1995), dialogue types are

characterised by an initial situation, a collective goal,

and individual goals, all stated informally. For inquiry

dialogues the initial situation is that both agents are

not certain of some proposition p. Both individual

goals and the collective goal are the same: to deter-

mine whether or not p. In persuasion one agent will

Atkinson K., Bench-Capon P. and Bench-Capon T..

EFFICIENCY IN PERSUASION DIALOGUES.

DOI: 10.5220/0003727400230032

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2012), pages 23-32

ISBN: 978-989-8425-96-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

argue that p, or that some action φ should be done

in order that the other agent will come to agreement.

The collective goal is to resolve whether p is true or φ

should be done. With regard to individual goals, per-

suasion is asymmetric: the persuader wishes to con-

vince the persuadee, whereas the persuadee wishes to

explore the possibility that its current opinion should

be revised in the light of information known to the

persuader: the persuadee is interested in what is true,

whether it be p or ¬p. A different case of persuasion

is what Walton terms a dispute. In this case the per-

suadee also wishes to convince the other agent that its

own original position is correct, so that its individual

goal is now that the other should believe ¬p or that

φ should not be done: we will not consider disputes

further in this paper. Deliberation is generally held

to concern actions: initially both agents are unsure

whether or not to φ, and individually and collectively

they wish to come to agreement as to whether or not

to φ. In the next section we will explore the distinc-

tions further, with a view to precisely characterising

persuasion dialogues in particular.

2 DISTINGUISHING THE

DIALOGUE TYPES

Instead of distinguishing between actions and propo-

sitions, we believe that the correct distinction is re-

lated to directions of ﬁt, a distinction made by Searle

(Searle, 2003). Searle distinguishes theoretical rea-

soning, reasoning about what is the case, from prac-

tical reasoning, reasoning about what it is desired to

be the case, and what should be done to realise those

desires. In the ﬁrst case it is necessary to ﬁt one’s be-

liefs to the world, whereas in the second the idea is to

make the world ﬁt one’s desires, in so far as one has

the capacity to do so. In these terms, inquiry repre-

sents an attempt to better ﬁt the beliefs of the agents

to the world, and deliberation how best to make the

world ﬁt the collective desires of the agents. Persua-

sion can be about either. Note, however, that when

we have two (or more) participating agents, we have

two (or more), probably different, sets of desires to

consider. In deliberation no set of desires should be

given pre-eminence, but rather the group as a whole

needs to come to an agreement on what desires they

will adopt collectively. In contrast, as discussed in

(Bench-Capon, 2002), in persuasion it is the desires

There has been some disagreement as to whether per-

suasion can be over actions. Walton in (Walton, 1998)

seems to suggest not. None the less it is clear that we are,

in ordinary language, fully prepared to speak of persuading

someone to do something.

of the persuadee that matter: a persuadee is fully en-

titled to use its own preferences to assess any propo-

sition or proposal, without any need to consider what

the persuader desires. The construction of a set of col-

lective desires introduces an additional order of com-

plication, and puts deliberation beyond the scope of

this paper. Therefore in what follows we will focus

exclusively on persuasion.

2.1 Deﬁnitions

An example, including example use of our notation,

is given in Section 3. The reader might ﬁnd it help-

ful to refer to this in conjunction with the following

deﬁnitions for concrete illustrations of their use.

The knowledge bases of agents can be partitioned

into factual elements, on which agents should agree

used when the direction of ﬁt is from world to beliefs,

and preference elements, which represent their own

individual desires, tastes and aspirations, and are used

when the direction of ﬁt is from desires to the world.

Thus, the preference elements represent the way the

agent evaluates possible futures to determine what it

wishes to bring about, and how it evaluates objects

and situations for value judgements such as best car

and acceptable restaurant.

Deﬁnition 1. Let AG denote a set of agents, each of

which, Ag ∈ AG, has a knowledge base KB

. KB

is partitioned into factual elements denoted by KB

and preference information denoted by KB

. KB

comprises facts, strict rules and defeasible rules.

comprises rules to determine the utility for Ag

of certain items based on their attributes, and the

weights used by these rules. These preference ele-

ments are deﬁned below.

Agents expand their KB

by taking information

from one another, but KB

remains ﬁxed throughout

the dialogue. Whereas, because it is intended to ﬁt the

world, KB

is objective, KB

represents the personal

preferences of an individual agent, and is entirely lo-

cal to the agent concerned. We will use f for factual

propositions, and p

(to be read as “p is the case for

Ag”) for propositions based on preferences. We will

not represent actions separately, so that p

may rep-

resent either propositions such as Roux Brothers is an

Of course, this does assume that there is a set of propo-

sitions which are objectively true. In practice there may be

room for dispute. None the less we will assume agreement

in judgements (even for matters such as whether a restau-

rant is near, or whether it is of good quality), reserving sub-

jectivity for differences in taste, based on preferences and

choice.

ICAART 2012 - International Conference on Agents and Artificial Intelligence

acceptable restaurant for Ag or propositions such as

it is desirable for Ag

that Ag

φ.

Deﬁnition 2. Let PROP be a set of atomic propo-

sitions and let f ∈ PROP be a factual proposition

and p

∈ PROP be a proposition based on prefer-

ences. Let KB

f denote that a factual propo-

sition can be defeasibly shown, using an appropri-

ate reasoning engine

, without using preference in-

formation. KB

records the preferences of Ag using

clauses with preference based propositions as heads

and bodies comprising factual propositions. Now

∪ KB

denotes that the preferences of

Ag are required for p

to be shown.

This reﬂects that a value judgement such as Rolls

Royce make the best cars, cannot be considered true

simpliciter, but is true (or false) relative to an agent,

and determined using that agent’s individual prefer-

ences. Next we may need to distinguish between the

knowledge base of an agent at the start of the dia-

logue, and the knowledge base of that agent at the end

of the dialogue

Deﬁnition 3. Let the knowledge base of an agent Ag

at the start of a dialogue be denoted by KB

, and its

knowledge base after n steps of dialogue be denoted

by KB

We now introduce some further deﬁnitions needed

for the protocoland strategy. Firstly, agents need to be

able to discuss the options under consideration within

the dialogue and the attributes of these options. For

example, in a dialogue about where to go on holi-

day, the options might cover different countries such

as France and Spain with relevant attributes being the

food and the weather. In the restaurant example the

various local restaurants will be the options and vari-

ous features such as distance, quality, type of cuisine,

ambience and the like are attributes of restaurants that

agents may use as reasons to choose between them.

Furthermore, agents can give individual weightings

to these attributes to reﬂect their different tastes and

aspirations.

Deﬁnition 4. Let O be a set of options that agents can

propose during the course of a dialogue. O has an

(Black and Hunter, 2009) use Defeasible Logic (Garc´ıa

and Simari, 2004).

Here only KB

changes during a dialogue. It is of

course possible that an agent may be persuaded to change

its preferences, but we will not consider this higher order

persuasion in this paper. This is not a straightforward matter

of simply adding to the existing KB

, as is the case with

facts.

associated set of attributes A

. An agent associates

each a

∈ A

with a weight w

≥ 0 to form a set of

weights W. Each set W is individual to an agent.

Next we need to be able to determine the truth

value of attributes of options, e.g. stating that the

option Spain does indeed have the attribute of good

weather, or that the Mogul Palace serves Indian food.

We also need to be able to determine the weight that

an agent assigns to an attribute of an option. The fol-

lowing two functions enable the above.

Deﬁnition 5. Let τ : O× A

→ {0,1} be a truth func-

tion that returns the truth value given by τ(O

) =

for option O

∈ O and attribute a

∈ A

Deﬁnition 6. Let w : AG× A

→ N ∪{0} be a weight

function that returns the weight w(Ag,a

) = w

)

of an attribute a

for agent Ag ∈ A

. Where the agent

Ag is clear from the context, we use w

Next we introduce notation to enable us to refer

to sets of attributes of options as determined by their

truth status (as will be required in section 4). Thus,

attributes of options will fall within one the following

disjoint sets: veriﬁed true, veriﬁed false, unveriﬁed

true and unveriﬁed false, where veriﬁed options have

been the subject of an inquiry dialogue (and so have

been agreed by the agents) and unveriﬁed have not

(and so could change in the light of information that

could be elicited by an inquiry dialogue).

Deﬁnition 7. τ

= 1 if option O

has attribute a

. If

this attribute for this option has been the subject of an

inquiry dialogue, τ

has been veriﬁed. Attributes of

options for which τ

= 1 has been veriﬁed form a set

; those for which τ

= 0 has been veriﬁed form a

setVF

, for both agents. For a particular agent, if for

an unveriﬁed attribute KB

= 1, the attribute is

unveriﬁed true and so an element of UT

: otherwise

the attribute is unveriﬁed false and so is an element of

. VT

∪UT

∪VF

∪UF

= A

Finally, we are able to deﬁne the utility of an op-

tion for an agent, based on attributes of the option that

are true.

Deﬁnition 8. Let A ⊆ A

be a set of attributes true

of O

. Then the utility of O

for an Agent Ag with re-

spect to these attributes, U

(A), is

∑

∈A

). Now

the current utility is U

(VT

∪UT

). This we will some-

times abbreviatetoU

when there is no ambiguity. The

maximum utility is U

(VT

∪UT

∪UF

) and the mini-

mum utility is U

(VT

EFFICIENCY IN PERSUASION DIALOGUES

2.2 Inquiry and Persuasion Dialogues

We can now characterise the distinction between in-

quiry and persuasion. Suppose we have two agents,

Wilma and Bert, so that AG = {W,B}: following the

conventions of chess, W will initiate the dialogues.

We may say that for an inquiry dialogue between

Wilma and Bert concerning a proposition f (inquiry

dialogues concern only factual propositions), the fol-

lowing two conditions should hold:

I1 Initially either Wilma does not believe that f:

6 f or Bert does not believe that f :

6 f or both.

I2 At the end of the dialogue both believe that f

if and only if f is a consequence of the joint

knowledge bases: (KB

f) ∧ (KB

f) ↔

∪ KB

An inquiry dialogue will always result in agree-

ment, since, if agreement does not arise before, the di-

alogue will terminate only after Bert and Wilma have

exchanged all their knowledge, so that, if the dialogue

has taken n steps, KB

= KB

∪ KB

Some have argued that neither should believe that f

at the outset, but we wish to allow Wilma to start an

inquiry dialogue to conﬁrm her beliefs, since, given

the defeasible reasoning mechanism we are using, it

is always possible that Bert may supply information

resulting in Wilma revising her beliefs.

The second condition is plausible (since we are

assuming that factual propositions are objectively as-

sessed by the agents) and is the condition used to

show soundness and completeness of the inquiry dia-

logues in Black and Hunter (Black and Hunter, 2009).

Since that paper shows soundness and completeness

for their inquiry dialogues, we shall suppose that

where Wilma and Bert wish to establish the truth of

some factual proposition, they will use a dialogue as

described there.

In contrast, persuasion can concern matters with

both directions of ﬁt, although probably evaluative

propositions are more usually the topic than factual

ones. This is because if the persuader is correct (and

honest), for factual topics an inquiry dialogue will

serve to achieve the goals of a persuasion dialogue.

It may be, however, that the persuader has some in-

terest in establishing the proposition, and this interest

will persist even if it becomes aware of information

suggesting that the proposition is in fact false. If one

of the agents is a salesperson, for example, this will be

what it will do. Since persuasion may have this adver-

sarial element we distinguish open persuasion, where

the persuader is expected to tell the truth, the whole

truth and nothing but the truth, and partial

persua-

sion where the persuader must tell only the truth and

nothing but the truth, but need not tell the whole truth

if that would damage its cause. Open persuasion

about a fact is simply an inquiry dialogue where the

persuader initially believes the proposition under con-

sideration, so that these dialogues can also be char-

acterised by I1 and I2 above. We will henceforward

conﬁne ourselves to persuasion dialogues that con-

cern matters of preference, so that there will subjec-

tive elements dependent of tastes and preferences as

well as fact.

Open Persuasion

OP1: Wilma believes that Bert does not believe

that p

: KB

6 p

OP2: Both wish that at the end of the dialogue

Bert believes that p

if and only if p

is a conse-

quence of their joint knowledge bases and Bert’s

preferences: KB

↔ KB

∪ KB

where the dialogue terminates in t steps.

Note that at the end of an open dispute, Bert and

Wilma may differ as to whether p or ¬p, since their

beliefs reﬂect their own individual preferences ap-

plied to the shared information. Again the dialogue

will always terminate because either the agent is per-

suaded, or all factual knowledge has been exchanged.

For partial persuasion we include the desire to, as

it were, win the dialogue, irrespective of the truth of

the matter. Although partial persuasion can be con-

ducted regarding a matter of fact, we will consider

here only persuasion relating to matters involving el-

ements of preference. The initial goal remains OP1,

and Bert’s ﬁnal goal remains OP2, but Wilma has a

different goal, PP3. PP4 represents the condition un-

der which Wilma can legitimately satisfy her goal.

Again the dialogue terminates in t steps.

Partial Persuasion Using Preferences

PP3: Wilma’s goal is that Bert should believe that

p: KB

PP4: Wilma can succeed if she has information to

enable Bert to believe p: KB

↔ (∃S) ⊆

such that S∪ KB

Note that open persuasion begins with a conﬂict,

but has the same goals for both participants, whereas

in partial persuasion they have different views as

to what constitutes a successful termination. Both

agents can realise their individual goals if p

does fol-

low from their collective knowledge and Bert’s pref-

erences. If not, strategic considerations may affect the

partial as in

biased

, not impartial, rather than as in in-

complete.

ICAART 2012 - International Conference on Agents and Artificial Intelligence

outcome: it may be that there is a subset of Wilma’s

KB which could be used to persuade Bert, but that she

reveals too much, so that Bert is unpersuaded. Here

Wilma could have succeeded according to PP4, but in

fact Bert is rightly unpersuaded, satisfying OP2.

Having made these distinctions we will now fo-

cus on a particular type of persuasion dialogue, open

persuasion involving preferences. This is the simplest

kind of dialogue after inquiry dialogues, in that only

one side is doing the persuasion, and the participants

have common goals. Our particular scenario is the

common situation where an agent is seeking a recom-

mendation, or comparing options, concerning things

such as restaurants, cars, digital cameras, insurance,

or any other product where competing options have

some out of a large number of features which vary in

importance for different agents. The persuading agent

will want what is best for the other agent, and will

have no particular interest in having its recommenda-

tion accepted. The particular topic we will consider is

what is the best restaurant for Bert?

3 EXAMPLE

For our example we will spell out choice of restau-

rant in detail. Let us suppose that Wilma and Bert

are standing outside Burger World. Bert can see that

Burger World is close by and appears cheap, but as a

stranger to the town knows nothing about any other

restaurant. Wilma, on the other hand, as a native to

the city, has complete information. So, initially, Bert

ﬁnds Burger World acceptable but Wilma will attempt

to persuade him of the merits of the Thai Palace.

Moreover suppose Bert wants a good quality restau-

rant, that is cheap, close by and licenced. Bert weights

these attributes 6,2,1 and 2 respectively. All other fea-

tures of restaurants, such as whether they have music,

and the type of cuisine, are matters on which Bert is

indifferent, and so have weights of 0, and need not be

considered. We can summarise the situation:

Set of Agents AG = {Wilma, Bert} . Wilma is the

persuader and Bert is the persuadee.

Set of Options O = {BurgerWorld, ThaiPalace} =

, O

}

Set of Attributes A

= { goodQuality, cheap, close,

licenced} = {a

}

Sets of weights. W

Wilma(

) = {6,4,0,2}; W

Bert

)

= {6,2,1,2}; for i = 1,2,3,4.

Truth values τ

. Burger world ( j = 1) {0,1,1,0}

(cheap and close). Thai Palace (j = 2) {1,1,0,1}:

(good quality, cheap and licenced).

Each agent, for each option, partitions A

into

four subsets, depending on its own knowledge base.

Attributes that are not known and have not yet been

the subject of an inquiry are unveriﬁed, while those

that have been the subject of an inquiry are veriﬁed,

and the agents are in agreement as to them.

So at the

start of the dialogue,

Bert has UT

= {cheap,close},UF

{good, licenced},VF

= VT

0 for Burger

World and

= {good,cheap,close,licenced},UT

= VT

0 for the Thai Palace.

As the dialogue progresses, inquiries regarding at-

tributes are made, and these attributes will move from

unveriﬁed to veriﬁed. Bert’s utility calculations for

Burger World at the start of the dialogue are shown in

Figure 1.

W1 I would go to the Thai palace. Wilma starts the

persuasion dialogue by making a recommenda-

tion.

B1 Burger World is right here and it looks cheap. Bert

indicates two criteria which he values and which

he believes are satisﬁed by Burger World

W2 The Thai Palace is also cheap, but it is a walk

away. Wilma supplies information about the cri-

terion satisﬁed by the Thai Palace. Bert increases

the current and minimum utilities of the Thai

Palace to 3.

B2 Is Burger World good? Bert seeks information

about another valued criterion.

W3 No. But the Thai Palace is. Wilma indicates a

point in favour of the Thai Palace. Bert must

now adjust his utilities: while the current utility of

Burger World remains 3, the maximum falls to 5.

But the minimum utility of the Thai Palace is now

6, and so cannot be bettered by Burger World.

B3 OK. Bert now has sufﬁcient information about

both restaurants for the criteria he values: he

does not ask about licensing because that can no

longer change the order for him.

At the end of the dialogue:

Bert has UT

0,UF

= {licenced},VF

{goodQuality},VT

= {cheap,close} for Burger

World and

0,UF

= {licenced},VF

= {close},

= {cheap,goodQuality} for the Thai Palace.

The utility calculations for Bert and Burger World

at the end of the dialogue are shown in Figure 1.

If an attribute cannot be shown true, it is considered

to be false since the defeasible reasoner uses negation as

failure.

EFFICIENCY IN PERSUASION DIALOGUES

Calculation of Utilities for Bert for Burger World at

the start of the dialogue:

Current Utility = U

(UT

∪ VT

)) =

({cheap,close}) = w

) + w

) = 2 + 1

= 3.

Minimum Utility = U

(VT

)) = 0

Maximum Utility = U

(UT

∪ VT

∪ UF

)) =

({goodQuality, cheap,close,licenced}) = 6 + 2 +

1+ 2 = 11.

Calculation of Utilities for Bert for Burger World at

the end of the dialogue:

Current Utility = U

(UT

∪ VT

)) =

({cheap,close}) = w

) + w

) = 2 + 1

= 3.

Minimum Utility = U

(VT

)) = 3

Maximum Utility = U

(UT

∪ VT

∪ UF

)) =

({cheap,close,licenced}) = 2+ 1+ 2 = 5.

Figure 1: Utility Calculations for Bert.

This is a fairly efﬁcient dialogue: restaurants have

many attributes and so Wilma could have told Bert

many things he did not know, whereas the dialogue is

able to conclude after Bert has received just six items

of information. How is this possible? It is because

Wilma is able to infer things about Bert’s criteria and

current knowledge beyond what Bert explicitly states

and asks, and so can recognise what will be relevant

to Bert’s opinion. This is Grice’s notion of conversa-

tional implicature. In (Grice, 1975), Grice advanced

four maxims intended to capture the pragmatics of ut-

terances in cooperative dialogues. The maxims ex-

press the cooperation principle:

Make your conversational contribution such

as is required, at the stage at which it occurs,

by the accepted purpose or direction of the

talk exchange in which you are engaged,

which arguably must be observed if misunderstand-

ings and conversational breakdown are to be avoided.

The four maxims relate to Quality (statements must

be believed on adequate evidence), Quantity (contri-

butions should be as informative as the situation re-

quires, and no more), Relevance (which may be de-

pendent on the dialogue type and its state) and Man-

ner (contributions should be clear and unambiguous).

Of these maxims, relevance will be of particular con-

cern to us here.

Thus Bert begins in B1 by stating that Burger

World satisﬁes two criteria. Burger World is not

chosen at random from the options of which Bert is

aware. It is Bert’s currently preferred option, the one

which the Thai Palace must overcome. Nor are the

criteria just any criteria, but criteria which Bert be-

lieves Burger World does, and the Thai Palace does

not, satisfy. Thus in Wilma’s reply she can improve

her case by stating that one of the criteria is satis-

ﬁed by the Thai Palace. Note here, that once a cri-

terion is put into play, it is considered for both op-

tions, thus verifying any existing beliefs Bert may

have about the options. In B2 Bert asks a question.

This again is not chosen at random but concerns a cri-

terion which, if satisﬁed would put Burger World be-

yond reach. Wilma can, however, truthfully say that it

does not satisfy this criterion, but that the Thai Palace

does. Bert now draws the dialogue to a close since he

has sufﬁcient knowledge of the criteria relating to the

two options relevant to him, according to his prefer-

ences. He does not ask about licencing because that

can make no difference to his choice, even if Burger

World is licenced and the Thai Palace is not. Note

that, in this dialogue features of the Thai Palace that

make it attractive to Wilma are not even mentioned,

while she supplies information about a feature she is

indifferent to: Bert is the sole arbiter of what makes

the restaurant good (in complete contrast to delibera-

tion). Bert could not ask about another criterion with-

out misleading Wilma by conversationally implying

that he valued a fourth criterion enough to overturn

his current view, which would prolong the dialogue

to no useful purpose. Note also the asymmetry in the

use of the criteria of the two participants. Wilma’s

criteria may determine her recommendation, but play

no part in the dialogue unless they are shown to be

valued by Bert.

The dialogue is not, however, as efﬁcient as it

might be. Given his weights, if Bert discovered that

either restaurant was, and the other was not, of good

quality, he could stop immediately, since this crite-

rion carries more weight than the other three com-

bined. Thus Bert’s best initial question would have

been B2, with Wilma’s reply in W3 enough to resolve

the discussion. We could extend our notion of conver-

sational implicature to suggest that mentioning a cri-

terion means not only that it matters to the persuadee

but additionally that there are no more important cri-

teria not yet mentioned. This is what we will do in the

algorithm developed in the next section. As we will

see in section 5, this algorithm, based on conversa-

tional implicature, is optimal in terms of minimising

the expected exchange of information.

Note also that Bert’s strategy is good only with

regard to open persuasion. Had this been a partial

persuasion situation, Bert’s question in B2 could only

have received the response that the Thai Palace was

good. Since Wilma is not obliged to tell the whole

truth, even if she had believed that the Burger World

ICAART 2012 - International Conference on Agents and Artificial Intelligence

was good, she would have remained silent on that

point, and indeed on all positive features of Burger

World. The question is answered only if the answer

does not improve Bert’s assessment of that restaurant.

In such a case there is no point in mentioning Bert’s

preferredoption, except to check that what he believes

is satisﬁed is indeed satisﬁed. In a partial persuasion

where Bert trusts his current knowledge, therefore,

Bert will ask only whether the Thai Palace is good. If

Bert does not know some relevant facts about Burger

World, he should attribute some kind of expected util-

ity to them. In this case discovery that the Thai Palace

was of good quality might not immediately displace

Burger World, and the question as to price would still

be important.

Beneath the surface of the dialogue, the pragmatic

meaning of the utterances in the context of persua-

sion is that Bert is asking a sequence of questions

about whether attributes that he values enough to be

able to change his current preference are satisﬁed by

the proposed option and (in open persuasion) by his

currently preferred option. Wilma’s role is to answer

these questions. We suggest also that Bert should ask

about criteria in order of their importance to him. We

now develop an algorithm based on this principle and

show that this represents an optimal strategy in sec-

tion 5. Thus following Grice’s maxims, and taking the

pragmatics of the dialogue type seriously, has compu-

tational beneﬁts.

4 PROTOCOL AND STRATEGY

The persuasion dialogue, (W1-B3 in the example),

once it has been initiated by the persuader, is a se-

ries of statements and requests for information on the

part of the persuadee. Either these will be a statement

of the form τ

= 1, or a question of the form whether

= 1. In either case, in the terms of (Black and

Hunter, 2009), the persuadee wishes to open inquiry

dialogues with τ

and τ

as topics (in open persua-

sion) or with τ

as the only topic (in partial persua-

sion).

This can be accomplished using a series of dia-

logues designed for inquiry such as that of (Black and

Hunter, 2009). Some difference in strategy within the

inquiry dialogue may be required for partial persua-

sion, but the inquiry dialogue of (Black and Hunter,

2009), which has been shown there to be sound and

compete, offers a means of ensuring that Bert will

gain possession of the answer dictated by the joint

knowledge of the two agents, which is the best in-

formation available. We will discuss the nature of the

inquiry dialogues no further. When should the per-

suasion dialogue terminate? If O

is Bert’s currently

best option, and Wilma is trying to persuade him of

, Bert should continue to seek information until the

minimum utility of O

is greater than the maximum

utility of O

, in which case Wilma’s proposal can be

rejected, or until minimum utility of O

exceeds the

maximum utility of O

, in which case her proposal

can be accepted. This state will be approached by

initiating inquiry dialogues to verify as yet unveriﬁed

features of the options. When UT

= UF

0, the dia-

logue must terminate, since the option with the high-

est current utility cannot be displaced. Often, how-

ever, it will terminate with only a subset of the at-

tributes veriﬁed: in the example above it may termi-

nate if good quality is true of one but not the other:

if true of both or neither it could terminate for Wilma

if cheap is true of one but not the other, and she will

consider whether they are licenced only if the options

are the same in terms of quality and price.

Deﬁnition 9. Termination condition. Let T

(X) be

the condition that the algorithm has terminated with

preferred when the status of all the attributes as-

sociated with the weights in X ⊆ W are known to the

persuadee.

(X) holds if and only if

∑

∈X

−

∑

∈X

∑

∈W\X

Similarly for T

(X).

The agent will attempt to resolve the dialogue in as

few steps as possible, and so should choose the topics

so as to minimise the expected number of steps. From

our observations about what is conversationally im-

plied in persuasion dialogues, we conjecture that an

optimal strategy, S for an agent would be to inquire

about attributes in descending order of their weights,

and so employing a kind of greedy algorithm

We now present the protocol and embedded strat-

egy S for our persuasion dialogue. We require that

agents can open and

the relevant dialogues, pro-

pose options and inquire about the status of attributes,

for which they may use inquiry dialogues as deﬁned

in (Black and Hunter, 2009).

A persuasion dialogue follows the following pro-

tocol:

[0]: Wilma opens by proposing an option, O

. If

Note that this is a different problem from that consid-

ered in (Dunne and McBurney, 2003). That paper con-

cerned the actual number of locutions in persuasion dia-

logues according to their rather different protocol, whereas

we are concerned with the information exchanged, i.e. the

expected number of inquiry dialogues: in our approach the

total number of locutions will therefore depend on the pro-

tocol employed for inquiry.

EFFICIENCY IN PERSUASION DIALOGUES

Bert’s currently preferred option is O

a persua-

sion dialogue will commence; otherwise he agrees

immediately. Initially A = X =

0; W = the set of

weights of all attributes about which Bert may in-

quire.

[1]: Bert opens inquiry dialogues with topics

,τ

for some attribute a

with which Bert asso-

ciates a positive weight w

; A becomes A ∪ {a

};

X becomes X ∪ {w

}; increment the utilities U

i ∈ {1,2} by τ

. This may change which option

is currently preferred.

[2]: If T

(X) holds terminate with O

preferred,

else if T

(X) hold terminate with O

preferred

else if X = W, return the currently preferred op-

tion; else go to [1].

The inquiry about a single attribute in [1] and [2]

will be termed a step in the remainder of this paper.

Moves are subscripted with W or B depending on

whether the move is made by the agent acting as

the persuader (W) or persuadee (B). There are two

options O

and O

. Thus the dialogue begins with

W proposing O

. Now B either agrees, or states its

preferred option and inquires about some attribute.

Since only B’s weights matter, w

will refer to the

weight given to a

by B.

open dialogue

propose

)

if agree

))

(

0), end dialogue

else

X =

0; A =

propose

), such that O

6= O

open persuasion dialogue

for all a

∈ A

sort A

into ordered descending list such that

≥ w

j+1

end for

j=1

while ¬T

(X) and ¬T

(X) do

inquire

(τ

,τ

)

A becomes A∪ {a

};

X becomes X ∪ {w

};

increment the utilities U

: i ∈ {1, 2} by τ

if τ

= 1 then a

∈ VT

else a

∈ VF

end if

if τ

= 1 then a

∈ VT

else a

∈ VF

end if

j++

end while

if T

(X) then disagree

) else agree

)

end if

end dialogue

The algorithm given above is for open persuasion;

for partial persuasion the inquiries will concern τ

only. As noted above, each pass through the while

loop is referred to as a step in the remainder of the

paper. Each step establishes the truth values for one

attribute.

5 RESULTS

In this section we describe a series of results that show

our strategy S to be an optimal strategy for a number

of representative situations. The ﬁrst of these is where

the persuadee has no initial opinions as to the facts:

the attributes of the options will be discovered from

the dialogue, and are all considered equally likely at

the outset. Theorem 1 shows that S is optimal for this

scenario

Theorem 1. Suppose we have two options O

and O

of equal prior utility, m attributes, which are equally

likely to be true or false for each option, and m pos-

itive weights assigned to the attributes. Then an op-

timal strategy, in the sense that the algorithm termi-

nates in the expected fewest number of steps, is to

inquire about the attributes in descending order of

weight (strategy S ). First we prove two preliminary

lemmas.

Lemma 1. Given a set A of n attributes, the probabil-

ity that the algorithm will terminate in not more than n

steps is independent of the order in which we inquire

about these attributes. We term this probability P(X)

where X = {w

) : a

∈ A}.

Since we are concerned with the opinions of only

one agent (the persuadee), we shall use the simpliﬁed

notation w

for w

Proof of Lemma 1. Let X = {w

,...w

} ⊆ W be the

set of weights associated with the attributes examined.

If T

(X) holds, the algorithm terminates in at most n

steps, by Deﬁnition 9.

Conversely if O

is determined in n

≤ n steps af-

ter considering X

⊆ X then T

) holds.

Subtracting

∑

∈X\X

from both sides of T

)

gives

[Inequality 1].

∑

∈X

−

∑

∈X

−

∑

∈X\X

∑

∈W\X

since (W \ X

) \ (X \ X

) = W \ X.

We would like to thank Michael Bench-Capon for his

insights regarding the proof strategy used in this section.

ICAART 2012 - International Conference on Agents and Artificial Intelligence

We aim to deduce that T

(X) holds.

LHS of T

(X) =

∑

∈X

−

∑

∈X

≥

∑

∈X

− (

∑

∈X

∑

∈X\X

)

≥

∑

∈X

−

∑

∈X

−

∑

∈X\X

since

≤ 1

∑

∈W\X

by Inequality 1

= RHS of T

(X), so T

(X) holds.

Hence the algorithm returns O

in no more than

n steps (by discovering the status of some or all ele-

ments of A) if and only if T

(X) holds. Similarly for

. Hence the probability P(X) is independent of the

order in which the elements of X are considered. 

Lemma 2. Let X,Y be n-element subsets of W which

differ only in one element: X = (X ∩Y) ∪ {w

} and Y

= (X ∩Y) ∪ {w

} with w

> w

. Then P(X) ≥ P(Y)

where P(X), P(Y) are as deﬁned in Lemma 1.

Proof of Lemma 2. Let X = {w

,...w

n−1

}, Y =

,...w

n−1

} where w

> w

. By Lemma 1, P(X)

and P(Y) are well deﬁned. We write TT, TF, FT,FF

for the 4 possible values of hτ

,τ

i. For each set

X,Y, there are 4

possible such assignments of truth

values, all equally likely by our hypothesis. For ex-

ample, when n = 3, one assignment is hTT,FT,TTi,

indicating the ﬁrst and third attributes are true for both

and O

, but the second is true only for O

. If the al-

gorithm terminates for r out of the 4

assignments, the

probability of termination in at most n steps is r/4

Suppose T

(Y) holds for a particular assignment:

we will show that it follows that T

(X) holds for that

assignment.

∑

∈X

−

∑

∈X

∑

∈Y

(τ

− τ

+ (τ

− τ

)(w

− w

)

≥

∑

∈Y

(τ

− τ

− (w

− w

)

since τ

− τ

∈ {−1, 0,1} and w

> w





∑

∈W\Y





− (w

+ w

) by T

(Y).

∑

∈W\X

so that T

(X) holds.

Hence the number r

of assignments for which

the algorithm terminates in not more than n steps is at

least r

P(X) = r

and P(Y) = r

so that P(X) ≥

P(Y) as required. .

Proof of Theorem 1. Suppose there exists a strategy

R better than S . Then there exists n ∈ N such that R

is more likely to terminate in at most n steps than S .

Let X

= {w

,..., w

}, be the set of the largest

n weights and let X

be the set of n weights used by

R .

We construct a chain of n-element sets X

,...X

so that each set X and its successor

Y satisfy the conditions of Lemma 2.

We retain elements of X ∩Y and replace others in

turn, substituting the largest in Y for the largest in X

and continuing in descending order. For example, if

X = {9,8,6,5} and Y = {8,4,3,1}, the ﬁrst intermediate

sets are {4,8,6,5}, {4,8,3,5}.

Since X

contains the largest weights, w

> w

satisﬁed for each pair in the chain. By Lemma 2,

for each pair hX,Yi, P(X) ≥ P(Y). Hence P(X

) ≥

P(X

), a contradiction. So no such better strategy ex-

ists, and we conclude that S is optimal. .

Suppose we relax the assumption that the per-

suadee knows nothing about the options in the initial

situation, and instead starts with a set of initial (per-

haps unveriﬁed) beliefs that lead to a preference for

one of the options, but where there still remain at-

tributes whose value for the options is unknown. This

was the case for Bert in the Burger World example

above. Corollary 1 demonstrates that S is an optimal

strategy in this case also.

Corollary 1. If the utilities of O

and O

are initially

unequal, S remains an optimal strategy.

Proof of Corollary 1. Let the current utilities be

with U

> U

and W = {w

..,w

} be the set

of weights.

Suppose, for contradiction, that a better strategy

R than S exists, expected to terminate in n(R ) steps

with n(R ) < n(S ). Let L be a number greater than

any weight in W.

Suppose there were additional attributes b

, b

with weights L +U

,L +U

. Now initiate a dialogue

with weights W ∪{L+U

,L+U

} and the initial util-

ities zero for both options.

Apply the following strategy.

Step 1: Inquire about b

Step 2: Inquire about b

After Step 2: if Step 1 assigns TF and Step 2

assigns FT, (difference between utilities is U

− U

continue as for R , otherwise continue in descending

order.

For this strategy the expected number of steps is 2

+ 1/4n(R ) + 3/4n(S ). The expected number of steps

for the descending order strategy is 2 + n(S ) which is

greater, contradicting Theorem 1. So no such strategy

R exists. 

Next consider partial persuasion, where nothing

improving the current estimated utility of the pre-

EFFICIENCY IN PERSUASION DIALOGUES

ferred option can be learned, since the persuader will

choose to remain silent. Now all inquiry will take

place concerning the option advocated by the per-

suader. That S remains an optimal strategy in the case

is established by Theorem 2.

Theorem 2. If τ

is known in advance for all at-

tributesa

, S is an optimal strategy for inquiring about

the τ

Sketch of Proof of Theorem 2. In this case U

constant throughout. After examining attributes with

weights in X ⊆ W, U

∑

∈X

The algorithm terminates when either U

> U

or U

−U

∑

∈W\X

∑

∈W

−

∑

∈X

increases monotonically.

The expected value of U

∑

∈X

so the algo-

rithm is expected to terminate when

either

∑

∈X

> U

∑

∈X

∑

∈W

−U

The RHS of each inequality is constant, so the best

strategy is to maximise the LHS at each step, that is

to choose the largest remaining weight. But this is

strategy S as in Theorem 1. 

Finally we consider the case where the persuadee,

agent B, has initial beliefs about attributes relating to

both options, but has varying degrees of conﬁdence

in these beliefs, and wishes to conﬁrm them during

the dialogue. Theorem 3 shows S to be an optimal

strategy on the assumption that the currently preferred

option is at least as likely as the alternative proposed

by the persuader to satisfy the criteria valued by the

persuadee. This will be the case where the persuadee

is quite sure that its preferred option satisﬁes some

desirable attributes, but has only tenuous beliefs about

the other option.

Theorem 3. S remains an optimal strategy if the

probabilities p

are not equal, provided that p

≥ p

for each attribute j, where p

= P(τ

= 1).

Sketch of Proof of Theorem 3. After examining at-

tributes with weights in X ⊆ W, (expected value of

) =

∑

∈X

. So the algorithm is expected to ter-

minate when

∑

∈X

− p

∑

∈W

−

∑

∈X

Arguing as before, an optimal strategy is, at each

step, to choose from the remaining weights so as to

maximise w

− p

+ 1). 

6 CONCLUDING REMARKS

In this paper we have considered the distinctive fea-

tures of persuasion dialogues. We have made these

precise, for the very common form of persuasion di-

alogue where one agent is trying to convince another

that its currently preferred option is not as good as

some other possibility known to the persuading agent.

We have also drawn attention to the pragmatic mean-

ings of utterances in these persuasion dialogues, as

revealed by considering what the utterances conver-

sationally imply in this context. We have used these

pragmatic meanings to develop a protocol and strat-

egy for agent persuasion dialogues, and have shown

the strategy to be an optimal strategy in a range of rep-

resentative scenarios for these persuasion dialogues.

In future work we intend to consider dialogues

with three or more participants, and dialogues which

attempt to change the preferences of the participants.

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