AutoMed - An Automated Mediator for Multi-Issue Bilateral Negotiations∗
Michal Chalamish1
1
Sarit Kraus2
Ashkelon Academic College
Ashkelon, 78211 Israel
[email protected]
2
Department of Computer Science,
Bar-Ilan University, Ramat-Gan, Israel 52900 and
Institute for Advanced Computer Studies
University of Maryland, College Park, MD 20742 [email protected]
Abstract
In this paper, we present AutoMed, an automated mediator
for multi-issue bilateral negotiation under time constraints.
AutoMed uses a qualitative model to represent the negotiators’ preferences. It analyzes the negotiators’ preferences,
monitors the negotiations and proposes possible solutions for
resolving the conflict.
We conducted experiments in a simulated environment. The
results show that negotiations mediated by AutoMed are concluded significantly faster than non-mediated ones and without any of the negotiators opting out. Furthermore, the subjects in the mediated negotiations are more satisfied from
the resolutions than the subjects in the non-mediated negotiations.
Introduction
Engaging in negotiations is an every day activity. Some
negotiations can not be concluded in a manner satisfying
both sides without the involvement of someone other than
the negotiators themselves. In such cases, the intervention of a non-bias, competent authority such as the court
of justice is required in order to finalize the debate. Another possible third party intervention can be that of a mediator. In mediation scenarios, the objective is to help the
negotiators reach a mutually beneficial agreement. Namely,
one that provides the best possible solution considering
the various preferences of each negotiator (Kraus 2001;
Fisher and Ury 1981).
Several types of mediators are described in the literature.
A manipulative mediator (Touval and Zartman 1985) uses
his position to manipulate the parties into agreement, while
the formulating mediator (Zartman and Touval 1996) proposes new solutions and assists the negotiators when an impasse in the negotiation is reached.
Aside from reaching an agreement, there are two additional options to concluding a negotiation. First, each negotiator can opt out of the negotiations, forcing the continuation of the present situation of status quo on both sides.
∗
This research is based upon work supported in part by the
U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF-08-1-0144 and under NSF grant
0705587.
c 2009, Association for the Advancement of Artificial
Copyright Intelligence (www.aaai.org). All rights reserved.
Second, the negotiation might reach the deadline, thereby
inflicting the status quo on issues not yet agreed upon. Concluding the negotiations with the status quo most probably
will not resolve the dispute but worsen it by intensifying a
strike or declaring the beginning of battles, etc.
Sometimes approaching a human mediator is undesirable
due to either high financial costs or because the parties are
unable to agree on a mutual mediator. One option is to
use Online Dispute Resolution (ODR) (Bonnet et al. 2002)
tools which usually act as support systems for dispute resolutions, such as negotiation, mediation, and arbitration provided online. In many cases, a completely automated mediator can present an alternative. It can be completely confidential, non-biased and can offer neutral ground. There have
been a number of attempts to create automated mediators.
Some act as support systems (i.e., SmartSettle (Thiessen and
Jr. 1999)), while others are topic embedded, such as Family Winner (Bellucci and Zeleznikow 2001) and the PERSUADER (Sycara 1991), which acts as a manipulative mediator. Our research focuses on developing an automated
formulating mediator which is not topic embedded.
Most negotiating systems use a quantitative model in order to represent the negotiators, mainly comprising utility
functions (Lin et al. 2006). Utility functions are ideal for
representing and reasoning with user preferences in quantitative models. Unfortunately, people find it difficult to express their preferences using a utility function. Moreover,
many real-world situations are not suitable for quantitative
modeling, especially delicate situations which might include
possible loss of lives, imprisonment or serious injuries. In
such cases, the association of numerical values to solution
possibilities is a highly difficult task, so that using utility
functions is equally difficult.
An alternative preference representation approach is qualitative modeling, which might be a better method in such
situations. Current qualitative methods include Quantitative
Belief Functions (Wong and Lingras 1994), preferences on
goals (Wellman and Doyle 1991), 3-points intervals (Öztürk
and Tsoukiàs 2006), CP networks (Boutilier et al. 1997;
1999; 2004) and others. These models allow the user to represent her preferences without assigning accurate numerical
values. CP-networks can be applicable to a much broader
range of situations than most other methods.
We make the following assumptions concerning the nego-
tiations with which we deal:
• Each negotiator knows his own preferences regarding the
possible solutions but has no accurate knowledge of the
other negotiator’s preferences. Thus we are concerned
with incomplete information environments.
• There is at least one agreement that is preferred by both
negotiators over the options of opting out of the negotiations and reaching the deadline with no resolution.
These assumptions are valid in several dispute domains,
such as e-commerce, settlement of labor disputes through labor contracts, etc. In such environments the duration of the
negotiation might have a great affect on its outcome, since
the dispute may incur high costs - financial or other - for
both or at least one of the parties or. costs might even rise as
time goes by. There might also be some deadline by which
an agreement must be reached before negotiations may no
longer be relevant (e.g. approaching the court of law, beginning of battles, intensifying a strike, etc.).
This research focuses on developing a new mediation tool
and presents AutoMed, an automated mediator for bilateral
negotiations under time constraints. The situations we consider are bilateral negotiations, in which, for simplicity reasons, each side is represented by a single negotiator.
A number of innovative approaches were used while developing AutoMed:
• Most negotiating tools existing today use utility functions
as the preferred user representation model. Since utility
functions might be very difficult to define in situations
like the ones described, AutoMed uses an innovative enhanced version of the CP-network model (Boutilier et al.
1997) named Weighted CP-networks (WCP-networks).
The original CP-networks are usually used to represent
a single user, while trying to maximize her benefit. AutoMed is also unique in its attempt to find a balance between two separate WCP-networks, each representing a
negotiator.
• The disputes AutoMed mediates can consist of a finite
number of multiple issues and a finite number of multiple
possible values for each issue, while the negotiators need
to agree on a single value for each issue. Since there is no
one agreement which is the best for both negotiators, AutoMed must find a middle ground which the negotiators
might agree upon. Looking for trade offs makes the negotiation - and the mediation - more complex than most of
the human-computer negotiations which have been dealt
with until now.
• AutoMed is a fully automatic mediator which is not topic
embedded and can be used for any bilateral dispute that
meets our assumptions. AutoMed can be presented with a
predefined set of issues and values to be discussed in the
current scenario. Alternatively, it can supply an environment for defining it.
• AutoMed acts as a formulating mediator, rather than a manipulative one. It tries to propose solutions and helps the
negotiators reach a mutually agreed outcome.
We conducted an experiment to demonstrate AutoMed
performance. In the experiment, 82 participants took part,
and the results show that negotiations mediated by AutoMed
are concluded significantly faster than non-mediated ones.
They also show that all the negotiations mediated by AutoMed were concluded with agreements accepted by both
parties, while in non-mediated negotiations, some ended
when reaching the time limit or with one side opting out.
The satisfaction level of the results reached was also higher
among the mediated negotiation participants.
Related Work
Mediation tools
Online Dispute Resolutions (ODR) (Bonnet et al. 2002) are
methods for resolving disputes, the major part of which is
provided online. Most ODR services are alternatives to litigation and to state justice. In this sense, they are the online
transposition of the methods developed as Alternative Dispute Resolutions (ADR) (Rabinovich-Einy 2003 04). One of
the main forms of ODR systems is on-line mediation. Many
online mediation service providers are available. For example, eBay designed a mediation room mainly in order to help
resolve buyer-seller conflicts (eBay’s mediation room ).
These Dispute Resolution services supply a neutral and
virtual negotiation forum and discussion rules. Most ODR
services use a human mediator to help resolve the disputes.
In recent years, a new term was introduced by Katsh &
Rifken (Katsh and Rifkin 2001) in the research and development of ODR tools. While the human mediator is considered
a “third party” to the dispute resolution process, the assisting
“fourth party” is the technology itself. The concept of the
“fourth party” suggests that ODR should not strive to create
online models that simply copy offline approaches, as suggested earlier (Rabinovich-Einy 2003 04), but provide capabilities that were not available before and that were not employed in face to face meetings (Katsh and Gaitenby 2003;
Katsh and Wing forthcoming). These capabilities are available today due to the globalization of business, information
and culture over the Internet (Kaufmann-Kohler and Schultz
2004), and might affect ODR as we know it today in many
new ways (Hattotuwa 2005). Extensive future research is
expected in this field (Turel and Yuan 2007).
A number of mediation support systems are described
in the literature. Family Winner (Bellucci and Zeleznikow
2001) is a Negotiation Support System in Australian Family
Law. SmartSettle (Thiessen and Jr. 1999) is another negotiation support system that networks multiple parties located
anywhere in the world and manages their confidential information with a neutral Internet site (Thiessen and Jr. 1999).
Unlike the Family Winner and SmartSettle, AutoMed is a
fully automated mediator.
PERSUADER (Sycara 1991) is a computer program
which acts as an automated labor mediator in hypothetical
negotiations relying on Case-Based Reasoning methods. It
is a manipulative mediation system (as defined in the introduction) - unlike our development of a formulation mediation tool. Another fundamental issue is that since PERSUADER relies mainly on CBR, it might find it difficult to
resolve disputes of a completely new nature not described in
its database. In contrast, AutoMed relies exclusively on the
definitions of the dispute at hand and the negotiators preferences over these definitions rather than on a database. Where
experimentation is concerned, PERSUADER was not simulated with people, while AutoMed was.
Preferences representation models
There are many approaches to representing and eliciting user
preferences (Sycara 1988; Boutilier et al. 1997; Royalty et
al. 2002; Chajewska et al. 1998). Elicitation is the process
by which the user’s preferences are obtained. It usually involves very long and thorough questioning, making the elicitation a heavy burden on the user.
An interesting elicitation algorithm is used in the POET
system which tries to simplify the process. POET (Royalty
et al. 2002) is used as a tool which attempts to automate
academic advising. The preferences are represented as a set
of decision trees built by the user, which are referred to as
dependency trees. A leaf in a dependency tree consists of an
issue value and a utility function which applies to the path
represented by that leaf.
In the PANDA system (Chajewska et al. 1998), elicitation
is dealt with as a classification problem. The researchers focused on prenatal testing domain. In the PANDA system
existing users’ utility functions stored in a data base are divided into non-overlapping groups, clusters, of functions.
Given that k clusters were found, the problem of finding
the corresponding cluster for a new user’s utility is a classification problem. To solve this problem a decision tree is
constructed, and when a new user’s utility function is determined to belong to a given cluster, the strategy of that cluster
is associated with that user.
Utility functions (Sycara 1988) are an ideal tool for representing and reasoning with preferences but they can be very
difficult to elicit. Moreover, they can be very difficult to calculate, especially in disputes which might include possible
loss of lives, imprisonment or serious injuries.
A conditional preference(CP)-network (Boutilier et al.
1997), on the other hand, is a qualitative rather than quantitative representation model for user preferences. It is graphical
in nature and exploits conditional preferential independence
in structuring a user’s preferences. Its great advantage in
comparison to other qualitative methods is its generality. It
can be easily used for all domains definable by a set of issues
and their values.
Negotiation Environment
Before detailing the models and algorithms AutoMed uses
in order to serve as a mediator in a bilateral negotiation, the
definitions and the negotiation protocol used must be specified. The protocol specified is based on the one used by
the negotiation support system SmartSettle (Thiessen and Jr.
1999).
Issues and agreements
Let Iss = {issue1, issue2 , . . . , issuem } be a set of issues
over which the negotiators disagree. Each issuei can have
some value from the domain of issuei , dom(issuei ) =
{val1i , val2i , . . . , valbi i } of possible values, where b is the
maximum number of values in all issue domains and bi ≤ b.
Denote a possible agreement reached in the negotiation
by agr. Therefore, agr ∈ dom(issue1 ) × dom(issue2 ) ×
· · · × dom(issuem ).
A partial agreement is an assignment of values to issues,
where not all issues are assigned a value. The unassigned
values are annotated with the empty value ε. For example,
agr = (val21 , ε, val23 , val14 , ε, val36 , val27 ) is a partial agreement where no value is specified for issue2 and issue5 .
Negotiation protocol
The negotiations are managed through a computer program
acting as a server. Both negotiators connect to a web based
interface, invoking the mediator which acts as a third client
to the server.
First, negotiations regarding the issues and possible values to be discussed are conducted through the negotiation
interface. Following the conclusion of these negotiations,
the preference elicitation interface is presented to the negotiators. In cases where the set of issues and possible values is predefined, the preliminary negotiation is skipped and
the preference elicitation interface is presented first. With
the completion of this stage, the negotiation interface is displayed, enabling the exchange of messages between the negotiators.
The negotiation protocol allows each negotiator to propose possible agreements to the other side. A proposal can
be sent to the other negotiator anytime - there is no predefined order. An offer is constructed by choosing a value for
each issue out of a list of all the values defined for that issue.
Each list of values also includes the ”not under discussion”
value, serving as the empty value ε, which indicates a certain
issue is not under discussion in this offer.
After sending an offer, the server delivers it to both the
other negotiator and the mediator. The other side can either
accept or reject it. A value already accepted by both can be
changed only by agreeing upon another value. Agreed upon
issues are accumulated to finally achieve a full agreement.
When the mediator is the one proposing, the proposals are
always full, that is, without any empty values. The server delivers the mediator’s proposal to both parties simultaneously.
If both sides accept its offer, a full agreement is reached and
the negotiations end.
If the time limit is reached before a full agreement has
been agreed upon, the values representing the status quo are
assigned to every issue not yet agreed upon. Also, if one side
opts out the full status quo serves as the reached agreement.
An example for a negotiation which follows this protocol
can be found in figure 1.
Notice that the mediator acts as a formulating mediator. It
proposes solutions but has no power to enforce one.
Qualitative Representation Method
Prior to engaging in the negotiation, both negotiators must
provide their preferences to AutoMed. AutoMed separately
orders all possible agreements according to each of the negotiators’ elicited preferences. After removing the nonpareto optimal agreements, AutoMed forms a combined list
Offer o1
Negotiator 1
Of
fe
Reject o1
Negotiator 2
Negotiator 1
Negotiator 2
ro
R
1
AutoMed
o1
ct
eje
AutoMed
(a) Negotiator 1 makes an offer to negotiator 2 while AutoMed is
listening.
(b) Negotiator 2 rejects the offer made by negotiator 1 while AutoMed is listening.
Offer o2
Reject o2
Negotiator 1
Negotiator 2
O
Negotiator 1
r o2
ffe
Re
Negotiator 2
jec
to
2
AutoMed
AutoMed
(c) Negotiator 2 makes an offer to negotiator 1 while AutoMed is
listening.
(d) Negotiator 1 rejects the offer made by negotiator 2 while AutoMed is listening.
Accept o3
Negotiator 1
Of
fe
Negotiator 2
ro
3
O
r
ffe
o3
Negotiator 1
Ac Accept o3
ce
t o3
pt
ep
cc
o
A
3
AutoMed
(e) AutoMed intervenes and makes a (full) offer to the negotiators.
Negotiator 2
AutoMed
(f) Both negotiators accept AutoMed’s offer thereby concluding the
negotiations.
Figure 1: An example of a negotiation. A circle signifies a person, a circled rectangle signifies a software agent, an arrow signifies the
transfer of a message and a dashed arrow signifies the side effect of the message transfer.
of agreements ordered according to the original positions of
the agreements in the separate lists. The combined list is
used for the suggestion of solutions.
The preference representation method used by AutoMed
is acyclic WCP-networks, which has two components. The
first component, an acyclic CP-network, is a qualitative
model developed by Boutilier et. al. (Boutilier et al. 1997;
1999; 2004). The second component, developed specifically for AutoMeds’ needs, is a Weighted Importance Table
which enables AutoMed to order the possible agreements
with greater accuracy.
We chose to use a qualitative user preferences representation model over a quantitative model after experimenting
on both. The experiment we conducted is detailed in (Chalamish 2009). It is important to emphasize that using a qualitative model allows the use of numerical values in expressing
preferences. However, it does not require to associate each
outcome with a specific utility values, and more over do not
expect the negotiators to maximize expected utility nor to
follow equilibrium strategies.
when vali2 holds she prefers valj2 over valj1 , ceteris paribus.
This is written as:
vali1 ≻ vali2
vali1 : valj1 ≻valj2
vali2 : valj2 ≻ valj1
Assuming the WCP-network is acyclic, there is at least
one node with an indegree of zero, corresponding to an independent issue.
Figure 2 illustrates a typical CP-network containing seven
issues, the defined relations and the corresponding CPT. For
readability, the issues in all the figures are annotated as upper
case letters, while their corresponding values are annotated
by lower case letters.
A
C
F
WCP-networks
A Weighted conditional preference(WCP)-network is a representation model for user preferences which consists of an
acyclic graph describing the preferential dependency relations between all the issues defined in a certain domain. The
preferences over the values defined for each issue are annotated in a conditional preference table (CPT).
Each dom(issuei ) can contain a different number of possible values, but for simplicity reasons, in all the examples,
the domains are binary. However, the scenario used in our
experiments contains triple and quadric valued issues.
The user is required to indicate her preference for the
values defined for each dom(issuei ), and any combination
dom(issuei )× · · · × dom(issuej ) she deems relevant.
For each issuei ∈ Iss, the user is asked to identify a set of
parent features P(issuei ) that can affect her preferences over
various issuei values. That is, given a particular value assignment for P(issuei ), the user should be able to determine
a preference order over dom(issuei ), all other things being
equal (ceteris paribus).
Denote all other issues aside from issuei and P(issuei )
by com(issuei ), i.e., issuei ’s complement. Therefore, issuei
and com(issuei ) are conditionally preferentially independent
given P(issuei ). Given this information, the user is asked to
explicitly specify her preferences over the values of issuei
for all possible values of P(issuei ). The above information
is used to create an annotated graph in which each issuei has
P(issuei ) as its set of parents. The node issuei is now annotated in a CPT describing the user’s preferences over the
node’s values given every combination of parent values.
Example 1 The user describes her preference over issuej ,
by indicating that this preference depends on the value of
issuei and on that value alone, while issuei is independent,
issuei is then made to be issuej ’s parent and the user is
asked about her preferences on issuei and issuej for each
value of issuei . She may say that vali1 is preferred to vali2
and that when vali1 holds, she prefers valj1 over valj2 , and
B
D
E
[a1 ≻ a2 ][b1 ≻ b2 ]
[a1 : c1 ≻ c2 ; a2 : c2 ≻ c1 ]
[b1 : d1 ≻ d2 ; b2 : d2 ≻ d1 ]
[b1 : e1 ≻ e2 ; b2 : e2 ≻ e1 ]
[c1 : f1 ≻ f2 ; c2 : f2 ≻ f1 ]
[d1 : g1 ≻ g2 ; d2 : g2 ≻ g1 ]
G
Figure 2: CP-network example
Adding the notion of weight to issues enables a greater
accuracy in the later task of outcome ordering.
We will further extend the CP-network definition and add
the property of importance by using the weighted importance table (WIT) defined below. This extra knowledge allows AutoMed to associate a numerical measure of preference to each outcome. The extended model will be referred
to as the Weighted Constraint Preferences Networks (WCPnetworks).
When using utility functions, an exact numerical valuation is associated with each outcome. These utility values
indicate not only that one outcome is preferred over another,
but also to what extent. In the WCP-network, a numerical
valuation is assigned only to issues and it merely captures
the concept of ”more important than”. There is no need
to assign relative valuations to different issues or numerical
valuations to values at all. This relaxed requirement makes
it much easier for the negotiator to specify her preferences.
Let us consider a CP-network N . Whenever N contains
two relations, P(issuej )=issuei ) and P(issuek )=issuej ) it is
clear that issuei is more important than issuej which is, in
turn, more important than issuek .
Example 2 Consider the CP-network illustrated in figure
2. The network’s graph contains a directed edge between
B and D indicating that P(D)=B, and another directed edge
between D and G indicating that P(G)=D. From these relations we can infer that B is more important than D, which is
more important than G.
A problem arises when the situation is not well defined.
This can happen in either one of two cases - if there is more
than one independent issue or if there are multiple successors belonging to a certain parent node and are on the same
level in the graph’s hierarchy. A node’s level in the graph’s
hierarchy is determined by the longest path from one of its
independent predecessor to it.
Case 1 - Multiple independent issues If |IND(N )| >1,
then the weighted importance table will define for every
issuei ∈ IND(N ) its importance with respect to all issuej ∈
IND(N ), issuej 6= issuei .
Case 2 - Multiple successors For every issuei ∈ Iss(N ),
let S(issuei ) be the collection of all of issuei ’s successors.
That is, issuej ∈ S(issuei ) if ∃edge(issuei ,issuej )∈ N . If
|S(issuei )| >1, then the weighted importance table will define for every issuej ∈ S(issuei ) its importance in relation to
all issuek ∈ S(issuei ), issuek 6= issuej .
The importance measurement itself will be represented
by a natural positive number corresponding to the importance level. Thus the most important issue will be given the
importance weight l, with l constituting the number of issues measured. The importance weights will be given for
IND(N ) and for S(issuei ) separately, so that the numeration
starts over for each such set.
Consider the WCP-network, N , illustrated in Figure
2.
Issuei and issuej are independent (IND(N ) =
{issuei ,issuei }), however when calculating the preferred settlement for the negotiator represented by this network, it is
not known which is more important. In particular, which
issues a given negotiator would prefer to trade-off is unknown. The same difficulties are raised with respect to
S(issuei )={issuej ,issuek }. This information is represented
by the Weighted Importance Table (WIT) in figure 3.
IND(N ) − A : 1, B : 1
S(B) − D : 1, E : 2
ence statements. Starting at the highest level and considering issues at the same level in the hierarchy, an outcome
dominates another if its assignments win the majority.
The definition of ML ordering includes two assumptions:
1. Issues in the same graph hierarchy level are uniformly distributed in the issues’ preference space.
2. Values of the same issue are uniformly distributed in the
issue’s preference space.
We enhance ML ordering in order to add the notion of importance levels represented by the WIT. We call this ordering weighted ML ordering (WML ordering). WML ordering
supports the second assumption of ML ordering, but rejects
the first if the WIT is defined.
An issue’s level is a combination of its level in the graph
hierarchy and its (weighted) importance, if defined. Formally, let riw(issuei ) be the relative importance weight defined for issuei in the WIT. If no such value is defined then
riw(issuei )=1. Let level(issuei ) be issuei ’s level in the WCPnetwork hierarchy.
If vali1 ≻ vali2 , then for the assignment of vali1 the outcome
receives riw(issuei ) and for the assignment of vali2 it receives
0. Similarly, if vali1 ≻ vali2 ≻ vali3 , then for the assignment
of vali1 the outcome receives riw(issuei ), for the assignment
i)
and for the assignment of vali3
of vali2 it receives riw(issue
2
it receives 0. A comparison of the summation of the results
will determine which assignment dominates the other, or a
tie.
AutoMed
Figure 3: Weighted Importance Table example
The negotiator represented by this WCP-network considers A and B to be at the same importance level. On the
second level, she considers E to be more important than
D. Note that unlike utility functions, where, given to two
issues, the weights capture the notion of the exact relative
importance between them, the WIT specifies only absolute
importance. Given D and E in figure 3, it is only known
that E is more important than D, but the extent of the importance is not known. It might be twice, three times or only
0.15 times more important. This is also true with respect to
≻, i.e., a1 ≻ a2 means that a1 is preferred over a2 , but no
indication is given as to the extent it is preferred.
Though this inaccuracy will naturally affect AutoMed’s
calculations, it is also the reason humans are more comfortable with qualitative representation methods, rather than
quantitative ones, as we show in our experiments.
Outcome ordering
The main objective of WCP-networks is to decide, given
two outcomes o1 and o2 , which is preferred according to
the user’s preferences.
Rossi et al (Rossi, Venable, and Walsh 2002) define an
ordering over CP-networks, to which they term majority
lexicographic ordering (ML ordering). ML ordering takes
into consideration all the issues that are at the same level
w.r.t. the hierarchy introduced by the CP-network’s prefer-
Design
AutoMed has to address several tasks. The first is to allow
the negotiators to define the issues to be resolved and the values which they can be assigned in the final agreement. Second, it enables the negotiators to elicit their preferences using WCP-networks, using a graphical interface. The WCPnetworks remain confidential throughout the negotiations.
Given the two WCP-networks, AutoMed has to identify
and eliminate the non-pareto optimal agreements and to find
what it believes to be the fairest agreement to resolve this
dispute. When using utility functions as the basis for mediation, two functions are defined, U1 which represents the first
negotiator’s preferences and U2 which represents the preferences of the second negotiator (Sycara 1988). A “fair”
agreement is defined as the combination of these two functions, U1 ◦ U2 . Then the comparison of different agreements
is done by calculating the composed function’s value. For
example, Nash (Nash 1953) proposed to use U1 ◦U2 (agr) =
[U1 (agr) − U1 (statusQuo)] ∗ [U2(agr) − U2 (statusQuo)].
The proposed agreement is the one that maximizes U1 ◦ U2 .
Since AutoMed does not use utility functions, function
composition is not an option. The only method AutoMed
can use is the WML ordering which is able to compare two
agreements from a single negotiator’s point of view. Therefore, AutoMed sorts the possible agreements twice - once
according to one negotiator’s preference and once according
to the second negotiator’s preference. After the agreements
are sorted, the position of an agreement in the lists can serve
as a substitute for its utility value. We refer to the position
of an agreement arg in some sorted list L as its rank in L
and denote it as rankL (arg).
After the lists are sorted, AutoMed identifies the pareto
optimal agreements, and uses their ranks in the separate lists
in order to determine which is the fairest agreement. This
process is done once at the beginning of the negotiations
and has a high complexity. But, since this process begins
automatically after both negotiators have finished specifying
their WCP-network and is done while they start to exchange
proposals, AutoMed has a long time period until it actually
has to send its own proposal to the negotiators. By then, this
process has already been completed.
During the negotiations, AutoMed attempts to find and
suggest an agreement it believes will be the fairest at the
given stage of the negotiations. It must also decide when to
intervene in the negotiations and when to simply track them.
Finally, when a non pareto optimal agreement is reached,
AutoMed tries to upgrade it by suggesting the nearest pareto
optimal one. These features will be discussed in the following subsections.
Suggesting a possible agreement
To the best of our knowledge, in the literature there are no
guidelines on which agreement to suggest and at which negotiation stage to suggest it. Thus, we have developed AutoMed’s approach through trial and error by analyzing preliminary experiments with people.
Ranking Agreements Denote the list of all possible
agreements by Agr. Since there is a finite number of issues and values, the list is also finite. Denote the number of
agreements in Agr by k, that is, |Agr| = k.
Definition 1 Let X⊆Agr be a set containing possible agreements, and let i be the wml ordering of negotiator i defined
according to her WCP-network. LX
i is a list of the agreements of X sorted in an increasing fashion by i , where ties
are resolved arbitrarily.
Given two agreements agr1 and agr2 , we assert that agr1
is better than agr2 according to negotiator i if agr1 i agr2 .
Next, we define the set of pareto optimal agreements.
Definition 2 The set of Pareto Optimal agreements,
PO(Agr), contains all the agreements in Agr excluding the non-pareto-optimal ones. PO(Agr)=Agr\{agrj |∃
agri 6=agrj s.t. ((agri 1 agrj )∧ (agri 2 agrj )) ∨
((agri ≻1 agrj ) ∧ (agri =2 agrj )) ∨ ((agri =1 agrj ) ∧
(agri ≻2 agrj ))}.
Each agreement, agr, that will be considered by AutoMed
P O(Agr)
P O(Agr)
must be a member of both L1
and L2
. However, in most cases, rankLP O(Agr) (agr)6= rankLP O(Agr) (agr).
1
P O(Agr)
2
P O(Agr)
AutoMed merges L1
and L2
into one list, denoted by L1,2 , by sorting the agreements according to their
sum of ranks in each of the pareto optimal sorted lists. If the
summed ranks of several agreements are equal, the agreements with the smaller absolute difference between their
ranks, will precede the others, assuming that they originate
in higher original ranks on both lists.
Definition 3 Let L1 and L2 be two lists, where L1 is sorted
according to 1 and L2 is sorted according to 2 .
SumL1,L2 (agr)=rankL1 (agr)+rankL2 (agr)
DiffL1 ,L2 (agr)=|rankL1 (agr)-rankL2 (agr)|
Using the functions SumL1 ,L2 and DiffL1 ,L2 , we formally
define an order reflecting both negotiators’ preferences.
Definition 4 argi 1,2 argj , with respect to L1 and L2 , in
the following cases:
• SumL1,L2 (agri )> SumL1 ,L2 (agrj ) or
• SumL1,L2 (agri )=SumL1 ,L2 (agrj ) and
DiffL1 ,L2 (agri )<DiffL1 ,L2 (agrj )
The set L1,2 that AutoMed considers is over PO(Agr).
The fairest pareto optimal agreement AutoMed can offer
is the highest one of the resulting list.
We will demonstrate the fairness of this approach with a
few simple examples.
Example 3 Consider the case where there are 5 possible
agreements: agr1 , ..., agr5 .
If the preferences of the negotiators conflict (e.g., a zero
sum game) then, without loss of generality we can assume
that L1 = {agr1 , agr2 , agr3 , agr4 , agr5 } and L2 = {agr5 ,
agr4 , agr3 , agr2 , agr1 }. The sum of ranks of all possible
agreements is 6, but the one with the lowest Diff is agr3 that
will be offered by AutoMed.
It is also interesting to observe that it is impossible for an
agreement that is most preferred by one negotiator and the
least preferred by the other to be the last (most preferred) on
AutoMed’s combined list. Suppose, as before that there are
5 possible agreements: agr1 , ..., agr5 and that agr1 appears
first in L1 and last (most preferred) in L2 . So its sum is 6 and
the diff is 4. It is not possible that the sum of all the other
agreements will be lower than 6. With out loss of generality
assume that L1 = {agr1 , agr2 , agr3 , agr4 , agr5 }. First,
agr5 ’s sum can’t be lower than 6. It can be at least 6, if it is
located first on L2 . Furthermore, in order for agr4 ’s sum to
be lower than 6, it must be ordered first in L2 ; however, this
is taken already by agr5 . So, its sum can be at least 6, but its
diff is lower. So, arg1 will not be the first on .
Agreement Suggestion During negotiations, AutoMed
searches for a middle ground agreement to suggest upon
which both sides can agree. According to the negotiation
protocol, the negotiators are allowed to propose full as well
as partial agreements. While partial agreements are used by
the negotiating parties, AutoMed always suggests full agreements, attempting to propose a good trade-off. The definition of the agreement to be suggested is as follows.
P O(Agr)
Assume L1,2
is given. The last offers made by each
side are considered when searching for the agreement to suggest during negotiations,. Denote last1 as the offer suggested
by the first negotiator and last2 as the offer suggested by
the second. AutoMed assumes that the suggested agreement
must be a pareto optimal one which is located within the
range of agreements constrained by the last proposals sent.
If the given offers are partial agreements, the empty values
are filled with the best value possible, according to the preferences as expressed in WCPi -network for the corresponding negotiator.
Example 4 Let partPropose be a partial proposal proposed
by the first negotiator, who is represented by the WCPnetwork specified in figures 2 and 3. If partPropose is missing the value for issue A, AutoMed will fill it in by assigning
the value a1 .
Should the same suggested offer be identified three consecutive times and the missing-value issues already have
been agreed upon, AutoMed will use the agreed values instead of the best one. After filling in the empty values, AutoMed searches for a pareto optimal agreement to propose.
Intervention After finding the agreement believed to be
the best one to propose at a given stage of negotiations, AutoMed should decide whether or not to present it to the negotiators. To the best of our knowledge there are no guidelines
on this subject in the literature. Thus, we have developed
AutoMed’s approach through trial and error by analyzing
preliminary experiments with people. AutoMed’s intervention algorithm is presented below.
AutoMed will intervene only if it has reason to believe
that its suggestion will be accepted or at least helpful to one
or both negotiators in opening new directions of thought. It
will wait until both negotiators have had an opportunity to
propose an agreement. If in the last round a partial agreement is achieved or if the calculated suggestion was already
presented to the negotiators in the last round it will not offer it again. If, according to its calculations, the potential
suggestion improves both parties’ position with respect to
their own proposals, AutoMed will choose to present it. The
suggestion will also be presented if AutoMed finds that it
improves at least one side’s position considerably.
Agreement upgrading When a full agreement is agreed
upon by both the negotiators, AutoMed checks for its pareto
optimality. If it finds that the reached agreement is not pareto
optimal, AutoMed consults the list of sorted pareto optimal
P O(Agr)
agreements L1,2
. Starting from the highest ranking
agreement it searches down the list for the first pareto optimal agreement which improves both negotiators’ outcome
and proposes it to them. If the upgraded suggestion is accepted by both negotiators, the negotiations conclude with
the mediator’s proposal. Otherwise, if at least one of the
negotiators rejects the upgraded suggestion, the originally
accepted full agreement stands.
AutoMed’s performance
In order to test the performance of AutoMed, we applied the
interface and specific domain used by Lin et al. in (Lin et
al. 2008) (pp.847-849). However, unlike Lin et al., who experimented with a negotiating agent, our experiments were
conducted using two sets of negotiating pairs. One set of
negotiations was mediated by AutoMed, while the other set
served as a control group. A total of 82 participants took
part in this experiment.
Domain In our scenario, England and Zimbabwe are
members of the World Health Organization’s Framework
Convention on Tobacco Control. In this convention, the
world’s first public health treaty is about to be formed, con-
cerning the trade in tobacco and the industrial countries
(tobacco users) support of the non-industrial ones (tobacco
growers). England, representing the industrial countries, and
Zimbabwe, representing the non-industrial countries, are negotiating the treaty. The time of the convention is limited. If
no treaty is agreed upon while the convention is at session, it
will not be implemented at all. Both England and Zimbabwe
have political as well as financial considerations when attempting to agree on the treaty and both prefer to reach an
agreement than to continue the current state of affairs.
The subjects in our experiment were divided into pairs,
where one negotiator acted on behalf of England and the
other acted on behalf of Zimbabwe. Each was given written material explaining the convention’s objective and their
own role in the negotiations, including political aspects and
the country’s goal in participating. Since our subjects were
unfamiliar with the economic issues and foreign affairs the
preferences were also specified. No information was given
regarding the other side’s preferences.
Five issues were defined: (a) The total amount to be deposited into the Tobacco Fund to aid countries seeking to
release themselves from economic dependency on tobacco
production, (b) The impact on other aid programs already
agreed upon, (c) Trade issues concerning Zimbabwe, (d)
Trade issues concerning England, and (e) Creation of a forum to explore comparable arrangements for other long-term
health issues. Each issue had 3 or 4 defined values, one of
which represented the status quo. Altogether, there were a
total of 432 possible agreements.
All the subjects playing the role of a country (England
or Zimbabwe) were given the same preferences in all experiments. The preferences presented to the negotiators can
be found in (Chalamish 2009). Since the preferences were
pre-defined and were exactly the same in all tests, there was
no need to repeat the first phase of WCP-network specification separately for each experiment. Instead, AutoMed
used the same WCP-networks representing the negotiators
we specified beforehand. Thus, the first phase in the negotiations, that of preference elicitation using WCP-networks,
was skipped and the negotiations actually began with AutoMed processing the WCP-networks and the mutual sending of messages monitored by AutoMed.
The negotiation lasted up to 14 time periods of 2 minutes
each. Upon termination of a time period a notification was
sent to both negotiators, but the negotiating process was not
interrupted. The exchanged messages were composed by
selecting values for the different issues from defined lists.
Each list included a ”not under discussion” value, which enabled the composition of a partial agreement. The negotiator
to which the proposal was sent could either except or reject
it.
The messages sent by AutoMed were sent simultaneously
to both negotiators and each was able to accept or reject
it. Issues agreed upon were accumulated to compose a full
agreement, which automatically invoked AutoMed to try
and upgrade it. Upon termination of the negotiations, the
negotiators were notified of the final agreement reached and
its monetary implications.
If no agreement was reached by the deadline - an undesir-
able situation for both England and Zimbabwe - the status
quo, representing the current situation of no signed treaty
and the continuance of Tobacco importing into the industrial countries, served as the agreement reached. If the time
limit was reached but the negotiators reached a partial agreement, it was valid with the assignment of the status quo values to the missing issues. Each party could also opt out of
the negotiations if it was not satisfied with its proceeding,
again, inflicting the status quo. The defined monetary implications of reaching the status quo and of opting out were
also specified for each negotiator, along with the monetary
influence of time passing. England gained money from each
time step she was still not supposed to support Zimbabwe,
while Zimbabwe naturally lost the amount of support. All
specific definitions are available in (Chalamish 2009).
Again, the negotiators were shown the interface and an
example of a full negotiation prior to the beginning of negotiations.
Methodology We had two sets of subjects, the first consisted of 21 pairs of negotiators and the second consisted of
20 pairs. All 82 subjects were students from the Exact Sciences faculty at Bar-Ilan University. The first group’s negotiations were mediated by AutoMed while the second group
served as a control group and no mediation was used. The
instructions and preference ordering given to both groups
were exactly the same.
The outcome of each simulation could be a full agreement, opting out - inflicting the status quo - or a partial
agreement completed by the status quo values due to reaching the time limit. After negotiations ended, both negotiators
were required to state their satisfaction level of the outcome
by stating a number between 1 and 10, where 1 represented
the lowest possible satisfaction level and 10 represented the
highest. The negotiators whose negotiations were mediated
were also asked whether they thought AutoMed helped find
the solution.
Results As mentioned before, both England and Zimbabwe preferred the negotiations to end with an agreement
over inflicting the status quo. Since negotiations were timelimited one of AutoMed’s goals was to conclude the dispute
as soon as possible. Table 1 summarizes the outcomes of the
negotiations as well as the average time period of its conclusion.
pairs
ended with full agr
ended by deadline
ended with opt out
avg time nego end
mediated nego
21
21
0
0
5.9
unmediated nego
20
15
3
2
8.55
Table 1: Outcomes and time of conclusion
All mediated negotiations ended with a full agreement
accepted by both sides. Only 75% of the unmediated negotiations was concluded with both sides agreeing fully.
Two unmediated negotiations ended with Zimbabwe opting
out, and three exceeded the time limit. We used the χ2
test on this data, and the results show that when AutoMed
was used, significantly more negotiations were concluded
with a full agreement compared to unmediated negotiations
(p < 0.025).
We used the 2-independent-sample Wilcoxon test to compare the final time period of negotiations with and without
AutoMed. Since 3 negotiations ended when the time limit
was reached, we calculated them as if they concluded in time
period 15. The test shows significance in this case as well,
i.e., negotiations mediated by AutoMed were concluded significantly faster than unmediated negotiations (p < 0.03).
Out of the 21 mediated negotiations, 7 were concluded by
both parties consenting to the offer made by AutoMed. Also,
an additional 10 negotiators claimed that AutoMed helped
them in finding the solution. That is, 24 of 42 negotiators
(57%) reported explicitly that AutoMed assisted them.
Table 2 reviews the average level of satisfaction provided
by the negotiators in the feedback. Avg total denotes the average satisfaction level stated by all the negotiators. Avg Eng
and avg Zim denote the average satisfaction level stated by
the negotiators playing the roles of England and Zimbabwe
separately.
avg total
avg Eng
avg Zim
mediated nego
7.3
7.9
6.71
unmediated nego
6.63
6.65
6.625
Table 2: Satisfaction level
We can see that in both total satisfaction level and in England’s satisfaction level, the average is much higher when using AutoMed. We can also see that where Zimbabwe’s satisfaction level is concerned, the average is slightly higher with
AutoMed. The higher satisfaction levels shown for England
can be easily explained by England’s favorable position in
the negotiations. In other words, England was the stronger
negotiator with less to lose and more to gain from a good solution than Zimbabwe. Furthermore, after dividing the level
of satisfaction into two groups, 1-6 and 7-10, and applying
the χ2 test, we found that AutoMed produced significantly
higher satisfaction levels as far as England’s role was concerned (p < 0.01).
Conclusions and Culture Related Future
Application
In this paper we have described the automated mediator
AutoMed. We have analyzed AutoMed’s performance by
conducting an experiment, with the participation of 82 people, to compare non-mediated negotiations with negotiations
mediated by the above specified version of AutoMed. The
results show a significantly shorter negotiation process in the
mediated ones. They also show that when AutoMed acts as
the mediator, significantly more negotiations are concluded
with a full agreement accepted by both sides and the satisfactory level is higher.
The interest in AutoMed for the cultural research field is
twofold. First, AutoMed can be used as a standard mediator in comparing between different styles of mediated negotiations in different cultures. For example, assuming the
same scenario is used whereby AutoMed serves as a mediator, the following questions can be answered: (1) what is
the impact of a mediator in these negotiations compared to
non-mediated negotiations? (2) are there differences in the
duration of mediated negotiations in the various cultures?
(3) is there a notable tendency to compromise or to opt out?
(4) are there differences in satisfactory levels? etc.
Following a study on culture differences, AutoMed can
be improved by taking these differences into consideration.
It would be beneficial to enhance AutoMed with a learning
module that, given a database of mediated negotiation sessions of a specific culture, AutoMed could adjust its behavior accordingly.
Currently, AutoMed acts as a formulating mediator. Designing a manipulative version of AutoMed can be used
for interesting studies on the impact of different mediation
styles on negotiation in different cultures.
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