L. Seabra Lopes et al. (Eds.): EPIA 2009, LNAI 5816, pp. 520–531, 2009.
© Springer-Verlag Berlin Heidelberg 2009
Computing Confidence Values: Does Trust Dynamics
Matter?
Joana Urbano, Ana Paula Rocha, and Eugénio Oliveira
Faculdade de Engenharia da Universidade do Porto
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
{joana.urbano,arocha,eco}@fe.up.pt
Abstract. Computational Trust and Reputation (CTR) systems are platforms
capable of collecting trust information about candidate partners and of comput-
ing confidence scores for each one of these partners. These systems start to be
viewed as vital elements in environments of electronic institutions, as they sup-
port fundamental decision making processes, such as the selection of business
partners and the automatic and adaptive creation of contractual terms and asso-
ciated enforcement methodologies. In this article, we propose a model for the
aggregation of trust evidences that computes confidence scores taking into
account dynamic properties of trust. We compare our model with a traditional
statistical model that uses weighted means to compute trust, and show experi-
mental results that show that in certain scenarios the consideration of the trust
dynamics allows for a better estimation of confidence scores.
1 Introduction
Computational Trust and Reputation (CTR) systems are systems capable of collecting
trust information about candidate partners and of computing confidence scores for
each one of these partners. In this document, we envision trust as the confidence that
the trustier agent has on the capabilities and the willingness of a candidate partner
(trustee) in fulfilling its assigned tasks, in conformance to a given associated Service
Level Agreement (SLA). CTR systems can be centralized, as adequate to electronic
institutions and virtual organizations (VO), or decentralized, as adequate to extremely
open environments where agents can enter and leave the society at any time.
Although practical examples of CTR systems do already exist (e.g. in e-commerce
sites of eBay.com, Amazon.com, and Epinions.com
1
), there are still many open ques-
tions in this research area. In fact, current work on trust and reputation has diversified
in multiple subfields. In the theoretical domain, there is important work on trust and
reputation as elements of social intelligence. Conte (2002) addresses the theoretical
issues related to reputation and image in artificial societies and social simulation [1],
and this cognitive model of reputation was recently extended in order to more thor-
oughly address the transmission of reputation [2]. In a more practical sense, a great
deal of research effort is being put in the representation and aggregation of social
1
http://ebay.com; http://www.amazon.com; http://www.epinions.com
Computing Confidence Values: Does Trust Dynamics Matter? 521
evaluations into trust and/or reputation scores, which would serve as input to partner
selection in electronic business scenarios. These models range from arithmetic means
and weighted means ([3] [4] [5]), to Beta ([6]) and Dirichlet distributions ([7]),
Bayesian approaches ([8] [9]), and trust learning approaches ([10] [11] [12]). Some of
these models are implemented using cognitive based beliefs, desires and intentions
(BDI) architectures ([5] [13]). A new trend of investigation in this area is the explora-
tion of the business context to improve the decision making, raising significantly the
number and type of information that the evaluator has in order to compute trust. How-
ever, few proposals have been made in this specific area ([14]).
Another area of little research work is the consideration of the dynamics of trust in
the computation of confidence scores. Our hypothesis is that the use of an aggregation
engine that encompasses the past experiences of the trustee agent and that accounts
for fundamental dynamics of trust could allow for a better estimation of the trustee
trustworthiness than probabilistic and statistical approaches that exist in the literature.
Due to the relevance of this issue on our work, we dedicate the next section to the
presentation of relevant dynamics of trust.
The remaining of this paper is structured as follows. In section 2, we present Si-
nAlpha, a non-statistical aggregation engine that uses an S-shape curve to compute
trust scores, taking into account three properties of trust dynamics: the asymmetry, the
distinguishability of past evidences and the consideration of distinct maturity phases
on the behaviour of target agents. Section 3 presents the experimental phase of our
work. It introduces STexVM, a simulated virtual textile marketplace that we have
developed in agent technology in order to evaluate the SinAlpha model and to com-
pare it with other strategies. Then it proceeds with the presentation of the results of
our experiments and with the analysis of these results. Section 4 presents the conclud-
ing remarks and future work.
1.1 The Dynamics of Trust
The evolution of trust over time was baptized by Elofson in 1997 [15] as the dynamics
of trust, and was addressed one year later by Castelfranchi and Falcone [16]. An in-
teresting formalization of the dynamics of trust is presented by Jonker and Treur in
1999 [17], who defend the need for a continuous verification and validation in the
trust building process, and define six different types of trust dynamics:
− Blindly positive: the agent is unconditionally trusted or after a certain number or
sequence of positive trust experiences (i.e. evaluated events) the agent reaches the
state of unconditional trust and stays there for good;
− Blindly negative: the agent is unconditionally distrusted or after a certain number
or sequence of negative trust experiences the agent reaches the state of uncondi-
tional distrust and stays there for good;
− Slow positive, fast negative: it takes a lot of trust-positive experiences to gain trust
and it takes only a few trust-negative experiences to lose trust;
− Balanced slow: trust moves in slow dynamics in both positive and negative sense;
− Balanced fast: trust moves in fast dynamics in both positive and negative sense;
− Slow negative, fast positive: it takes a lot of trust-negative experiences to lose trust
and it takes only a few trust-positive experiences to gain trust.
522 J. Urbano, A.P. Rocha, and E. Oliveira
The authors also suggest that the dynamics of trust can be formalized through trust
evolution functions (mathematical functions that relate sequences of experiences to
trust representation) or through trust update functions (mathematical functions that
relate a current trust representation and a current experience to the next trust represen-
tation). They formally define both functions and provide a set of interesting properties
that can be associated to each one of the functions. Although this work is based on
simple assumptions such as past direct experiences and binary evaluated events, it
provides important considerations that shall be taken into account when designing an
aggregation engine. Also, the slow positive, fast negative type of trust dynamics re-
sponds to the common sense idea that trust shall grow slower and decline faster, as
interestingly put in the famous words of the English poet Alexander Pope: ‘At every
word a reputation dies’. At this respect, Marsh [18] also strongly suggested to penal-
ize deceit behaviour stronger than to award the cooperative ones, as in the real world
it is easier to loose, than to gain trust.
Melaye and Demazeau (2005) [19] further explore the dynamics of trust, proposing
a Bayesian trust formalism based on Castelfranchi and Falcone’s cognitive model.
They use a Kalman filter to address two dimensions of the trust dynamics: the asym-
metric increase/decrease of trust and the inherent speed of switching from trust to
distrust and vice versa, which they name inertia; and the erosion of trust that happens
due to the absence of new observations. In their model, the outcome of an execution is
statistically dependent of previous executions, supporting, therefore, the mentioned
trust dynamics. The introduction of the erosion dimension is of particular interest, as
current trust and reputation systems tend to omit this characteristic, particularly those
whose aggregation engine is based on statistical operations. However, the proposed
Bayesian presents some drawbacks. In one hand, the model seems not to be scalable
in the case of several beliefs and several source beliefs, and the authors assume statis-
tical independence between each one of the belief and source beliefs’ levels. Also, as
the authors indicate, the inertia of trust and distrust is fixed a priori by a specialist,
requiring one instance of the model per context. Finally, the proposed model seems to
be too sensitive in relation to single occurrences of deceptive behaviour. In fact, in
one experiment described in [19], a single negative observation that happens after a
high number of previously observed positive experiences makes the trust level to
decrease sharply, after which it takes a long sequence of positive observations to
getting back to the previously trust value. In our opinion, this strong penalization does
not reflect the real world response to one exceptional bad result of a previously trust-
able partner.
2 The SinAlpha Aggregation Engine
As already mentioned, we are interested in designing and implementing mechanisms
that allow for an expressive representation of the dynamics of trust, when aggregating
trust evidences. Particularly, we are interested in the asymmetry property, that stipu-
lates that trust is hard to gain and easy to lose; in the maturity phase of targets prop-
erty, where the slope of growth can be different in different stages of the partner
trustworthiness; and in the distinguishability property of past behaviour. The sigmoid
curve represented in Figure 1 presents interesting characteristics that seem to fit the
Computing Confidence Values: Does Trust Dynamics Matter? 523
desideratum well. For simplicity, we assume that the available information about a
candidate partner is given by a central trust authority (e.g. a CTR service that serves
the VO), and that it takes the form of binary values, either representing past success-
ful (1) or violated (0) contracts by the partner.
2
0,00
0,20
0,40
0,60
0,80
1,00
1,20
(3π/2) (0) (5π
/
2)
Sigmoid
SinAlpha
Fig. 1. Two S-shape curves, one exponential (Sigmoid) and one trigonometric (SinAlpha)
The constructing of trust for this partner using the sigmoid curve implies a slow
growth upon positive results when the partner is not yet trustable, it accelerates when
it is acquiring confidence, and finally slows down when the partner is considered
trustable (i.e., in the top right third of the curve). The decrease movement upon nega-
tive results follows the same logic. However, we intuitively feel by graphically ana-
lysing the curve that it permits a probably too soft penalisation of partners that proved
to be trustable but that failed the last n contracts. Therefore, we lightly soften the
slope of the sigmoid shape at the top and bottom thirds of the curve, by using instead
the trigonometric formula presented in (1) and depicted in Figure 1, with the name of
SinAlpha.
y(α) = δ.sin α + δ, α
0
= 3π/2 ,
α = α + λ.ω .
(1)
In the formula above, δ is a constant value of 0.5, and α ranges from 3π/2 to 5π/2,
allowing for aggregated trust scores within the range [0, 1]. The incremental step of α
is also shown in (1); ω represents the pace of trust growth (we assume the value of π/2
in our experiments), and λ is the parameter of the incremental step that allows to
differentiate between positive and negative results (in our experiments, λ equals +1
for each positive result to be aggregated, and -1.5 for each violated contract). This
way, in each one of the three stages of trust construction, trust grows slower and de-
creases faster. At this point, we must remind our interest in studying how a curve like
the one we propose, which, in a certain way, ‘encompasses’ the historical behaviour
2
We use these two assumptions in our experiments, although our proposed aggregation engine
might be extended in the future to more complex and diversified representation of trust infor-
mation. In the same way, the aggregation engine might be used in decentralized systems, to
aggregate information from distinct sources of information (e.g. reputation and image).
524 J. Urbano, A.P. Rocha, and E. Oliveira
of the partner under evaluation, is able to catch the dynamics of trust in the presence
of certain partners’ patterns of behaviour. We are also willing to know how this model
can be compared with the common statistical approach that aggregates trust informa-
tion using weighted means.
3 Experiments
3.1 The STexVM System
In order to run our experiments, we developed the STexVM system. This is a simu-
lated virtual marketplace for trading textile goods that aims to ensure reliable transac-
tions, in a sense that it is able to detect business partners that in some moment start
behaving in a defective way. The simulated environment is based on existent online
virtual marketplaces where buyers and sellers in the textile and fashion industry can
post buying and selling leads (e.g. the Fibre2Fashion marketplace
3
). It follows the
multi-agent paradigm, and is implemented over Jade platform, using the standard
behaviours of Jade and FIPA performatives and interaction protocols
4
. The key agents
in this environment have the roles either of buyers or suppliers (Figure 2).
At each round, a buyer issues a call for proposal (cfp) stipulating a specific good
and associated quantity that needs to be provided, and each candidate partner re-
sponds indicating the quantity it is able to provide in the present business opportunity,
or refusing the offer. A contract-net like negotiation occurs, and the buyer selects a
number n > 0 of partners that optimizes the expected utility E(u), using equation (2).
E(u) = arg max
i
for each i Σ
j
util
j
* trust
j
.
(2)
In the equation above, i stands for the possible combinations of suppliers’ proposals
that fit the quantity specified in the current cfp, not exceeding it; j represents the sup-
pliers considered in each of these combinations, and trust
j
is the confidence score
computed for supplier j at selection time. Finally, util
j
is the quantity proposed by
each supplier j in the round, normalized by the quantity specified in the cfp, i.e.,
quant
j
/Quant. In our system, a buyer can accept less quantity than the maximum
quantity (Quant) defined in the cfp, but it cannot exceed Quant. Also, a buyer cannot
accept partial quantities of the received bids.
Each supplier that enters the simulated virtual marketplace sells two different types
of fabric (e.g. cotton and chiffon). These and their associated quantities (e.g. 180,000
meters) are randomly assigned at creation time. Buyers are characterized by the good
and quantity they need to purchase, also randomly picked up at creation time. The
remaining agents of the STexVM system are the Agent Simulation Manager, who
manages the configuration parameters related with buyers and suppliers; the Agent
DF, which registers competences of buyers and suppliers; and the Agent CTR, which
gathers information about the performance of suppliers and computes their confidence
scores on-demand, when requested by the buyers. Figure 2 illustrates the relation
between these agents.
3
http://fibre2fashion.com/
4
Jade: http://jade.tilab.com/; FIPA: http://www.fipa.org/
