Trust metric
Encyclopedia
In psychology
and sociology
, a trust metric is a measurement
of the degree to which one social actor (an individual or a group) trusts another social actor. Trust metrics may be abstracted in a manner that can be implemented on computer
s, making them of interest for the study and engineering of virtual communities, such as Friendster
and LiveJournal
.
Trust escapes a simple measurement for several reasons, be it its unclear definition, its complexity, subjectivity or the fact that it is a mental process, unavailable to instruments. There is a strong argumentation against the use of a simplistic metrics to measure trust that validly points to the complexity of the process and the embeddedness of trust that makes it impossible to capture trust in a clear form. For a detailed discussion about different trust metrics see.
There is no generally agreed set of properties that make a particular metric better than others, as each metric is designed to serve different purposes, e.g. provides certain classification scheme for trust metrics. Two groups of trust metrics can be identified:
Trust metrics enable trust modelling and reasoning about trust. They are closely related to reputation system
s. Simple forms of binary trust metrics can be found e.g. in PGP. The first commercial forms of trust metrics in computer software were in applications like eBay
's Feedback Rating. Slashdot
introduced its notion of karma, earned for activities perceived to promote group effectiveness, an approach that has been very influential in later virtual communities.
The willingness to cooperate and actual cooperation are commonly used as an evidence and a measure of trust. The actual value (level of trust, level of trustworthiness) is assessed from the difference between the observed behaviour and the theoretical behaviour that should have been observed in the absence of any cooperation.
The outcome of empirical measurements is essential to verify hypothesis, and it servers as the ultimate reference point in simulating human confidence in artificial environments.
One of the earliest surveys are McCroskey's scales that have been used to determine authoritativeness (competence) and character (trustworthiness) of speakers. Rempel's trust scale and Rotter's scale are quite popular in determining the level of interpersonal trust in different settings. The Organizational Trust Inventory (OTI) is an example of an exhaustive, theory-driven survey that can be used to determine the level of trust within the organisation.
For a particular research area a more specific survey can be developed. For example, the interdisciplinary model of trust, has been verified using a survey while uses a survey to establish the relationship between design elements of the web site and perceived trustworthiness of it.
Games of trust are designed in a way that their Nash equilibrium
differ from Pareto optimum so that no player alone can maximise his own utility by altering his selfish strategy without cooperation while cooperating partners can benefit. Trust can be therefore estimated on the basis of monetary gain attributable to cooperation.
The original 'game of trust' has been described in as an abstracted investment game between an investor and his broker. The game can be played once or several times, between randomly chosen players or in pairs that know each other, yielding different results.
Several variants of the game exist, focusing on different aspects of trust as the observable behaviour. For example, rules of the game can be reversed into what can be called a game of distrust, declaratory phase can be introduced or rules can be presented in a variety of ways, altering the perception of participants.
Other interesting games are e.g. binary-choice trust games, the gift-exchange game and various other forms of social games. Specifically the Prisoners Dilemma are popularly used to link trust with economic utility and demonstrate the rationality behind reciprocity. For multi-player games, different forms of close market simulations exist
or web of trust
). Consequently, they may provide weaker insight into the psychology of trust, or in particulars of empirical data collection. Formal metrics tend to have a strong foundations in algebra
, probability
or logic
.
There is also a disagreement about the semantics of some values. The disagreement regarding the attribution of values to levels of trust is specifically visible when it comes to the meaning of zero and to negative values. For example, zero may indicate either the lack of trust (but not distrust), or lack of information, or a deep distrust. Negative values, if allowed, usually indicate distrust, but there is a doubt whether distrust is simply trust with a negative sign, or a phenomenon of its own.
Subjective probability creates a valuable link between formalisation and empirical experimentation. Formally, subjective probability can benefit from available tools of probability and statistics. Empirically, subjective probability can be measured through one-side bets. Assuming that the potential gain is fixed, the amount that a person bets can be used to estimate his subjective probability of a transaction.
) has been introduced by Josang , on the basis of the Dempster-Shafer theory of evidence (e.g. ). This elegant concept combines probability distribution with uncertainty, so that each opinion about trust can be viewed as a distribution of probability distributions where each distribution is qualified by associated uncertainty. The foundation of the logic is the observation that the opinion (an evidence or a confidence) can be represented as a four-tuple (belief, disbelief, uncertainty, atomicity).
The logic for uncertain probabilities is an example of a metric of trust where uncertainty is inherently embedded in the calculation process and is visible at the output. It is not the only one, as is e.g. possible to use another quadruplet (trust, distrust, unknown, ignorance) to express the value of confidence, for as long as the appropriate operations are defined. Despite the sophistication of this representation, the particular value of a four-tuple related to trust can be easily derived from a series of binary opinions about a particular actor or event, thus providing a strong link between this formal metric and empirically observable behaviour.
Finally, there are CertainTrust and CertainLogic . Both share a common representation, which is compatible with subjective logic, but based on three independent parameters named 'average rating', 'certainty', and 'initial expectation'.
Application of fuzzy logic to trust has been studied in the context of peer to peer networks to improve peer rating. Also for grid computing it has been demonstrated that fuzzy logic allows to solve security issues in reliable and efficient manner.
The intuition behind transitivity follows everyday experience of 'friends of a friend' (FOAF
) , the one that is a foundation of social networks. However, the attempt to attribute exact formal semantics to transitivity reveals problems, related to the notion of a context. For example, defines conditions for the limited transitivity of trust, distinguishing between direct trust and referral trust. Similarly, shows that simple trust transitivity does not always hold, based on information on the Advogato
model and, consequently, have proposed new trust metrics.
The simple, holistic approach to transitivity is characteristic to social networks (FOAF
, Advogato
). It follows the everyday intuition and assumes that trust and trustworthiness apply to the whole person, i.e. regardless of the particular context. If one can be trusted as a friend, one can be also trusted as a recommender for another friend. Therefore transitivity is semantically valid without any constraints. and is a natural consequence of this approach.
The more thorough approach distinguishes between different contexts of trust, and does not allow for transitivity between contexts that are semantically incompatible or inappropriate. Contextual approach may e.g. distinguish between trust in particular competence, trust in honesty, trust in the ability to formulate the opinion, trust in the ability to consolidate other's opinions etc. Contextual approach is often used in trust-based service composition. The understanding that trust is contextual is a foundation of a collaborative filtering
.
The exact semantic of both operators are specific to the metric. Even within one representation, there is still a possibility for a variety of semantic. For example, for the representation as the logic for uncertain probabilities, operations can be interpreted by applying different rules (Yager's modified Dempster's rule, Inagaki's unified combination role, Zhang's centre combination rule, Dubois and Prade's disjunctive consensus rule etc.). Each interpretations leads to different results, depending whether uncertainty is maximised, evenly distributed, minimised and whether conflicts of opinions are excluded or included in calculations. See for a detailed discussion.
The free software
developer resource Advogato
is based on a novel approach to attack-resistant trust metrics of Raph Levien
. Levien observed that Google
's PageRank
algorithm can be understood to be an attack resistant trust metric rather similar to that behind Advogato.
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
and sociology
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...
, a trust metric is a measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
of the degree to which one social actor (an individual or a group) trusts another social actor. Trust metrics may be abstracted in a manner that can be implemented on computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
s, making them of interest for the study and engineering of virtual communities, such as Friendster
Friendster
Friendster is a social gaming site that is based in Malaysia, KL. The company now operates mainly from the three Asian countries namely in the Philippines, Malaysia and Singapore....
and LiveJournal
LiveJournal
LiveJournal is a virtual community where Internet users can keep a blog, journal or diary. LiveJournal is also the name of the free and open source server software that was designed to run the LiveJournal virtual community....
.
Trust escapes a simple measurement for several reasons, be it its unclear definition, its complexity, subjectivity or the fact that it is a mental process, unavailable to instruments. There is a strong argumentation against the use of a simplistic metrics to measure trust that validly points to the complexity of the process and the embeddedness of trust that makes it impossible to capture trust in a clear form. For a detailed discussion about different trust metrics see.
There is no generally agreed set of properties that make a particular metric better than others, as each metric is designed to serve different purposes, e.g. provides certain classification scheme for trust metrics. Two groups of trust metrics can be identified:
- Empirical metrics focusing on supporting the capture of values of trust in a reliable and standardised way
- Formal metrics that focus on formalisation leading to the ease of manipulation, processing and reasoning about trust; formal metrics can be further classified depending on their properties.
Trust metrics enable trust modelling and reasoning about trust. They are closely related to reputation system
Reputation system
A reputation system computes and publishes reputation scores for a set of objects within a community or domain, based on a collection of opinions that other entities hold about the objects...
s. Simple forms of binary trust metrics can be found e.g. in PGP. The first commercial forms of trust metrics in computer software were in applications like eBay
EBay
eBay Inc. is an American internet consumer-to-consumer corporation that manages eBay.com, an online auction and shopping website in which people and businesses buy and sell a broad variety of goods and services worldwide...
's Feedback Rating. Slashdot
Slashdot
Slashdot is a technology-related news website owned by Geeknet, Inc. The site, which bills itself as "News for Nerds. Stuff that Matters", features user-submitted and ‑evaluated current affairs news stories about science- and technology-related topics. Each story has a comments section...
introduced its notion of karma, earned for activities perceived to promote group effectiveness, an approach that has been very influential in later virtual communities.
Empirical metrics
Empirical metrics capture the value of trust by exploring the behaviour or introspection of people, to determine the perceived or expressed level of trust. Those methods combine theoretical background (that determines what it is that they measure) with defined set of questions and statistical processing of results.The willingness to cooperate and actual cooperation are commonly used as an evidence and a measure of trust. The actual value (level of trust, level of trustworthiness) is assessed from the difference between the observed behaviour and the theoretical behaviour that should have been observed in the absence of any cooperation.
The outcome of empirical measurements is essential to verify hypothesis, and it servers as the ultimate reference point in simulating human confidence in artificial environments.
Surveys
Surveys capture the level of trust by means of both observations or introspection, but without engaging into any experiments. Respondents are usually providing answers to a set of questions or statements and responses are e.g. structured according to a Liker scale. Differentiating factors are the underlying theoretical background and contextual relevance.One of the earliest surveys are McCroskey's scales that have been used to determine authoritativeness (competence) and character (trustworthiness) of speakers. Rempel's trust scale and Rotter's scale are quite popular in determining the level of interpersonal trust in different settings. The Organizational Trust Inventory (OTI) is an example of an exhaustive, theory-driven survey that can be used to determine the level of trust within the organisation.
For a particular research area a more specific survey can be developed. For example, the interdisciplinary model of trust, has been verified using a survey while uses a survey to establish the relationship between design elements of the web site and perceived trustworthiness of it.
Games
Another method to empirically measure trust is to engage participants in an experiments and to treat the outcome of such experiment as estimate of trust. Several economical games and game-like scenarios have been tried, with certain preferences to those that allow to estimate confidence in monetary terms (see for an interesting overview).Games of trust are designed in a way that their Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
differ from Pareto optimum so that no player alone can maximise his own utility by altering his selfish strategy without cooperation while cooperating partners can benefit. Trust can be therefore estimated on the basis of monetary gain attributable to cooperation.
The original 'game of trust' has been described in as an abstracted investment game between an investor and his broker. The game can be played once or several times, between randomly chosen players or in pairs that know each other, yielding different results.
Several variants of the game exist, focusing on different aspects of trust as the observable behaviour. For example, rules of the game can be reversed into what can be called a game of distrust, declaratory phase can be introduced or rules can be presented in a variety of ways, altering the perception of participants.
Other interesting games are e.g. binary-choice trust games, the gift-exchange game and various other forms of social games. Specifically the Prisoners Dilemma are popularly used to link trust with economic utility and demonstrate the rationality behind reciprocity. For multi-player games, different forms of close market simulations exist
Formal metrics
Formal metrics focus on facilitating trust modelling, specifically for large scale models that represent trust as an abstract system (e.g. social networkSocial network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...
or web of trust
Web of trust
In cryptography, a web of trust is a concept used in PGP, GnuPG, and other OpenPGP-compatible systems to establish the authenticity of the binding between a public key and its owner. Its decentralized trust model is an alternative to the centralized trust model of a public key infrastructure ,...
). Consequently, they may provide weaker insight into the psychology of trust, or in particulars of empirical data collection. Formal metrics tend to have a strong foundations in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
or logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
.
Representation
There is no widely recognised way to attribute value to the level of trust, with each representation of a 'trust value' claiming certain advantages and disadvantages. There are systems that assume only binary values, that use fixed scale, where confidence range from -100 to +100 (while excluding zero), from 0 to 1 or from [-1 to +1); where confidence is discrete or continuous, one-dimensional or have many dimensions. Some metrics use ordered set of values without attempting to convert them to any particular numerical range (e.g. See for a detailed overview.There is also a disagreement about the semantics of some values. The disagreement regarding the attribution of values to levels of trust is specifically visible when it comes to the meaning of zero and to negative values. For example, zero may indicate either the lack of trust (but not distrust), or lack of information, or a deep distrust. Negative values, if allowed, usually indicate distrust, but there is a doubt whether distrust is simply trust with a negative sign, or a phenomenon of its own.
Subjective probability
Subjective probability focuses on trustor's self-assessment about his trust in the trustee. Such an assessment can be framed as an anticipation regarding future behaviour of the trustee, and expressed in terms of probability. Such a probability is subjective as it is specific to the given trustor, his assessment of the situation, information available to him etc. In the same situation other trustors may have a different level of a subjective probability.Subjective probability creates a valuable link between formalisation and empirical experimentation. Formally, subjective probability can benefit from available tools of probability and statistics. Empirically, subjective probability can be measured through one-side bets. Assuming that the potential gain is fixed, the amount that a person bets can be used to estimate his subjective probability of a transaction.
Uncertain probabilities (subjective logic)
The logic for uncertain probabilities (subjective logicSubjective logic
Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and belief ownership into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and incomplete knowledge...
) has been introduced by Josang , on the basis of the Dempster-Shafer theory of evidence (e.g. ). This elegant concept combines probability distribution with uncertainty, so that each opinion about trust can be viewed as a distribution of probability distributions where each distribution is qualified by associated uncertainty. The foundation of the logic is the observation that the opinion (an evidence or a confidence) can be represented as a four-tuple (belief, disbelief, uncertainty, atomicity).
The logic for uncertain probabilities is an example of a metric of trust where uncertainty is inherently embedded in the calculation process and is visible at the output. It is not the only one, as is e.g. possible to use another quadruplet (trust, distrust, unknown, ignorance) to express the value of confidence, for as long as the appropriate operations are defined. Despite the sophistication of this representation, the particular value of a four-tuple related to trust can be easily derived from a series of binary opinions about a particular actor or event, thus providing a strong link between this formal metric and empirically observable behaviour.
Finally, there are CertainTrust and CertainLogic . Both share a common representation, which is compatible with subjective logic, but based on three independent parameters named 'average rating', 'certainty', and 'initial expectation'.
Fuzzy logic
Fuzzy systems ( ), as a trust metrics can link natural language expressions with a meaningful numerical analysis.Application of fuzzy logic to trust has been studied in the context of peer to peer networks to improve peer rating. Also for grid computing it has been demonstrated that fuzzy logic allows to solve security issues in reliable and efficient manner.
Properties of trust metrics
The set of properties that should be satisfied by the trust metric vary, depending on the application area. Following is the list of typical properties of the formal metric.Transitivity
Transitivity is a highly desired property of a trust metric. In situations where A trusts B and B trusts C, transitivity determines if, what and how much A should trust C. Without transitivity, trust metrics are unlikely to be used to reason about trust in more complex relationships.The intuition behind transitivity follows everyday experience of 'friends of a friend' (FOAF
FOAF (software)
FOAF is a machine-readable ontology describing persons, their activities and their relations to other people and objects. Anyone can use FOAF to describe him or herself...
) , the one that is a foundation of social networks. However, the attempt to attribute exact formal semantics to transitivity reveals problems, related to the notion of a context. For example, defines conditions for the limited transitivity of trust, distinguishing between direct trust and referral trust. Similarly, shows that simple trust transitivity does not always hold, based on information on the Advogato
Advogato
Advogato is an online community and social networking site dedicated to free software development, and was created by Raph Levien. It describes itself as "the free software developer's advocate." Advogato was an early pioneer of blogs, formerly known as "online diaries", and one of the earliest...
model and, consequently, have proposed new trust metrics.
The simple, holistic approach to transitivity is characteristic to social networks (FOAF
FOAF (software)
FOAF is a machine-readable ontology describing persons, their activities and their relations to other people and objects. Anyone can use FOAF to describe him or herself...
, Advogato
Advogato
Advogato is an online community and social networking site dedicated to free software development, and was created by Raph Levien. It describes itself as "the free software developer's advocate." Advogato was an early pioneer of blogs, formerly known as "online diaries", and one of the earliest...
). It follows the everyday intuition and assumes that trust and trustworthiness apply to the whole person, i.e. regardless of the particular context. If one can be trusted as a friend, one can be also trusted as a recommender for another friend. Therefore transitivity is semantically valid without any constraints. and is a natural consequence of this approach.
The more thorough approach distinguishes between different contexts of trust, and does not allow for transitivity between contexts that are semantically incompatible or inappropriate. Contextual approach may e.g. distinguish between trust in particular competence, trust in honesty, trust in the ability to formulate the opinion, trust in the ability to consolidate other's opinions etc. Contextual approach is often used in trust-based service composition. The understanding that trust is contextual is a foundation of a collaborative filtering
Collaborative filtering
Collaborative filtering is the process of filtering for information or patterns using techniques involving collaboration among multiple agents, viewpoints, data sources, etc. Applications of collaborative filtering typically involve very large data sets...
.
Operations
For the formal metric to be useful, it should define a set of operations over values of trust in such way that the result of those operations produce values of trust. Usually at least two elementary operators are considered:- fusion that provides a quasi-additive functionality, allowing to consolidate trust values coming from several sources;
- discount that provide a quasi-multiplicative functionality, discounting one trust by another one.
The exact semantic of both operators are specific to the metric. Even within one representation, there is still a possibility for a variety of semantic. For example, for the representation as the logic for uncertain probabilities, operations can be interpreted by applying different rules (Yager's modified Dempster's rule, Inagaki's unified combination role, Zhang's centre combination rule, Dubois and Prade's disjunctive consensus rule etc.). Each interpretations leads to different results, depending whether uncertainty is maximised, evenly distributed, minimised and whether conflicts of opinions are excluded or included in calculations. See for a detailed discussion.
Scalability
The growing size of networks of trust make scalability another desired property, meaning that it is computationally feasible to calculate the metric for large networks. Scalability usually puts two requirements of the metric:- The elementary operation (e.g. fusion or discount) is computationally feasible, e.g. that relationships between context of trust can be quickly established.
- The number of elementary operations scale slowly with the growth of the network.
Attack resistance
Attack resistance is an important non-functional property of trust metrics which reflects their ability not to be overly influenced by agents who try to manipulate the trust metric and who participate in bad faith (i.e. who aim to abuse the presumption of trust).The free software
Free software
Free software, software libre or libre software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions that only ensure that further recipients can also do...
developer resource Advogato
Advogato
Advogato is an online community and social networking site dedicated to free software development, and was created by Raph Levien. It describes itself as "the free software developer's advocate." Advogato was an early pioneer of blogs, formerly known as "online diaries", and one of the earliest...
is based on a novel approach to attack-resistant trust metrics of Raph Levien
Raph Levien
Raphael Levien is an influential member of the free software developer community, through his creation of the Advogato virtual community and his work with the free software branch of Ghostscript. He is currently employed by Google...
. Levien observed that Google
Google
Google Inc. is an American multinational public corporation invested in Internet search, cloud computing, and advertising technologies. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program...
's PageRank
PageRank
PageRank is a link analysis algorithm, named after Larry Page and used by the Google Internet search engine, that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set...
algorithm can be understood to be an attack resistant trust metric rather similar to that behind Advogato.
See also
- Trust (sociology)Trust (sociology)In a social context, trust has several connotations. Definitions of trust typically refer to a situation characterised by the following aspects: One party is willing to rely on the actions of another party ; the situation is directed to the future. In addition, the trustor abandons control over...
- TrustworthinessTrustworthinessTrustworthiness is a moral value considered to be a virtue. A trustworthy person is someone in whom you can place your trust and rest assured that the trust will not be betrayed. A person can prove their trustworthiness by fulfilling an assigned responsibility - and as an extension of that, not to...
- Web of trustWeb of trustIn cryptography, a web of trust is a concept used in PGP, GnuPG, and other OpenPGP-compatible systems to establish the authenticity of the binding between a public key and its owner. Its decentralized trust model is an alternative to the centralized trust model of a public key infrastructure ,...
- Subjective logicSubjective logicSubjective logic is a type of probabilistic logic that explicitly takes uncertainty and belief ownership into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and incomplete knowledge...
- Moderation systemModeration systemOn Internet websites which invite users to post comments, a moderation system is the method the webmaster chooses to sort contributions which are irrelevant, obscene, illegal, or insulting with regards to useful or informative contributions....
External links
- Trust Metrics Evaluation Project of Paolo Massa ] is a Wiki whose goal is to review, understand, code and compare on same data all the trust metrics proposed so far.. The Analyzed Trust Metrics page provides an extensive bibliography of work on the theory and implementation of trust metrics.
- Trustcomp.org is an online community of more than 150 academic and industrial members who research computational trust management and online reputation. There is also a mailing list.
- Online demonstrations of subjective logic.
- Raph LevienRaph LevienRaphael Levien is an influential member of the free software developer community, through his creation of the Advogato virtual community and his work with the free software branch of Ghostscript. He is currently employed by Google...
, 2000. Advogato's trust metric. Electronic manuscript. - Raph LevienRaph LevienRaphael Levien is an influential member of the free software developer community, through his creation of the Advogato virtual community and his work with the free software branch of Ghostscript. He is currently employed by Google...
, 2002. Attack Resistant Trust Metric Metadata HOWTO. Electronic manuscript. - Trust Metrics - by P2P Foundation
- Rummble - Recommendations engine based on trust networking, including a Trust Network API for 3rd parties