Method and system for ascribing a reputation to an entity as a rater of other entities6895385Abstract A method and system for ascribing a reputation of an entity as a rater of other entities is provided. A first rating indicative of a rating of a rated entity by the first entity, and one or more second ratings, each second rating indicative of a rating of the rated entity provided by another entity, are provided. The second ratings are combined to produce a first combined rating. The first rating is compared to the first combined rating to produce a first rating predictability of the first rating, the first rating predictability being a negative function of a magnitude of a difference between the first rating and the first combined rating. A resulting rater reputation is generated based at least in part on the first rating predictability. Claims 1. A method of determining a rater reputation of a first entity as a rater of other entities, wherein provided is a first rating indicative of a rating of a rated entity by the first entity, and one or more second ratings, each second rating indicative of a rating of the rated entity provided by another entity, the method comprising computer-implemented acts of: Description BACKGROUND OF THE INVENTION
Zacharia discloses that the damping function may be calculated by applying the following equation: ##EQU2##
(Throughout this application, if a value represented by a symbol from a current equation was described in connection with a previously-described equation, the description of the value will not be repeated for the current equation.) The Sporas technique implements an entity reputation mechanism based on the following principles. First, new entities start with a minimum reputation value, and build-up their reputations as a result of their activities on the system. For example, if a reputation mechanism has a rating range from 1 to 100, then an entity may start with an initial reputation value, R0, of 1. By starting with the minimum reputation value, Sporas reduces the incentive to, and effectively eliminates, that ability of an entity with a low reputation to improve the entity's reputation by reentering the system as a new anonymous identity. Second, the reputation of an entity never falls below the reputation of a new entity. This may be ensured by applying equation 1 above. This second principle also reduces the incentive, and effectively prevents, an entity with a low reputation from reentering the system as a new anonymous entity. Third, after each electronic exchange, the reputations of each of the two or more entities involved are updated according to the feedback or ratings provided by the other entities, where the feedback or ratings represent the demonstrated trustworthiness of the two or more entities in the latest exchange. For example, referring to Equation 1 above, the ratee reputation Ri of an entity is updated for each new rating, Wi. Fourth, two entities may rate each other only once. If two entities exchange more than once, then, for each entity, the reputation mechanism only applies the most recently submitted rating to determine the reputation of the rated entity. This fourth principle prevents two or more entities from fraudulently inflating their reputations, as describe above, by frequently rating each other with artificially-high ratings. Fifth, entities with very high reputation values experience smaller rating changes after each update. This fifth principle is implemented by the damping function, damp(Ri-1), of Equations 1 and 2 above. The damping function increases as the ratee reputation of the rated entity decreases, and decreases as the ratee reputation of the rated entity increases. Thus, a high reputation is less susceptible to change by a single poor rating provided by another entity. Sixth, the reputation mechanism adapts to changes in an entity's behavior. For example, a reputation may be discounted over time so that the most recent ratings of an entity have more weight in determining the ratee reputation of the entity. For example, in Equation 1, above, ratings are discounted over time by limiting the effective number of ratings considered, C. The Sporas reputation mechanism also weights the reputation of a rated entity according to the reputation, Rother, of another entity providing the rating, where this reputation of the other entity may be determined by applying Equation 1. Therefore, ratings from entities having relatively higher reputations have more of an impact on the reputation of the rated entity than ratings from entities having relatively lower reputations. As described in the Zacharia thesis, Histos is a reputation mechanism better-suited for a highly-connected community, where entities have provided ratings for a significant number of the other entities. Histos determines a personalized reputation of a first entity from a perspective of a particular entity. Histos represents the principle that a person or entity is more likely to trust the opinion of another person or entity with whom she is familiar than trust the opinion of another person or entity who she does not know. Unlike Sporas, a reputation of first entity in Histos depends on the second entity from whose perspective the determination is made, and other ratings of the second entity provided by other users in an on-line community or population. FIG. 1 is a block diagram illustrating a representation of an on-line community or population 300 of entities A1-A11 interconnected by several rating links, including rating links 302, 303, 304, 306, 308 and 310. Each rating link indicates a rating of a rated entity (i.e., a ratee) by a rating entity (i.e., a rater) with an arrowhead pointing from the rating entity to the rated entity. As used herein, a ratee is an entity in a position of being rated by one or more other entities, and a rater is an entity in a position of rating one or more other entities. For example, rating link 302 represents a rating of 0.8 for ratee A3 by rater A1, and rating link 303 represents a rating of 0.9 for ratee A1 by rater A3. Although in FIG. 1, each rating link only indicates a single rating, it is possible that an entity has provided more than one rating for another entity. The Zacharia reference discloses that if entity has provided more than rating for another entity, the most recent rating should be selected to determine a personalized reputation of a first entity from the perspective of a second entity. To determine a personalized reputation of a first entity from the perspective of a second entity, the first and second entity must be "connected". A first and second entity are connected if a rating path connects the first and second entity. A rating path is a series of rating links that connect a first entity to a second entity. For example, in FIG. 1, entities A1 and A11 are connected by several rating paths, including rating paths 312 and 314. Rating path 312 includes rating links 302, 304 and 310, and rating path 314 includes rating links 302, 306 and 308. As described in the Zacharia thesis, and referring to FIG. 1, to determine a personalized reputation of a first user from the perspective of a second user, the following methodology may be applied. First, a breadth-first search algorithm is applied to find all of the rating paths connecting A1 to A11 that are of a length less than or equal to a specified value. If a rating link indicates more than one rating, then the most recent rating is selected for the determination of the personalized reputation. The number of rating links included in a rating path is referred to herein as the "length" of the rating path. For example, the rating path 312 has a length=3 because it includes three rating links 302, 304 and 310. Further, an entity included along a rating path between the first rated entity and the second rating entity has a "level" equal to a number of links between the entity and the second entity. For example, in FIG. 1, the entity A8 is disposed along the rating path 314. The entity A8 has a level 2 in the context of the rating path 314 because two rating links 302 and 306 lie between the entity A8 and the second entity A1. Further, an entity having a level, L, may be said to be a distance L away from the second entity. Accordingly, the personalized reputation of a first entity from the perspective of a second entity may be determined by application of the following equation: ##EQU4##
Referring to FIG. 1, the following example illustrates applying Equation 4 to determine the personalized ratee reputation of entity A11 from the perspective of entity A1, where D=1. ##EQU5## where ##EQU6## and where ##EQU7## such that ##EQU8## SUMMARY OF THE INVENTION The Sporas reputation mechanism described in the Zacharia thesis uses a single reputation value to represent the reputation of an entity both as a ratee and a rater. This single reputation represents the reputation of an entity as a combination of ratings provided by other entities, but does not provide an indication of the reputation or trustworthiness of an entity as a rater of other entities. Thus, an entity may receive high ratings from other entities and thus have a high single-valued reputation, although the entity is a poor rater of other entities and thus should not truly have a high reputation as a rater of other entities. As used herein, a "rater reputation" of an entity is a reputation or trustworthiness of the entity as a rater of one or more other entities, and a "ratee reputation" of an entity is the reputation of the entity according to the ratings of the entity provided by one or more other entities. Therefore, Sporas does not provide a method or system for determining and maintaining a rater reputation of an entity. Accordingly, provided herein is a method and system for determining a rater reputation of an entity. Further, provided is a method and system for determining a ratee reputation of an entity based at least in part on the rater reputations of one or more of the entities that have rated the rated entity. In one embodiment, a rater reputation of a first entity as a rater of other entities is determined. A first rating indicative of a rating of a rated entity by the first entity, and one or more second ratings, each second rating indicative of a rating of the rated entity provided by another entity, are provided. The second ratings are combined to produce a first combined rating. The first rating is compared to the first combined rating to produce a first rating predictability of the first rating, the first rating predictability being a negative function of a magnitude of a difference between the first rating and the first combined rating. A resulting rater reputation is generated based at least in part on the first rating predictability. This embodiment may be implemented as a computer program product that includes a computer readable medium and computer readable signals stored on the computer readable medium that define instructions. These instructions, as a result of being executed by a computer, instruct the computer to perform the Acts described above for this embodiment. In another embodiment, a system for determining a rater reputation of a first entity as a rater of other entities is provided. A first rating indicative of a rating of a rated entity by the first entity, and one or more second ratings, each second rating indicative of a rating of the rated entity provided by another entity, is provided to the system. The system includes a rater reputation generator to combine the second ratings to produce a first combined rating. The rater reputation generator is further operative to compare the first rating to the first combined rating to produce a first rating predictability of the first rating, the first rating predictability being a negative function of a magnitude of a difference between the first rating and the first combined rating. The rater reputation generator is further operative to generate a resulting rater reputation based at least in part on the first rating predictability, and to output this generated rater reputation. In yet another embodiment, a system for determining a rater reputation of a first entity as a rater of other entities is provided. A first rating indicative of a rating of a rated entity by the first entity, and one or more second ratings, each second rating indicative of a rating of the rated entity provided by another entity are provided for the system. The system includes: means for combining the second ratings to produce a first combined rating; means for comparing the first rating to the first combined rating to produce a first rating predictability of the first rating, the first rating predictability being a negative function of a magnitude of a difference between the first rating and the first combined rating; and means for generating a resulting rater reputation based at least in part on the first rating predictability. In another embodiment, a ratee reputation of a first entity is determined. A first rating of the first entity by a second entity is received. One or more rater reputations including a first rater reputation of the second entity as a rater of other entities are accessed, and a ratee reputation of the first entity is generated by combining the one or more rater reputations and the first rating. This embodiment may be implemented as a computer program product that includes a computer readable medium and computer readable signals stored on the computer readable medium that define instructions. These instructions, as a result of being executed by a computer, instruct the computer to perform the Acts described above for this embodiment. In another embodiment, a system for determining a ratee reputation of a first entity is provided. The system includes a ratee reputation generator to receive as input a first rating of the first entity by a second entity. The ratee reputation generator is operative to access one-or more rater reputations including a first rater reputation of the second entity as a rater of other entities, and to generate a ratee reputation of the first entity by combining the one or more rater reputations and the first rating signal. The ratee reputation generator is further operative to provide as output the generated ratee reputation. In yet another embodiment, a system for determining a ratee reputation of a first entity is provided. The system includes: means for receiving a first rating of the first entity by a second entity; means for accessing one or more rater reputations including a first rater reputation of the second entity as a rater of other entities; and means for generating a ratee reputation of the first entity by combining the one or more rater reputations and the first rating signal. The features and advantages of the invention described above and other features and advantages of the invention will be more readily understood and appreciated from the detailed description below, which should be read together with the accompanying drawing figures. BRIEF DESCRIPTION OF THE DRAWINGS In the drawings: FIG. 1 is a block diagram illustrating a representation of an on-line community of entities interconnected by several rating links; FIG. 2 is a flowchart illustrating an example embodiment of a method of to determining a rater reputation of an entity; FIG. 3 is a flow chart illustrating an example embodiment of a method of combining rating predictabilities to produce a rater reputation; FIG. 4 is data flow diagram illustrating an example embodiment of a system for generating a rater reputation of an entity; FIG. 5 is a data flow diagram illustrating an example embodiment of a system for generating a rater reputation of an entity; FIG. 6 is a data flow diagram illustrating an example embodiment of a system for generating a ratee reputation deviation of an entity; FIG. 7 is a data flow diagram illustrating an example embodiment of a system for generating a rater reputation deviation of an entity; FIG. 8 is a flowchart illustrating an example embodiment of a method of generating a ratee reputation of an entity; FIG. 9 is a data flow diagram illustrating an example embodiment of a system for generating a ratee reputation of an entity; FIG. 10 is a flowchart illustrating an example embodiment of a method of determining a personalized ratee reputation; FIG. 11 is a data flow diagram illustrating an example embodiment of a system for determining a personalized ratee reputation; FIG. 12 is a flow chart illustrating an example embodiment of recursively estimating the impact of one or more ratings on a result; FIG. 13 is a data flow diagram illustrating an example embodiment of a system for recursively estimating the impact of one or more ratings on a result; FIG. 14 is a flowchart illustrating an example embodiment of a method of generating a weighting vector for a set of multiple ratings; FIG. 15 is a data flow diagram illustrating an example embodiment of a system for generating a weighting vector for a set of multiple ratings; FIG. 16 is a flow chart illustrating an example embodiment of a method of combining multiple estimated reputations to produce a new reputation; FIG. 17 is a data flow diagram illustrating an example embodiment of a system for combining multiple estimated reputations to produce a new estimated reputation; and FIG. 18 is a data flow diagram illustrating an example system architecture for implementing the methods and systems of FIGS. 2-17. DETAILED DESCRIPTION I. Determining a Rater Reputation Described below is a method and system for determining a rater reputation of a first entity. Although determining a rater reputation is described below primarily in connection to ratings developed in connection with electronic exchanges, such determination may be applied to any of a variety of ratings, regardless of whether the rating is provided as a result of an electronic exchange. For example, a rating may represent a qualitative assessment of an in-person interview of a job candidate, an in-person sale or a credit transaction. The rater reputation produced using the method and system described below may have any of a variety of applications such as, for example, assessing the trustworthiness (as a rater) of a reference, an employment recruiter, a rating agency, or any other entity that provides recommendations, scores, rankings or ratings of other entities. A rater reputation may be determined, for one or more ratings of one or more rated entities, respectively, provided by a first entity, by comparing each rating to other ratings of the rated entity provided by other entities. For each rated entity, the statistical similarity between the rating provided by the first entity and ratings provided by the other entities as determined by the comparison, i.e., the rating predictability, may serve as a basis for a rater reputation of the first entity. Optionally, the ratings provided by the other entities may be ratings provided at points in time that occur after a point in time at which the rating by the first entity is provided. Determining a rater reputation of a first entity by comparing ratings provided by the first entity to such future ratings may provide a more accurate estimate of the first entity's rater reputation than comparing these ratings to past ratings of other entities. This more accurate estimate may result from the fact that if past ratings are used for the comparisons, and the first entity is aware that past ratings are being used, the first entity may access the past ratings and bias her ratings to be consistent with the past ratings, thus resulting in a higher reputation of the first entity than otherwise would occur. Accordingly, by using future ratings, which are necessarily unknown to the first user, for the comparisons, the first entity has less incentive to bias her ratings, resulting in more honest ratings being provided by the first entity. These more honest ratings result in a more accurate estimation of the rater reputation of the first entity. In an aspect of determining a rater reputation of an entity, the result of the comparison of (a) the rating provided by the first B rater of a rated entity and (b) other ratings of the rated entity provided by other raters may be weighed over a ratee reputation deviation of the rated entity, as will be described in more detail below in relation to FIG. 5. This ratee reputation deviation represents a deviation of ratings of the rated entity from an expected value of the rating of the rated entity. Entities whose ratee reputations fluctuate over a wide range of values, such as new entities and entities that receive a wide range of ratings (i.e., unstable entities), typically have high ratee reputation deviations. This weighting of the comparison results in a rating predictability that is greater for greater values of ratee reputation deviation and less for lesser values of ratee reputation deviation. FIG. 2 is a flowchart illustrating an example embodiment of a method of generating a rater reputation of an entity, where a first rating of a rated entity by a first entity and second ratings of the rated entity provided by other entities are provided. The first and second ratings may be provided by accessing two or more entries of a data structure such as, for example, a database, stored on a computer-readable medium such as, for example, a non-volatile memory (e.g., a magnetic disk, CD ROM, or magnetic tape) or a volatile memory (e.g., an integrated semiconductor memory such as RAM). Such a data structure may reside on a computer-readable medium located on a same computer at which an application running the method of generating resides and may be accessed by a bus or other known means. Alternatively, the data structure may reside at a remote location from such application, where access of the data structure may include use of one or more networks, bridges, routers, switches, hubs, other network devices, or any combination thereof. Such access may include wireless and wire (i.e., cable) transmissions. In Act 2, two or more of the second ratings of the rated entity may be combined to produce an expected rating. This expected rating represents an expected value of the first rating in consideration of the values of the two or more second ratings. The two or more ratings to be combined may be selected according to each rating's temporal proximity to the rating provided by the first entity (i.e., the first rating), or may be selected with other criteria such as, for example, demographic similarity of the entity that provided the second rating to the first entity. Optionally, only second ratings provided temporally after the first rating are selected. Such selected second ratings may be referred to herein as future ratings. Although all of the second ratings may be selected, which may produce a more accurate expected rating, the computational time and cost will increase as the number of second ratings combined increases; consequently, it may be desirable to select less than all of the second ratings. A limiting factor may be provided to determine a number of the second ratings to select. The value of the limiting factor may be selected to achieve an acceptable balance between (a) rater reputation accuracy and (b) the time and cost of determining the rater reputation. In an aspect of selecting second ratings, second ratings provided by the first entity are excluded from selection. Such exclusion prevents the first entity from providing multiple ratings of the rated entity, and intentionally providing a same or similar-value as each of the multiple ratings to artificially increase the first entity's rater reputation. The selected second ratings may be combined by calculating an average of the second ratings. Optionally, this calculated average may be weighted, where each selected second rating is weighted according to the reputation of the entity that provided the second rating relative to the reputation of the other entities that provided second ratings. For example, a weighted average of second ratings provided by other entities may be determined by applying the following equation: ##EQU9##
Weighting each second rating according to the reputation of the entity that provided the second rating generates an expected rating that gives more weight to ratings by those entities that have higher rater reputations. For example, if most of the higher second ratings were provided by entities having a low rater reputation, and most of the lower second ratings were provided by entities having a higher rater reputation, then the calculated expected rating would be lower than a raw average. This lower expected rating represents a bias towards the second ratings provided by the entities having a higher rater reputation. Such weighting of each selected second rating represents the principle that entities having higher rater reputations give more accurate ratings, and thus the ratings they provide are more valuable in determining a rater reputation, of an entity (by definition) and, therefore, should be given more weight than ratings provided by entities having lower rater reputations. The average rating of the selected second ratings also may be weighted according to the relative proximity of the times at which the selected second ratings are provided to the time at which the first rating is provided. In other words, a rating provided closer in time to the first rating time will have a greater weight and thus more of an impact on the calculated average than a temporally more distant rating. This weighting reflects the principle that an entity's ratee reputation may change over time. Thus, for a given time at which a first rating is compared to other ratings, temporally closer ratings should be given more weight in determining the rater reputation of the first entity. Conversely, temporally more distant ratings should have lesser weight in determining the rater reputation of the first entity. If only second ratings occurring after the first point in time (i.e., future ratings) are selected, then the earlier the second rating is provided, the greater is the weight attributed to the second rating. Further, time may be divided into a number of intervals, where each second ratings is provided during one of the intervals. Each second rating may be weighted according to the temporal proximity to the first point in time of the interval in which the second rating was provided. Optionally, each selected second rating may be placed in a temporal order according to its relative temporal proximity to the first point in time, and each selected second rating may be weighted according to its position in this order. If only future ratings are selected, then the earlier the second rating is provided, the lower (i.e., the closer to the beginning) the rating is in the temporal order. Thus, a temporally-weighted average may be defined by the following equation: ##EQU10##
Combining Equations 6 and 7, an expected rating may be calculated by applying the following equation: ##EQU12## Other statistical methods may be used to determine an expected rating of an entity. Returning to the method of FIG. 2, next, in Act 4, the first rating of the rated entity, provided by the first entity, may be compared to the expected rating, to produce a rating predictability. This rating predictability may be a negative function of an absolute difference between the first rating and the expected rating. As used herein, a first value is a negative function of a second value if the first value decreases as a result of the second value increasing, and increases as a result of the second value decreasing. Further, as used herein, a first value is a positive function of a second value if the first value increases as a result of the second value increasing, and decreases as a result of the second value decreasing. For example, comparing the first ratings and the second ratings may include determining the absolute difference (i.e., magnitude of the difference) between the first rating and the second rating and then applying a Gaussian distribution function to the determined absolute difference to produce the first rating predictability. If a Gaussian distribution function is being applied, then the absolute difference between the first rating and the expected rating may first be divided by a ratee reputation deviation of the rated entity. The ratee reputation deviation defines a deviation of ratings by other entities of the rated entity from an expected rating, and is described in more detail below in relation to FIG. 6. Thus, a rating predictability for the first rating may be determined by applying the following equation: ##EQU13##
Dividing the absolute difference by the rates reputation duration has the effect of weighting the absolute difference over the ratee reputation deviation. This weighting may be desirable to account for the stability or reliability of rater ratings of the rated entity in determining the rates reputation of the first entity. For example, if the ratee reputation of the rated entity is unstable (i.e., ratings provided for the rated entity vary considerably), the rater reputation of the first entity should be changed less by the difference between the expected rating and the first rating. Conversely, if the ratee reputation of the rated entity is stable, the rater reputation of the first, entity should be changed more by the difference. Alternatively, other functions may be applied to determine the rating predictability of the first rating. For example, the absolute difference may be subtracted from a constant such as, for example, a constant representing a maximum allowed rater reputation value. For example, if the range of allowed rater reputation values is from 0 to 1, then the absolute difference between the first rating and the expected rating may be subtracted from 1, such that the rating predictability is a negative function of the absolute difference. Accordingly, the rating predictability of the first rating may be determined by applying the following equation: ##EQU14##
If the first rating is a first-time rating by the first entity, then the generated rating predictability may alone serve as the rater reputation of the first entity. Alternatively, if the first entity has provided other ratings of other entities, and rating predictabilities have been generated from these other ratings (e.g., by performing Acts 2 and 4 on the provided ratings), then, in Act 5, the other rating predictabilities may be combined with the rating predictability generated in Act 4 to produce the rater reputation of the first entity. Act 5 may be implemented in any of several different ways. In one implementation, Act 5 may be implemented by averaging all of the generated rating predictabilities associated with each rating provided by the first entity. Accordingly, a rater reputation may be determined by applying the following equation: ##EQU15## where n is the number of ratings provided by the first entity and Rrater is the rater reputation. If the rater reputation of the first entity is determined by averaging the first entity's rating predictabilities, the average may be a weighted average. For example, each rating predictability may be weighted as a positive function of the time at which the rating associated with the rating predictability is provided. For example, the earlier the associated rating is provided, and thus the further away in time from when the rater reputation is being determined, the lower the weighting of the predictability. Optionally, each rating predictability may be placed in a temporal order according to the time at which its associated rating was provided, and each predictability may be weighted according its position in this order. Further, time may be divided into a number of intervals, and the temporal intervals may be placed in a temporal order. A rating predictability then may be weighted according to the position of the temporal interval in the temporal order. Weighting the rating as such represents the principle that an entity's rater reputation may change over time, and thus more recent ratings should be given more weight than older ratings in determining the rater reputation of an entity. A rater reputation, determined by applying such a weighted average of predictabilities, may be determined by applying the following equation: ##EQU16##
Determining a rater reputation of a first entity by averaging rating predictabilities of the first entity may become more cost prohibitive as the number of ratings of other entities provided by the first entity increases. Accordingly, as an alternative implementation of Act 5, the rater reputation may be determined recursively. Determining a rater reputation recursively, for example, as described below, saves computational space and time, particularly as the number of ratings of other entities provided by the first entity grows. Such a recursive determination may include: providing a previously determined rater reputation (i.e., an initial rater reputation) of the first entity; determining a rater reputation adjustment (which may be a positive or negative value) based on the generated rating, and adding the reputation adjustments to the previously determined rater reputation to produce the rater reputation. FIG. 3 is a flow chart illustrating an example implementation of Act 5. In Act 6, the rating predictability may be subtracted from the initial rater reputation to produce a reputation modification. Next, in Act 8, the reputations of the entities that provided the selected second ratings may be combined to produce a combined reputation such as, for example, by calculating an average reputation from these reputations. For example, a combined reputation may be determined by applying following equation: ##EQU18## where Rcombined is the combined reputation and Ruother is the rating of an entity that provided one of the selected second ratings. Act 8 may be performed in sequence or concurrently with Acts 2-6. Next, in Act 10, the reputation modification may be scaled by the combined reputation to produce a scaled reputation modification. This scaling has the effect of weighting the reputation modification according to the reputations of the entities corresponding to the second ratings. If the combined reputation is an average reputation of the entities that provided the selected second ratings and has a relatively high value, then the reputation modification is scaled such that the reputation adjustment is relatively high. Conversely, if the average rater reputation of these raters is relatively low, then the reputation adjustment resulting from the scaled reputation modification is relatively low. The scaled reputation modification may be determined by applying the following equation: where Rj-1rater is the initial rater reputation, [P(X)-Rj-1rater] is the reputation modification, and Rscaled is the scaled reputation modification. Next, in Act 12, the scaled reputation modification maybe divided by a change rate factor to produce a reputation adjustment. This change rate factor controls the rate at which the first rating and the resulting rating predictability can change the rater reputation of the first entity. For example, if the rate change factor has a high value, then the rate of change will be slower such that a relatively higher number of ratings will have to be provided by an entity before the rater reputation of the entity approaches an Actual reputation of the entity. Next, in Act 14, the reputation adjustment is added to the initial rater reputation to produce a resulting rater reputation. The resulting rater reputation may be determined by applying the following equation: ##EQU19##
In an aspect of recursively determining a rater reputation of an entity, for example, by applying Equation 16, an original rater reputation (i.e., an entity's rater reputation before a first rater reputation has been determined for the entity), R0rater, is initialized to zero. Consequently, an entity's rater reputation has its lowest value before the entity provides a first rating of another entity. Such an original rater reputation prevents an entity with a low rater reputation from creating a new identity as a new entity and beginning with a higher rater reputation than the low reputation of the entity. Recursively determining a rater reputation of a first entity, for example, by applying Equation 16, may result in an rater reputation that asymptotically approaches an Actual rater reputation of the first entity as the number or ratings of other entities provided by the first entity increases. An Actual rater reputation of the entity may be determined by averaging the determined rating predictabilities (and possibly weighting the average) for each rating provided by the first entity, for example, by applying Equation 11 or 12, or a variation thereof. As described above, this averaging may become cost prohibitive as the number of ratings provided by the first entity increases. Further, this averaging does not penalize an entity from starting over as a new entity by initializing to zero an original rater reputation of the entity. Both of these shortcomings of calculating an Actual reputation are avoided by initializing to zero an original rater reputation of an entity and by recursively determining the rater reputation of the entity, for example, by applying Equation 16 and variations thereof. In an aspect of recursively determining a rater reputation of an entity, in response to receiving a rating of a rated entity, the rater reputations of the entities that provided the most recent M ratings may be determined. In other words, each of the selected second ratings is one of the most recent M ratings. Further, the determined rater reputation for each rating entity may be weighted as a function of how recent the rating entity provided its rating in relation to how recent the other rating entities provided their ratings. For example, for each of rating entities corresponding to one of the last M ratings received, the rating entity's rater reputation may be determined by application of the following equation: ##EQU20##
For example, if rater reputations are being determined for the rating entities that provided the most recent 20 ratings, then, M=20. For the rating entity that provided the earliest rating, m=20 and m/M=1. Further, for the rating entity that provided the most recent rating, m=1 and m/M=1/20. By weighting the adjustment to the rater reputation of an entity by m/M, the amount that a rating entity's rater reputation is adjusted is proportional to the number of ratings received for a rated entity after the rating provided by the rating entity. This weighting reflects the principle that if there are more ratings received after the rating provided by the rating entity, then there is more information to estimate the predictability of the rating entity, as described above in relation to Equations 9 and 10, from which the rater reputation adjustment is determined. This use of more information results in more accurate estimations of the predictability of the rating entity, and a more accurate rater reputation adjustment. Accordingly, by weighting the rater reputation adjustment as described above in relation to Equation 17, the rater reputation adjustment is weighted as a function of this accuracy. Other techniques may be used for weighting a rater reputation adjustment as a function of how recent the rating entity provided its rating in relation to how recent the other rating entities provided their ratings. As described above, in an aspect of determining a rater reputation of an entity, each time a new entity enters a population or community of entities that use a rating system incorporating rater reputation, the new entity may have an original rater reputation initialized to zero. Initializing an original rater reputation to zero may be desirable if an entity is capable of having multiple identities. In a system where an entity is restricted to a lifetime persistent identity, for example, a social security number, then the original rater reputation may not be initialized to zero, but may be initialized to another value. For example, the original rater reputation may be initialized to an average rater reputation value. In some situations, an entire population of entities that have been using a rating system to rate each other, and thus have pre-collected ratings, may want to determine a rater reputation of one or more, possibly all, entities of the population using these pre-collected ratings. Such determination of rater reputations for a population of entities using pre-collected ratings may be referred to herein as "seeding" a reputation system. If seeding a reputation system, one or more first entities of the population may not have provided a sufficient number of ratings of other entities such that a recursively generated rater reputation of these first entities approximates an Actual rater reputation of these first entities, respectively. Consequently, the resulting rater reputation of one or more first entities that have provided relatively few ratings is lower than the resulting reputation of one or more first entities that have provided relatively many ratings, irrespective of the Actual ratings provided by the first entities. Accordingly, in an aspect of seeding a reputation system by recursively determining a rater reputation of a first new entity, pre-collected ratings may be used to determine the rater reputation as follows. In a first pass of determining the rater reputation, for example, by applying Equation 16 or variations thereof, the pre-collected ratings are used and the original rater reputation of the first new entity may be initialized to zero. A second pass of determining the rater reputation may use the same pre-collected ratings and initialize the original rater reputation of the first new user to the rater reputation resulting from the first pass. This initialization to a resulting reputation may be repeated in other passes until the resulting reputation adequately approximates the Actual rater reputation of the first new entity. Further, to seed a reputation system by recursively determining a rater reputation of a first entity, the expected rating for each first rating provided by the first entity may be determined by applying the following equation: ##EQU21## where Ri-1 is the ratee reputation of the rated entity at i-1, D is the range of allowed reputation values, 1/C is the change rate factor and Eiratee is the determined expect rating. FIG. 4 is a data flow diagram illustrating an example embodiment of a system 19 for generating a rater reputation 38. The rater reputation generator 20 may receive a request 21 from a user indicating a request for a first entity's reputation. In response to the user request 21, the rater reputation generator 20 may receive as input a first rater rating 26 and selected second ratings 28, and generate the resulting rater reputation 38 as output, for example, by performing Acts 2-5 of FIG. 2. In one implementation, the rater reputation generator 20 may also receive as input other rating predictabilities 49 to generate a resulting rater reputation 38 by averaging rating predictabilities, as described above in relation to FIG. 2. In another implementation, the rater reputation generator 20 may also receive as input an initial rater reputation 22, other rater reputations 24, a ratee reputation deviation 30, a range 32, and a change rate factor 34, and use these inputs in addition to inputs 26 and 28 to generate a resulting rater reputation 38 such as, for example, by applying Acts 6-14 of FIG. 3. In yet another implementation, the rater reputation generator further may receive a value 31 indicating a number of most recent ratings and a value 33 indicating the number of ratings provided for the rated entity after the first rater rating 26 was provided. Values 31 and 33 correspond to values M and m, respectively described above in relation to Equation 17. FIG. 5 is a data flow diagram illustrating a more detailed example embodiment of the system 19 for generating a resulting rater reputation 38. The rater reputation generator 20 may include an expected rating generator 40, a predictability generator 44, a reputation modification generator 48, a combined predictability generator 47, a combined reputation generator 52, a reputation adjustment generator 56 and an adder 60. In response to the rater reputation generator 20 receiving the user request 21, the expected rating generator 40 may receive as input the selected second ratings 28 and generate as output an expected rating 42. The expected rating generator 40 also may receive as input other rater reputations 24, and use this input 24 in addition to input 28, to generate the expected rating 42. The other rater reputations 24 may be the reputations of the entities that provided the selected second ratings 28. Expected rating generator 40 may generate expected ratings 42 in accordance with the various techniques described above in relation to Act 2 of FIG. 2. The predictability generator 44 may receive as input the expected ratings 42 and the first rater rating 26 and produce a rating predictability 46 as output. The predictability generator 44 also may receive the ratee reputation deviation 30 and the range 32, and use both of these inputs to help produce the rating predictability 46. The predictability generator 44 may generate the rating predictability 46 in accordance with the various techniques discussed above in relation to Act 4 of FIG. 2. The rater reputation of a first entity may be determined according to Equations 11 or 12 by including in the rater reputation generator the combined predictability generator 47 that receives as input rating predictability 46 and other rating predictabilities 49 (which may have been generated by predictability generator 44) and generates as output a resulting rater reputation 38. The reputation modification generator 48 may receive a rating predictability 46 and an initial rater reputation 22, and generate a reputation modification 50. The reputation modification generator 48 may generate the reputation modification 50 by subtracting the rating predictability from the initial rater reputation as described above in relation to Act 6 of FIG. 3. The combined reputation generator 52 may receive other rater reputations 24 and generate a combined reputation value 54. The combined reputation generator 52 may calculate the average of the other rater reputations to determine the combined reputation 54. A reputation adjustment generator 56 may receive the combined reputation 54 and the reputation modification 50 and generate a reputation adjustment 58. The reputation adjustment generator 56 may also receive the change rate factor 34. The reputation adjustment generator 56 may generate the reputation adjustment 58 in accordance with the techniques described above in relation to Acts 10 and 12 of FIG. 3. As described above, the combined reputation 54 may scale the reputation modification 50 in accordance with the combined reputation 54 of the other raters. In an embodiment, the reputation adjustment generator further receives values 31 and 33 corresponding to values M and m, respectively, and generates the rater reputation adjustment 58 as described above in relation to Equation 17. The adder 60 may add the initial rater reputation 22 to the reputation adjustment 58 to produce the resulting rater reputation 38. The rater reputation generator 20 and any components thereof, including expected rating generator 40, predictability generator 44, combined reputation generator 52, combined predictability generator 47, reputation modification generator 48, reputation adjustment generator 56 and adder 60, may be implemented as software, hardware, firmware or any combination thereof. The rater reputation generator 20 and any components thereof may reside on a single machine (e.g., a computer), or may be modular and reside on multiple interconnected (e.g., by a network) machines. Further, on each of the one or machines that include the rater reputation generator 20 or a component thereof, the generator 20 or component may reside in one or more locations on the machine. For example, different portions of the rater reputation generator 20 or different portions of a component may reside in different areas of memory (e.g., RAM, ROM, disk, etc.) on a computer. The range 32 and the change rate factor 34 may be constants for the system 19 and may be stored in a reputation database or other data structure, as described in more detail below in relation to FIG. 18. The first rater rating 26, the other reputations 24, the selected second ratings 28, the ratee reputation deviation 30, the initial rater reputation 22, and values 31 and 33 also may be stored in the reputation database or other structure. In response to receiving the user request 21, the rater reputation generator 20 may access the reputation database or similar data structure and retrieve values 26, 32, 24, 28, 26, 30, 31, 32, 33 and 34 to generate the resulting rater reputation 38 as described above. The resulting rater reputation 38 then may be stored in the reputation database or other data structure for later access. System 19, and the components thereof, are merely example embodiments of a system for generating a rater reputation. Such example embodiments are not meant to limit the scope of the invention and are provided merely for illustrative purposes, as any of a variety of other systems and components for determining a rater reputation, determining a may fall within the scope of the invention. II. Determining a Ratee Reputation Deviation FIG. 6 is a data flow diagram illustrating an example embodiment of a system 69 for recursively generating the ratee reputation deviation 30 of a rated entity. Similarly to as described above in relation to recursively determining a rater reputation, determining a ratee reputation deviation recursively saves computational space and time, particularly as the number of provided ratings for the rated entity grows. The ratee reputation deviation generator 72 may receive as input a ratee reputation 70, a rater reputation 74, an initial ratee reputation deviation 75, a most recent rating 76 and a forgetting factor 77. The ratee reputation deviation generator 72 may also receive the range 32. The ratee reputation 70 is the ratee reputation determined from the most recent rating 76 of the rated entity, for example, by applying Equation 1 as disclosed in the Zacharia thesis, or by applying a variation of Equation 1, where the rater reputation is determined in accordance with Equation 15 or a variation thereof, as described above in relation to FIG. 2. The initial ratee reputation deviation 75 is the ratee reputation deviation of the rated entity before the most recent rating 76 was provided. The rater reputation 74 is the rater reputation of an entity that provided the most recent rating 76. The ratee reputation generator 72 may generate from these inputs the ratee reputation deviation 30 that represents a reliability of the rated entity's ratee reputation. Optionally, the ratee reputation deviation generator 72 also may receive a minimum allowed rater reputation deviation and compare it to the determined rater reputation deviation 30. If the minimum deviation is greater than deviation 30, then the rater reputation deviation 30 may be set equal to the minimum allowed rater reputation. Accordingly, the ratee reputation deviation generator 72 may generate the ratee reputation deviation 30 by applying the following equation: ##EQU22## where RDminratee is a minimum allowed ratee reputation deviation, F is the forgetting factor 172, RDi-1ratee is the initial ratee reputation 75, Rirater is the rater reputation 74, Wi is the most recent rating 76, T0 is an effective number of reputation determinations, Eirater,past is the expected rating, and RDiratee is the resulting ratee reputation deviation 30. The expected rating may be calculated by applying Equation 2 as described in the Zacharia thesis. The forgetting factor is a constant having a value <1 such that older ratings have less weight in determining the resulting ratee reputation deviation than more recent ratings. To may be derived from F by applying the following equation: ##EQU23## Optionally, the effective number of determined reputations may be used to determine the change rate factor described above by setting C=T0. Other statistical methods may be used to determine a reliability of a ratee reputation. For example, a forgetting factor may not be applied, or an average deviation may be determined for all determined ratee reputations of the rated entity, or such an average deviation may be calculated with each ratee reputation weighted according to how recent the ratee reputation was determined. In an aspect of recursively determining a ratee reputation deviation of a rated entity, for example, by applying Equation 19, an original ratee reputation deviation, RDiratee, is initialized to a maximum allowed value for a ratee reputation deviation. Such a maximum value may be predetermined. Consequently, a rated entity's ratee reputation deviation has its highest value before the rated entity is rated by other entities. Assigning a maximum value to an original ratee reputation deviation prevents an entity with a high ratee reputation deviation from creating a new identity as a new entity and beginning with a more desirable lower ratee reputation deviation. Equation 19 may be considered a recursive estimation algorithm of Recursive Least Squares (RLS) with a forgetting factor of F. Equation 19 estimates recursively an average square deviation of an actual rating from an expected (i.e., estimated) rating described in more detail below in relation to FIGS. 8 and 9. For more information regarding Recursive Least Squares, please refer to Chapter 9 of "Lecture Notes and Non-Linear and Non-Stationary Time Series Analysis," by H. Madsen and J. Holst, Institute of Mathematical Modeling (IMM), Technical University of Denmark, Lyngby, Denmark, 1998 (hereinafter the Madsen text), the contents of which is herein incorporated by reference in its entirety. Other statistical methods may be used to determine a reliability of a ratee reputation. For example, a forgetting factor may not be applied, or an average deviation may be determined for all determined ratee reputations of the rated entity, or such an average deviation may be calculated with each ratee reputation weighted according to how recent the ratee reputation was determined. The ratee reputation deviation generator 72 may be implemented as software, hardware, firmware or any combination thereof. The ratee reputation deviation generator 72 may reside on a single machine (e.g., a computer), or may be modular and reside on multiple interconnected (e.g., by a network) machines. Further, on each of the one or more machines that include the ratee reputation deviation generator 72 or modules thereof, the generator 72 or modules may reside in one or more locations on the machine. For example, different portions of the ratee reputation deviation generator 72 or modules may reside in different areas of memory (e.g., RAM, ROM, disk, etc.) on a computer. The range 32 and the forgetting factor 77 may be constants stored in a reputation database or similar data structure as described in more detail in relation to FIG. 18. The ratee reputation 70, the rater reputation 74, and the initial ratee reputation deviation 75 also may be stored in the reputation database or similar structure. The ratee reputation deviation generator 72, in response to receiving the most recent rating 76, may access the reputation database or similar structure to generate the ratee reputation deviation 30 as described above. The ratee reputation deviation 30 then may be stored in the reputation database or similar structure for later access. System 69 is merely an example embodiment of a system for generating a ratee reputation deviation. Such an example embodiment is not meant to limit the scope of the invention and is provided merely for illustrative purposes, as any of a variety of other systems for determining a ratee reputation deviation may fall within the scope of the invention. III. Determining a Rater Reputation Deviation In addition to having an estimate of the reliability of the ratee reputation, for example, the ratee reputation deviation 30, it may be desirable to have an estimate of the reliability of the rater reputation of an entity that is providing a rating. Such a reliability may be estimated by calculating of a rater reputation deviation. Similarly to as described above in relation to ratee reputation deviation, computational space and time may be saved by calculating a rater reputation deviation recursively, particularly as the number of ratings of other entities provided by the first entity increases. Accordingly, a rater reputation deviation may be determined recursively by applying the following equation: ##EQU24## ##EQU25## where RDminrater is a minimum allowed rater reputation deviation, RDj-1rater is an initial rater reputation deviation, RDjrater is the resulting rater reputation deviation, and the other symbols are as described above. Equation 21, and variations thereof, estimate recursively an average square deviation of a rater reputation of an entity from an expected (i.e., estimated) rater reputation. For each recursive estimate, the initial rater reputation deviation, RDj-1rater, may be weighted by the forgetting factor, F, and the average square deviation may be divided by the effective number of determined reputations, T0. Such recursive estimation is described in more detail in chapter 9 of the Madsen text. Other statistical methods may be used to determine a reliability of a rater reputation. For example, a forgetting factor may not be applied, or an average deviation may be determined for all determined rater reputations of the rating entity, or such an average deviation may be calculated with each rater reputation weighted according to how recent the rater reputation was determined. In an aspect of recursively determining a ratee reputation deviation of a first entity, for example, by application of Equation 21, an original rater reputation deviation, RDjrater, is initialized to a maximum value. This maximum value may be predetermined. Consequently, a first entity's rater reputation deviation has its highest value before the first entity provides a first rating of another entity. Assigning a maximum value for the rater reputation deviation prevents a first entity with a high rater reputation deviation from creating a new identity as a new entity and beginning with a lower rater reputation deviation. FIG. 7 is a data flow diagram illustrating an example embodiment of a system 79 for generating a rater reputation deviation. A rater reputation deviation generator 82 may receive as input an initial rater reputation 22, a rating predictability 46, an initial rater reputation deviation 80 and a forgetting factor 77. Rater reputation deviation generator 82 also may receive other rater reputations 24. The rater reputation deviation generator 82 may generate the rater reputation deviation 84 from inputs 22, 24, 46 and 80. Alternatively, in place of inputs 22, 24 and 46, deviation generator 82 may receive the scaled reputation modification as input and generate the rater reputation deviation 84 in accordance with Equation 21 or variations thereof. Optionally, the rater reputation deviation generator 82 may receive a minimum allowed rater reputation deviation, RDratermin, and compare it to the determined rater reputation deviation 84. If the minimum deviation is greater than deviation 84, then the rater reputation deviation 84 may be set equal to the minimum allowed rater reputation. The rater reputation deviation generator 82 may be implemented as software, hardware, firmware or any combination thereof. The rater reputation deviation generator 82 may reside on a single machine (e.g., a computer), or may be modular and reside on multiple interconnected (e.g., by a network) machines. Further, on each of the one or more machines that include the rater reputation deviation generator 82 or modules thereof, the generator 82 or modules thereof, the generator 82 or modules may reside in one or more locations on the machine. For example, different portions of the rater reputation deviation generator 82 may reside in different areas of memory (e.g., RAM, ROM, disk, etc.) on a computer. The forgetting factor 77 may be stored as a constant in a reputation database or similar data structure as described below in relation to FIG. 18. The initial rater reputation 22, the rating predictability 46, the other rater reputations 24 and the initial rater reputation deviation 80 also may be stored in the reputation database or similar data structure. In response to receiving the rating predictability 46, the rater reputation deviation generator 82 may access the reputation database or similar data structure to access and retrieve values 22, 24, 80 and 77, and generate rater reputation deviation 84. The rater reputation deviation 84 then may be stored in the reputation database or similar structure for later access. System 79 is merely an example embodiment of a system for generating a rater reputation deviation. Such an example embodiment is not meant to limit the scope of the invention and is provided merely for illustrative purposes, as any of a variety of other systems and components for determining a rater reputation deviation may fall within the scope of the invention. IV. Determining a Ratee Reputation Using a Rater Reputation If a rater reputation is determined for a first entity, and the first entity provides a first rating of a rated entity, the rater reputation and the first rating may be used to determine, at least in part, a ratee reputation of the rated entity. Accordingly, provided herein is a method and system for determining a ratee reputation of a rated entity based at least in part on one or more ratings of the rated entity provided by one or more entities and the rater reputations of these one or more entities. In one embodiment of determining a ratee reputation, the ratee reputation of a rated entity is determined by averaging all of the ratings provided by other entities for the rated entity, and by weighting each rating with the rater reputation of the entity that provided the rating, to produce a weighted average. Accordingly, a ratee reputation may be determined by applying the following equation: ##EQU26## where Wj is a rating supplied, Rjrater is the rater reputation of the entity who provided the rating Wj. In generating such a weighted average, each rating may be further weighted with a positive function of the time at which the rating was provided. For example, the earlier the rating is provided, and thus the further away in time from when the ratee reputation is being determined, the lower the weighting of the rating. Optionally, each rating may be placed in a temporal order according to the time at which the rating was provided, and each rating may be weighted according its position in this order. Further, time may be divided into a number of intervals, and the temporal intervals may be placed in a temporal order. A rating then may be weighted according to the position of the temporal interval in the temporal order. Similar to as described above in relation to determining a rater reputation, temporally weighting each rating represents the principle that an entity's ratee reputation may change over time. Thus, more recent ratings should be given more weight than older ratings in determining the ratee reputation of an entity. Accordingly, a ratee reputation may be determined by applying the following equation: ##EQU27## where f(j) is a temporal function such as, for example, Equation 12, above. Other weightings and combinations of weightings may be applied to a rating to determine a ratee reputation of an entity. Determining a ratee reputation of an entity by averaging ratings may become more cost prohibitive as the number of ratings provided by other entities for the first entity increases. Accordingly, in another embodiment of determining the ratee reputation of an entity, the ratee reputation may be determined recursively. Similarly to as described above in relation to determining a rater reputation, determining the ratee reputation recursively saves computational space and time, particularly as the number of ratings provided for the rated entity increases. A recursive determination may include: providing a previously determined ratee reputation (i.e., an initial ratee reputation) of the entity; determining a ratee reputation adjustment (which may be a positive or negative value) based on a received rating, and adding the reputation adjustments to the previously determined rater reputation. FIG. 8 is a flow chart illustrating an example implementation of a method of recursively determining a ratee reputation of an entity. In Act 90, an expected rating may be determined from the range and the ratee's initial reputation. An expected rating may be determined by applying Equation 4 or a variation thereof. Next, in Act 92, the expected rating may be subtracted from the first rating to produce a ratee reputation modification. The ratee reputation modification may be produced as described in relation to Equation 23 below. Next, in Act 94, the ratee reputation modification may be scaled by a rater reputation of the rating entity to produce a scaled ratee reputation modification. This rater reputation may be the resulting rater reputation generated according to one of the methods described in relation to FIGS. 2 and 3, or a variation thereof. Combining Acts 92 and 94, the scaled ratee reputation modification may be produced by applying the following equation: where Rirater is the rater reputation, Wi is the first rating, Ei is the expected rating, and Wi-Ei is the ratee reputation modification. Next, in Act 96, the scaled ratee reputation modification may be damped by a damping factor to produce a damped ratee reputation modification. The damped ratee reputation modification may be produced by applying the following equation: where Ri-1ratee is the initial ratee reputation, and damp(Ri-1ratee) is the damping factor. Optionally, the damping factor may be determined (in series or concurrently with Acts 90-94) by applying Equation 2, where the acceleration factor, a, may be predetermined to control the rate at which the ratee reputation can change. In a next Act 98, the damped ratee reputation modification may be divided by a change rate factor to produce a ratee reputation adjustment. The change rate factor affects the rate at which the ratee reputation may change. Next, in Act 100, the ratee reputation may be added to the initial ratee reputation to produce a resulting ratee reputation. In accordance with Acts 98 and 100, the resulting ratee reputation may be determined by applying the following equation: ##EQU28## where C is the change rate factor and Riratee is the resulting ratee reputation. In an aspect of recursively determining a ratee reputation of an entity using one or more rater reputations, for example, by applying Equation 26, an original ratee reputation, R0rater, for the entity has its lowest value before any ratings are provided for the entity. Assigning a lowest value to an original ratee reputation prevents an entity with a low ratee reputation from creating a new identity as anew entity and beginning with a higher ratee reputation. Other methods of determining a ratee reputation may be used. A ratee reputation of a first entity may be used for a variety of purposes, including determining whether to transact with the first entity, determining a price to pay for a good or service of the first entity and determining a price to pay for insuring a quality of a good or service of the first entity. FIG. 9 is a data flow diagram illustrating an example embodiment of a system 109 for generating a resulting ratee reputation 140. A ratee reputation generator 110 may receive an acceleration factor 112, a range 32, an initial ratee reputation 114, a first rating 116, a rater reputation 118 and a change rate factor 120, and generate a resulting ratee reputation 140 as output. The ratee reputation generator 110 may include a damping factor generator 130, an expected rating generator 122, a ratee reputation modification generator 126, a ratee reputation adjustment generator 134 and an adder 138. The expected rating generator 122 may receive as input the range 32 and the initial ratee reputation 114, and generate an expected rating 124, for example, by applying Equation 3. The ratee reputation modification generator 126 may receive the first rating 116 and the expected rating 124, and generate the ratee reputation modification 128, for example, as described above in relation to Equation 23. The damping factor generator 130 may receive the acceleration factor 112, the initial ratee reputation 114 and the range 32, and generate the damping factor 132, for example, by applying Equation 3 above. The ratee reputation adjustment generator 134 may receive the ratee reputation modification 128, the damping factor 132, the rater reputation 118 and the change rate factor 120 and generate the ratee reputation adjustment 136, for example, by applying Equation 25 above. The adder 138 may receive the initial ratee reputation 14 and the ratee reputation adjustment 136 and generate the resulting ratee reputation 140, for example, by applying Equation 26 above. Although not shown in FIG. 9, the system 109 also may include a transaction module such as transaction module 528 described below in relation to FIG. 11. The transaction module may receive the resulting ratee reputation 140, determine whether to transact with the rated entity based on the resulting ratee reputation, and then output a value, for example, a boolean value, which indicates whether or not to transact with the rated entity. The ratee reputation generator 110, and any combination of its components 110, 122, 126 and 134 may be implemented using software, firmware or hardware, or any combination thereof. The ratee reputation generator 110 and any components thereof may reside on a single machine (e.g., a computer), or may be modular and reside on multiple interconnected (e.g., by a network) machines. Further, on each of the one or machines that include the ratee reputation generator 110 or a component thereof, the generator 110 or component may reside in one or more locations on the machine. For example, different portions of the ratee reputation generator 110 or different portions of a component may reside in different areas of memory (e.g., RAM, ROM, disk, etc.) on a computer. The acceleration factor 112, the range 32 and the change rate factor 120 may be stored as constants in a reputation database or similar data structure as described below in relation to FIG. 18. The initial ratee reputation 114 and the rater reputation 118 may also be stored in the reputation database or similar data structure. In response to receiving the first rating 116, the ratee reputation generator may access the reputation database and retrieve values 112, 32, 114, 116, 118 and 120 to generate the resulting ratee reputation 140 as described above. The resulting ratee reputation 140 then may be stored in the reputation database or similar structure for later access. System 109, and components thereof, are merely example embodiments of a system for generating a ratee reputation. Such example embodiments are not meant to limit the scope of the invention and are provided merely for illustrative purposes, as any of a variety of other systems and components for determining a ratee reputation may fall within the scope of the invention. V. Determining a Reputation of an Entity From a Perspective of Another Entity FIG. 10 is a flowchart illustrating an example embodiment of a method for determining a personalized ratee reputation. In a first Act 402, a breadth-first search is performed beginning at the second entity to determine, from one or more rating paths, one or more first rating paths that have a first length. In a next Act 404, for each determined first rating path, a third entity that has a level equal to or less than the first length is identified. In a next Act 406, for each identified third party, a first rating of the first identity provided by the third entity is determined. For each identified third entity, it may be determined that the third entity has provided more than one rating of the first entity. For each third entity for which it has been determined that more than rating has been provided, a most recent rating may be selected from the one or more ratings to serve as the first rating of the first entity provided by the third entity. In a following Act 408, the first ratings are combined. The first ratings may be combined in any of a variety of ways. In one embodiment, an average of the first ratings is calculated. Calculating this first average may include, for each first rating, weighting the first rating as a function of a personalized ratee reputation of the corresponding third entity from the prospective of the second entity. This weighting may be relative to personalized ratee reputations of the other third entities from the perspective of the second entity. The personalized ratee reputation of the third entity may be determined in any of a variety of ways. In one embodiment, one or more fourth entities that are on the first rating paths, that have provided a second rating of the third entity and that have a level equal to one less than the level of the third entity are determined. The second ratings provided by these one or more fourth entities are then combined to produce the personalized ratee reputation of the third entity from the perspective of the second entity. Combining the second ratings may include calculating an average of the second ratings. Optionally, Equation 4 or a variation thereof may be applied to combine the ratings. In a next Act 410, the personalized ratee reputation is produced by weighting the combined first rating as a function of the first length. Act 410 may be performed by application of the following Equation: ##EQU29## where Rk(n) is the personalized ratee reputation of an entity k from a perspective of a second entity a distance n from the entity k, Wjk(n) is a rating provided by an entity j for the entity k, where; the entity j is a distance n-1 from the second entity, Rf(n-1) is the personalized ratee reputation of the entity j from the perspective of the second entity, D is a range of allowable personalized ratee reputation valves, and f(n) is a function of the distances n between the second entity and the entity K (i.e., a function of the length of the rating paths between the second entity and entity K), such as, for example: ##EQU30## where T is a con | ||||||