A fair ranking method, system, and device based on the Atkinson social welfare function.

Abstract

This invention discloses a fair ranking method, system, and device based on the Atkinsonian social welfare function. First, a fair ranking framework based on trust bias and position bias is constructed, defining the utility of ranking and its impact on projects. A fair ranking objective is introduced based on fair allocation theory, addressing the issue of exposure fairness. Then, a new fair ranking objective function is constructed based on the Atkinsonian social welfare concept in economics, satisfying the proposed fairness objective by solving a constrained optimization problem. Analysis shows that adjusting the inequality aversion parameter can generate rankings that conform to different fairness value judgments, achieving a better fairness-utility tradeoff. Finally, the BvN decomposition method is used to calculate the ranking strategy, and rankings are sampled and displayed based on probability.

Description

Technical Field

[0001] This invention belongs to the field of computer technology and relates to a fair ranking method, system and device for network ranking, and more particularly to a fair ranking method, system and device based on the Atkinson social welfare function for network ranking. Background Technology

[0002] With the popularization and development of internet technology, users are faced with a massive amount of information. Ranking systems have emerged to help users filter out the content they need from this vast amount of information. Ranking systems play a crucial role in modern information society, influencing not only users' information access and experience but also significantly shaping their perceptions of the world. However, in their design and operation, these systems may lead to some users or items being over-recommended while others are ignored. For example, music recommendation systems provide personalized music recommendations by analyzing users' historical listening records. However, recommendation loops may cause users to be constantly exposed to similar types of music, reducing diversity. Against this backdrop, many researchers have dedicated themselves to integrating the concept of fairness into ranking algorithms and systems to ensure they are more equitable, inclusive, and transparent.

[0003] Fairness is a vague concept, and its meaning and requirements vary across different application scenarios. Existing research defines fairness according to three dimensions: hierarchy, aspects, and output diversity. Hierarchically, fairness can be divided into individual fairness and group fairness; based on the aspects involved, it can be divided into producer fairness and consumer fairness; and according to the diversity of output rankings, it can be divided into single-output fairness and multi-output fairness. Several specific fairness models have been proposed to express fairness requirements, including the fairness constraint model, the cumulative loss fairness model, and the exposure fairness model. Currently, the most widely used fairness model is the exposure fairness model. For different groups, even if their utilities are similar, their exposure differences can be significant. The exposure fairness model, by modeling positional bias, requires that the differences in exposure between groups or individuals meet fairness requirements, maximizing the utility of rankings for users and requiring that the exposure received by an item be proportional to its value.

[0004] In the process of implementing this invention, the inventors of this application discovered that the methods of the prior art have at least the following technical problems:

[0005] (1) Existing fair ranking methods do not consider the existence of trust bias. In ranking, in addition to position bias, trust bias also affects the degree of attention of viewers. Due to their trust in the ranking system, viewers are more likely to click on or approve of higher-ranked items, and modeling position bias alone is insufficient to meet the requirements of fairness.

[0006] (2) Existing exposure-based fair ranking methods have limitations. Most existing fair ranking methods adopt exposure fairness. The impact of trust bias in the ranking system on projects is mainly reflected in click-through rate, revenue, and traffic, rather than just exposure. In addition, exposure fairness assumes that there is a certain relationship between project exposure and its value (e.g., proportionality), but this relationship lacks a theoretical basis.

[0007] (3) Existing fair ranking methods based on fair allocation are insufficient in balancing fairness and utility, have a limited range of adjustment, and are difficult to meet different fairness requirements. In addition, as the value of the trade-off parameter increases, the ranking will be more favorable to items that achieve better results, with limited improvement on ranking utility and exacerbation of unfairness. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention proposes a fair ranking method and apparatus based on the Atkinson social welfare function.

[0009] The technical solution adopted by the method of the present invention is: a fair ranking method based on the Atkinson social welfare function, comprising the following steps:

[0010] Step 1: Calculate the confidence bias p for item i, which is ranked at position k. + (k) and p - (k); where p + (k) and p - (k) represent the click probability of relevant items and the click probability of irrelevant items at ranking position k, respectively;

[0011] p + (k)=P(C=1|E=1,R=1,k);

[0012] p - (k)=P(C=1|E=1,R=0,k);

[0013] Where C∈{0,1} is a binary random variable representing whether a user clicks on an item, E∈{0,1} is a binary random variable representing whether a user checks an item, and R∈{0,1} is a binary random variable representing the relevance of an item; relevant items are those for which the binary random variable R=1, and irrelevant items are those for which the binary random variable R=0.

[0014] Step 2: Calculate the attention level v(k) for item i;

[0015] Step 3: Calculate the impact of ranking strategy π on project i based on trust bias and attention level.

[0016] Step 4: According to Define an objective function F(π) based on Atkinson's social welfare;

[0017]

[0018] Where I is a set of projects containing m projects, and ε is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to projects that have lower utility in the ranking, that is, it pays more attention to improving the utility of projects that have poor results.

[0019] Step 5: Obtain a fair ranking strategy π by solving the constrained optimization problem. ASW The corresponding double random matrix

[0020]

[0021] Step 6: Convert the double random matrix It is decomposed into a convex combination of permutation matrices, which is then transformed into a ranking strategy π, thereby sampling to obtain a fair ranking displayed to the user.

[0022] As a preferred option, in step 1,

[0023]

[0024]

[0025] Where p + (1) is the probability that a user clicks on an irrelevant item in the first ranking position, which is used as a hyperparameter to adjust for trust bias.

[0026] As a preferred option, in step 2...

[0027] As a preferred option, in step 3...

[0028]

[0029] Where, Δp(k)=p + (k)-p - (k); This represents the probability that item i is displayed to user u at ranking position k in the ranking strategy π. It is a double random matrix of size m×m, where the sum of each row and each column is 1, meaning the sum of the probabilities of each position is 1, and the sum of the probabilities of each item is also 1, represented as: and m is the number of items; U is the user set containing n users in the ranking system, r u,i ∈[0,1] represents the relevance score of each item i to user u.

[0030] As a preferred option, in step 5...

[0031]

[0032]

[0033] in, This represents the probability that item i is displayed to user u at ranking position k in the ranking strategy π. It is a double random matrix of size m×m, where the sum of each row and each column is 1.

[0034] Preferably, in step 6, the fair ranking displayed to the user is determined by decomposing the birandom matrix P. π get:

[0035]

[0036] Where L≤m 2 -m+1 is the number of permutation matrices generated by the decomposition, where m is the number of items; P l It is a permutation matrix, corresponding to a deterministic ranking σ. l ;α l It is P l The coefficient, corresponding to the ranking σ l The probability π of being sampled u (σ l This yields the random ranking strategy π, which uses a specified probability π. u (σ l ) Rank σ l Show it to the user u.

[0037] The technical solution adopted by the system of this invention is: a fair ranking system based on the Atkinson social welfare function, comprising the following modules:

[0038] The project trust bias calculation module is used to calculate the trust bias p of project i, which is ranked at position k. + (k) and p - (k); where p + (k) and p - (k) represent the click probability of relevant items and the click probability of irrelevant items at ranking position k, respectively;

[0039] p + (k)=P(C=1|E=1,R=1,k);

[0040] p - (k)=P(C=1|E=1,R=0,k);

[0041] Where C∈{0,1} is a binary random variable representing whether a user clicks on an item, E∈{0,1} is a binary random variable representing whether a user checks an item, and R∈{0,1} is a binary random variable representing the relevance of an item; relevant items are those for which the binary random variable R=1, and irrelevant items are those for which the binary random variable R=0.

[0042] The project attention calculation module is used to calculate the attention v(k) obtained by project i;

[0043] The strategy-to-project impact calculation module is used to calculate the impact of ranking strategy π on project i based on trust bias and attention level.

[0044] The Atkinsonian social welfare objective function definition module is used to define the objective function based on... Define an objective function F(π) based on Atkinson's social welfare;

[0045]

[0046] Where I is a set of projects containing m projects, and ε is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to projects that have lower utility in the ranking, that is, it pays more attention to improving the utility of projects that have poor results.

[0047] The double random matrix calculation module is used to obtain a fair ranking strategy π by solving constrained optimization problems. ASW The corresponding double random matrix

[0048] The fair ranking calculation and display module is used to calculate and display the double random matrix. It is decomposed into a convex combination of permutation matrices, which is then transformed into a ranking strategy π, thereby sampling to obtain a fair ranking displayed to the user.

[0049] The technical solution adopted by the device of the present invention is: a fair ranking device based on the Atkinson social welfare function, comprising:

[0050] One or more processors;

[0051] A storage device for storing one or more programs that, when executed by one or more processors, enable the one or more processors to implement the fair ranking method based on the Atkinson social welfare function.

[0052] Compared with the prior art, the beneficial effects of the present invention include:

[0053] (1) This invention constructs a fair ranking framework based on trust bias and position bias, in which the utility of ranking and the impact of ranking on projects are defined, and fair ranking objectives are introduced based on fair distribution theory: no envy and proportionality principle, which solves the problem of exposure fairness.

[0054] (2) This invention constructs a new objective function for fair ranking based on the Atkinsonian social welfare concept in economics, and satisfies the proposed fairness objective by solving a constrained optimization problem. Analysis shows that adjusting the inequality aversion parameter can produce rankings that conform to different fairness value judgments, achieving a better fairness-utility tradeoff, and with higher operating efficiency.

[0055] (3) This invention employs the Birkhoff-von Neumann (BvN) decomposition method to calculate the ranking strategy, sampling and displaying rankings based on probabilities. Since positions in the ranking are indivisible, and the attention received by an item is often influenced by its ranking position, it is difficult to ensure that items with similar relevance receive the same level of attention in a single deterministic ranking. Furthermore, achieving fairness through a single deterministic ranking also presents a difficult combinatorial optimization problem. Therefore, a randomized probabilistic ranking strategy is considered, generating a fair ranking distribution to achieve expected fairness, thus better satisfying the proposed fair ranking objective. Attached Figure Description

[0056] The technical solutions of the present invention will be further illustrated below using embodiments and specific implementation methods. In addition, some accompanying drawings are used in the description of the technical solutions. Those skilled in the art can obtain other drawings and the intent of the present invention from these drawings without any creative effort.

[0057] Figure 1 This is a flowchart of a fair ranking method based on the Atkinson social welfare function provided by an embodiment of the present invention;

[0058] Figure 2 This is a framework diagram of the fair ranking task in an embodiment of the present invention;

[0059] Figure 3 The diagram shows a comparison of the fairness and utility of the method used in this invention with other methods in the prior art. (a) is a comparison diagram of MME under different degrees of trust bias, (b) is a comparison diagram of PII under different degrees of trust bias, (c) is a comparison diagram of PDI under different degrees of trust bias, and (d) is a comparison diagram of Util under different degrees of trust bias.

[0060] Figure 4This is a schematic diagram comparing the fairness and utility trade-offs of the method used in this invention with the FRFD method in the prior art, wherein (a) is a schematic diagram comparing the trade-offs of Util and MME, (b) is a schematic diagram comparing the trade-offs of Util and PII, and (c) is a schematic diagram comparing the trade-offs of Util and PDI. Detailed Implementation

[0061] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0062] This invention, through extensive research and practice, reveals that existing fair ranking methods only model positional bias, neglecting trust bias. In this context, exposure-based fairness is difficult to apply and lacks theoretical support, while most existing methods are based on exposure fairness. In recommendation and ranking systems, the system's fairness goals and requirements may change in different application scenarios and real-world situations. Existing methods based on fair allocation are insufficient in balancing fairness and utility, failing to meet diverse fairness needs.

[0063] Atkinson argues that measures of inequality in distribution implicitly contain social value judgments. He introduces welfare analysis into inequality measurement, proposing the Atkinson social welfare function and constructing an inequality index based on it, thus making value judgments explicit. The Atkinson social welfare function reflects relative inequality aversion in value judgments through a single parameter, ranking various social states (such as resource allocation) according to societal value preferences. Therefore, it can be well applied to the problem of equitable allocation based on ranking positions.

[0064] Please see Figure 1 and Figure 2 This embodiment provides a fair ranking method based on the Atkinson social welfare function, which includes the following steps:

[0065] Step 1: Calculate the confidence bias p for item i, which is ranked at position k. + (k) and p - (k); where p + (k) and p - (k) represent the click probability of relevant items and the click probability of irrelevant items at ranking position k, respectively;

[0066] p + (k)=P(C=1|E=1,R=1,k);

[0067] p - (k)=P(C=1|E=1,R=0,k);

[0068] Where C∈{0,1} is a binary random variable representing whether a user clicks on an item, E∈{0,1} is a binary random variable representing whether a user checks an item, and R∈{0,1} is a binary random variable representing the relevance of an item; relevant items are those for which the binary random variable R=1, and irrelevant items are those for which the binary random variable R=0.

[0069] In one implementation,

[0070]

[0071]

[0072] Where p + (1) is the probability that a user clicks on an irrelevant item in the first ranking position, which is used as a hyperparameter to adjust for trust bias.

[0073] Location bias affects users' inspection of items, while trust bias affects their clicking on items. These two biases often coexist and influence users' judgments about items. Therefore, it is necessary to model trust bias in ranking to more accurately capture user behavior, thereby eliminating these biases in fair ranking and achieving better fairness.

[0074] Step 2: Calculate the attention v(k) obtained for project i, i.e., the exposure.

[0075] In one implementation,

[0076] Step 3: Calculate the impact of ranking strategy π on project i based on trust bias and attention level.

[0077] In one implementation,

[0078]

[0079] Where, Δp(k)=p + (k)-p - (k); This represents the probability that item i is displayed to user u at ranking position k in the ranking strategy π. It is a double random matrix of size m×m, where the sum of each row and each column is 1, meaning the sum of the probabilities of each position is 1, and the sum of the probabilities of each item is also 1, represented as: and m is the number of items; U is the user set containing n users in the ranking system, r u,i ∈[0,1] represents the relevance score of each item i to user u.

[0080] In achieving a fair ranking objective, focusing directly on the impact of ranking on a project, rather than on exposure, is more reasonable and has a wider applicability. The impact of ranking on a project can be the result of ranking strategies such as click-through rate and subscription rate.

[0081] Step 4: According to Define an objective function F(π) based on Atkinson's social welfare;

[0082]

[0083] Where I is a set of projects containing m projects, and ε is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to projects that have lower utility in the ranking, that is, it pays more attention to improving the utility of projects that have poor results.

[0084] Step 5: Obtain a fair ranking strategy π by solving the constrained optimization problem. ASW The corresponding double random matrix

[0085]

[0086] In one implementation,

[0087]

[0088]

[0089] in, This represents the probability that item i is displayed to user u at ranking position k in the ranking strategy π. It is a double random matrix of size m×m, where the sum of each row and each column is 1.

[0090] The above formula maximizes the objective function F(π), which incorporates Atkinson's social welfare ideas. The constraint indicates that the sum of the probabilities of each item being placed in different positions is 1, and the sum of the probabilities of each position receiving different items is also 1. In this ranking optimization problem, the objective function F(π) is concave, and the constraint that P is a doubly random matrix is ​​a linear constraint, thus resulting in a solvable convex optimization problem.

[0091] This invention dynamically controls the trade-off between fairness and utility by adjusting the parameter ε, providing a larger trade-off space and flexibly meeting different fairness standards, making it suitable for different fair ranking scenarios.

[0092] When ε = 0, the aversion to unfairness is zero, and the objective function F(π) is expressed as:

[0093]

[0094] At this point, F(π) represents the sum of the ranking's impact on the project, which is also equal to the ranking's utility to the user. π ASW Maximizing the utility of rankings without considering fairness aligns with the utilitarian principle.

[0095] As ε gradually increases, the demand for fairness gradually grows. Since the objective function F(π) is a concave function, the second derivative... Therefore, in maximizing F(π), improving the ranking has a relatively greater impact on weaker projects and will generate more social welfare.

[0096] When ε = 1, the objective function F(π) undergoes the following transformation:

[0097]

[0098] The objective function F(π) here takes the form of a Nash product, equivalent to the Nash social welfare function. Maximizing this function ensures that the impact of ranking on items is neither zero nor a very small decimal, achieving a more equitable distribution of item impact compared to ranking strategies that only consider user utility. According to existing research, in the case of Top-K rankings, when K=1, the fair ranking problem is equivalent to the classic fair allocation problem of divisible goods under additive utility, where π... ASW Maximizing the Nash social welfare function guarantees the absence of envy and the proportionality principle, satisfying Pareto optimality. When K > 1, π ASW It still satisfies Pareto optimality and approximately guarantees no envy and the proportionality principle.

[0099] Step 6: Use the BvN (Birkhoff-von Neumann) decomposition algorithm to decompose the double random matrix. It is decomposed into a convex combination of permutation matrices, which is then transformed into a ranking strategy π, thereby sampling to obtain a fair ranking displayed to the user.

[0100] In one implementation, the fair ranking displayed to the user can be achieved by decomposing the birandom matrix P. π get:

[0101]

[0102] Where L≤m 2 -m+1 is the number of permutation matrices generated by the decomposition, where m is the number of items; P l It is a permutation matrix, corresponding to a deterministic ranking σ. l ;α l It is P l The coefficient, corresponding to the ranking σ l The probability π of being sampled u (σ l This yields the random ranking strategy π, which uses a specified probability π.u (σ l ) Rank σ l Show it to the user u.

[0103] In the case of Top-K rankings, P π The matrix is ​​an m×K matrix, no longer a strictly m×m double random matrix. According to existing research, the BvN decomposition method is still applicable in this case.

[0104] This embodiment also provides a fair ranking system based on the Atkinson social welfare function, including the following modules:

[0105] The project trust bias calculation module is used to calculate the trust bias p of project i, which is ranked at position k. + (k) and p - (k); where p + (k) and p - (k) represent the click probability of relevant items and the click probability of irrelevant items at ranking position k, respectively;

[0106] p + (k)=P(C=1|E=1,R=1,k);

[0107] p - (k)=P(C=1|E=1,R=0,k);

[0108] Where C∈{0,1} is a binary random variable representing whether a user clicks on an item, E∈{0,1} is a binary random variable representing whether a user checks an item, and R∈{0,1} is a binary random variable representing the relevance of an item; relevant items are those for which the binary random variable R=1, and irrelevant items are those for which the binary random variable R=0.

[0109] The project attention calculation module is used to calculate the attention v(k) obtained by project i;

[0110] The strategy-to-project impact calculation module is used to calculate the impact of ranking strategy π on project i based on trust bias and attention level.

[0111] The Atkinsonian social welfare objective function definition module is used to define the objective function based on... Define an objective function F(π) based on Atkinson's social welfare;

[0112]

[0113] Where I is a set of projects containing m projects, and ε is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to projects that have lower utility in the ranking, that is, it pays more attention to improving the utility of projects that have poor results.

[0114] The double random matrix calculation module is used to obtain a fair ranking strategy π by solving constrained optimization problems. ASW The corresponding double random matrix

[0115] The fair ranking calculation and display module is used to calculate and display the double random matrix. It is decomposed into a convex combination of permutation matrices, which is then transformed into a ranking strategy π, thereby sampling to obtain a fair ranking displayed to the user.

[0116] This embodiment also provides a fair ranking device based on the Atkinson social welfare function, including:

[0117] One or more processors;

[0118] A storage device for storing one or more programs that, when executed by one or more processors, enable the one or more processors to implement the fair ranking method based on the Atkinson social welfare function.

[0119] This invention first calculates the trust bias term and location-based project attention in the ranking, then calculates the impact of the ranking on the project, then obtains the double random matrix corresponding to the fair ranking strategy by solving a constrained optimization problem based on the Atkinson social welfare function, and finally uses the BvN decomposition method to decompose the double random matrix to obtain the fair ranking strategy.

[0120] This invention is based on the Atkinson social welfare function, which simultaneously models trust bias and position bias in the ranking, and introduces the principle of fair allocation as the goal of fair ranking. By adopting the idea of ​​Atkinson social welfare, it can achieve different fairness standards and better meet the needs of fairness.

[0121] The invention will be further illustrated below through specific experiments.

[0122] Please see Figure 3 and Figure 4 This is a comparison chart of fairness and utility between the method used in this invention and other methods. FRASW is the method used in this invention, while Uniform, Utility-Max, FOE-DTC, FOE-DIC, and FRFD are methods in the prior art.

[0123] The table below compares the runtime of the method used in this invention with existing methods for optimizing fairness:

[0124] Runtime Comparison (Unit: seconds)

[0125]

[0126] The Util metric represents the utility of ranking for users. MME calculates the average maximum envy generated by each item under ranking strategy π, measuring the envy-free nature of a fair ranking objective. PII calculates the impact of items under ranking strategy π compared to a uniformly random ranking strategy π. unif The percentage of projects increased by at least 10%, measuring the proportionality principle of achieving a fair ranking objective. PDI calculated the impact of ranking strategy π compared to the uniform random ranking strategy π. unif The percentage of projects was reduced by at least 10%, which measures the proportionality principle of the goal of fair ranking.

[0127] Experiments show that the present invention can significantly improve the technical problems of existing methods being unsuitable for situations where there is trust bias in rankings and having difficulty meeting different fairness requirements, and it is more efficient in operation.

[0128] It should be understood that the embodiments described above are only some, not all, of the embodiments of the present invention. Furthermore, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form feasible technical solutions. Such combinations are not constrained by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0129] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A fair ranking method based on the Atkinson social welfare function, characterized in that, Includes the following steps: Step 1: Calculate the ranking position at the [number]th position. Project Trust bias and ;in, and These represent the ranking positions. The click probability of relevant items and the click probability of irrelevant items; in, A binary random variable representing whether a user clicked on an item. A binary random variable to indicate whether a user has checked an item. Let R be a binary random variable representing the relevance of items; relevant items are those with R=1, and irrelevant items are those with R=0. in It is the probability that a user clicks on the first irrelevant item in the ranking position, and is used as a hyperparameter to adjust for trust bias; Step 2: Calculate the project The attention received ; Step 3: Calculate the ranking strategy based on trust bias and attention level. For the project Impact ; ； in, ; Ranking strategy In the middle, the project In ranking position Shown to users The probability of; It is the size of A doubly random matrix, where the sum of each row and each column is 1, meaning the sum of the probabilities of each position is 1 and the sum of the probabilities of each item is also 1, is represented as: and ; m Number of projects; For the ranking system to include A collection of users named [name] For each project For users The relevance score; Step 4: According to Define the objective function based on Atkinson's social welfare. ; Where I represents the inclusion A collection of projects, It is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to items that have lower utility in the ranking, that is, it pays more attention to improving the utility of items that have poor results. Step 5: Obtain a fair ranking strategy by solving the constrained optimization problem. The corresponding double random matrix ; Step 6: Convert the double random matrix Decompose it into a convex combination of permutation matrices and transform it into a ranking strategy. This allows us to sample and obtain a fair ranking that is displayed to users.

2. The fair ranking method based on the Atkinson social welfare function according to claim 1, characterized in that: In step 5, in, Ranking strategy In the middle, the project In ranking position Shown to users The probability of; It is the size of A double random matrix, wherein the sum of each row and each column is 1.

3. The fair ranking method based on the Atkinson social welfare function according to any one of claims 1-2, characterized in that: In step 6, the fair ranking displayed to users is determined by decomposing the double random matrix. get: in, , is the number of permutation matrices generated by the decomposition. m Number of projects; It is a permutation matrix, corresponding to a deterministic ranking. ; yes The coefficient, corresponding to the ranking Probability of being sampled This leads to the random ranking strategy. By a specified probability Ranking Show to users .

4. A fair ranking system based on the Atkinson social welfare function, characterized in that, Includes the following modules: The project trust bias calculation module is used to calculate the ranking position of the [number]th [position]. Project Trust bias and ;in, and These represent the ranking positions. The click probability of relevant items and the click probability of irrelevant items; in, A binary random variable representing whether a user clicked on an item. A binary random variable to indicate whether a user has checked an item. Let R be a binary random variable representing the relevance of items; relevant items are those with R=1, and irrelevant items are those with R=0. in It is the probability that a user clicks on the first irrelevant item in the ranking position, and is used as a hyperparameter to adjust for trust bias; The project attention calculation module is used to calculate project attention. The attention received ; The strategy impact calculation module is used to calculate the ranking strategy based on trust bias and attention level. For the project Impact ; ； in, ; Ranking strategy In the middle, the project In ranking position Shown to users The probability of; It is the size of A doubly random matrix, where the sum of each row and each column is 1, meaning the sum of the probabilities of each position is 1 and the sum of the probabilities of each item is also 1, is represented as: and ; m Number of projects; For the ranking system to include A collection of users named [name] For each project For users The relevance score; The Atkinsonian social welfare objective function definition module is used to define the objective function based on... Define the objective function based on Atkinson's social welfare. ; Where I represents the inclusion A collection of projects, It is an inequality aversion parameter. The larger the value, the more sensitive it is to the degree of unfairness. It also gives more weight to items that have lower utility in the ranking, that is, it pays more attention to improving the utility of items that have poor results. The double random matrix calculation module is used to obtain a fair ranking strategy by solving constrained optimization problems. The corresponding double random matrix ; The fair ranking calculation and display module is used to calculate and display the double random matrix. Decompose it into a convex combination of permutation matrices and transform it into a ranking strategy. This allows us to sample and obtain a fair ranking that is displayed to users.

5. A fair ranking device based on the Atkinson social welfare function, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the fair ranking method based on the Atkinson social welfare function as described in any one of claims 1 to 3.

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