Fairness judgment device, fairness judgment method, and fairness judgment program

Abstract

To provide a fairness determining apparatus, a fairness determining method and a fairness determining program which can efficiently determine fairness in view of performance-based evaluation in matching.SOLUTION: A fairness determination apparatus 1 according to the present invention has a selected order acquiring unit 11 for acquiring a selected order of a pair of two groups with respect to each element, a popularity calculating unit 12 for calculating popularity of each element by integrating selected orders, a popularity order calculating unit 13 for sorting the respective elements in an ascending order of popularity to give a popularity order to each element, a determination table generating unit 14 for generating a determination table storing the minimum value or the maximum value of the selected order with respect to each popularity order, a table-by-table determination unit 15 for determining that conditions are satisfied if in the determination table there is no i where the maximum values of selected orders of first to ith popularity is larger than the minimum value +1 of the selected orders of i+k+1th popularity orders, and a fairness determination unit 16 for determining fairness in view of performance-based evaluation if the conditions are satisfied with respect to both of the two groups.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an apparatus, a method, and a program for determining the fairness of a match. [Background technology]

[0002] The optimization problem of matching in a bipartite graph has long been studied as a mathematical model for the problem of allocating workers to jobs. Matching that optimizes overall satisfaction is reduced to a minimum flow problem in a weighted minimal complete bipartite graph. The stable marriage problem in Non-Patent Document 1 is a problem that adopts the concept of stability to this matching, and stable matching can be found in O(n 2 An algorithm has been proposed to find the

[0003] Various extension problems have been considered for the stable marriage problem, and fairness is one area of ​​extension problems. The stable matching found by the algorithm in Non-Patent Document 1 is the optimal matching for either the man or the woman, and the optimization of the overall cost was not taken into consideration. Therefore, optimization problems that extend the stable marriage problem, such as minimum-cost stable matching, minimum-regret stable matching (Non-Patent Document 2), and gender-equality stable matching (Non-Patent Document 3), have been studied. These problems aim for fairness in the sense of global optimization.

[0004] However, such a matching result that satisfies fairness through global optimization may, for example, cause a relative disadvantage to participants with high abilities or high evaluations. Non-Patent Document 4 defines meritocratic fairness in problems such as male-female matching, which is not necessarily stable, and also proposes an index that can quantitatively evaluate the degree of meritocratic fairness. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] D. Gale and L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, Vol. 69, pp. 9-15, 1962. [Non-Patent Document 2] R. W. Irving, P. Leather, and D. Gusfield. An efficient algorithm for the "optimal" stable marriage. Journal of the ACM, Vol. 34, No. 3, pp. 532-543, 1987. [Non-Patent Document 3] A. Kato. Complexity of the sex-equal stable marriage problem. Japan Journal of Industrial and Applied Mathematics, Vol. 10, pp. 1-19, 1993. [Non-Patent Document 4] Toru Nakamura, Shuya Nitta, Takamasa Isahara. Individualistic fairness in matching and its violation detection. Computer Security Symposium 2021 (CSS2021), Vol. 1D1-1, 2021. [Summary of the Invention] [Problems to be Solved by the Invention]

[0006] In Non-Patent Document 4, a definition of meritocratic fairness was proposed, but an efficient method for determining whether a matching satisfies meritocratic fairness was not mentioned. For this reason, when searching for a fair matching, the processing load required for determining fairness, which occurs each time a matching candidate is obtained, has been a problem.

[0007] An object of the present invention is to provide a fairness determination device, a fairness determination method, and a fairness determination program that can efficiently determine meritocratic fairness in matching. [Means for solving the problem]

[0008] The fairness determination device according to the present invention includes a preference ranking acquisition unit that acquires preference rankings of pairs in each element of two mutually prime sets from the preference ranking of the other set in each element of the two sets and information on pairs matched between the two sets; a popularity calculation unit that combines the preference rankings for each element of the two sets to calculate a popularity of each element; a popularity ranking calculation unit that sorts each element of the two sets in ascending order of the popularity and assigns the same popularity ranking to elements with the same popularity ranking; and a popularity ranking calculation unit that calculates a popularity ranking for each of the two sets by comparing the popularity rankings of the elements with the popularity rankings of the other set and information on pairs matched between the two sets. The system includes a judgment table generation unit that generates a judgment table storing the minimum and maximum values ​​of the preference rankings, a table-specific judgment unit that judges that a condition is met if there is no i in the judgment table where the maximum value of the preference rankings up to the i-th popularity ranking is greater than the minimum value+l of the preference ranking for the i+k+1th popularity ranking, and that the condition is not met if there is such a value, and a fairness judgment unit that judges that meritocratic fairness is met if it is judged that the condition is met for both of the two sets, and that it is not meritocratic fair if it is judged that the condition is not met for either of them.

[0009] The popularity ranking calculation unit may sort the elements in ascending order of the popularity and in ascending order of the preference ranking of the pair.

[0010] The judgment table generating unit may omit storing the maximum value of the preference ranking in the maximum popularity ranking for each of the two sets.

[0011] The judgment table generating unit may omit storing the minimum value of the preference ranking in the minimum popularity ranking for each of the two sets.

[0012] The fairness determination method according to the present invention includes a preference ranking acquisition step of acquiring a preference ranking of pairs in each element of two mutually prime sets from the preference ranking of the other set in each element of the two sets and information on pairs matched between the two sets; a popularity calculation step of combining the preference rankings for each element of the two sets to calculate a popularity of each element; a popularity calculation step of sorting each element of the two sets in ascending order of the popularity and assigning the same popularity ranking to elements with the same popularity ranking; and a preference ranking calculation step of calculating the preference ranking for each popularity ranking for each of the two sets. a table-by-table determination step of determining that a condition is satisfied if there is no i in the determination table in which the maximum value of the preference rankings up to the i-th popularity ranking is greater than the minimum value+l of the preference rankings for the i+k+1th popularity ranking, and that the condition is not satisfied if there is such a value; and a fairness determination step of determining that meritocratic fairness is satisfied if it is determined that the condition is satisfied for both of the two sets, and determining that meritocratic fairness is not satisfied if it is determined that the condition is not satisfied for either of the two sets.

[0013] A fairness determination program according to the present invention causes a computer to function as the fairness determination device. Effect of the Invention

[0014] According to the present invention, meritocratic fairness in matching can be determined efficiently. [Brief description of the drawings]

[0015] [Figure 1] FIG. 2 is a diagram illustrating a functional configuration of a fairness determination device according to an embodiment. [Diagram 2] FIG. 13 is a diagram showing an algorithm by which a preference ranking acquisition unit in the embodiment obtains preference rankings of pairs. [Diagram 3] FIG. 13 is a diagram showing an algorithm used by a popularity calculation unit in the embodiment to calculate the popularity of each element. [Figure 4] FIG. 13 is a diagram showing an algorithm used by a popularity ranking calculation unit in the embodiment to calculate the popularity ranking of each element. [Diagram 5] 11 is a diagram showing an algorithm by which a judgment table generating unit generates a judgment table in the embodiment. FIG. [Figure 6] FIG. 13 is a diagram illustrating an algorithm used by a table-by-table determination unit in an embodiment to determine meritocratic fairness for each determination table. [Figure 7] FIG. 13 is a diagram showing an algorithm by which the fairness determination unit 16 in the embodiment determines relaxed (k, l)-meritocratic fairness. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] An example of an embodiment of the present invention will now be described. The fairness determination method of this embodiment uses a matching obtained in a bipartite graph as an input and quickly determines whether the matching satisfies meritocratic fairness. Here, male-female matching is used as an example, but this embodiment can also be applied to similar use cases such as job matching.

[0017] A matching instance I consists of two relatively prime sets M and W of size n, where M is the set of men and W is the set of women, and each set has a strict total ordering, called the preference order, with respect to the elements of the other set. A matching X is a pair of M and W. That is, X ⊆ M × W. For simplicity, we will only consider the case where n one-to-one pairs are created.

[0018] In a matching X, a man m and a woman w are a pair, i.e., (m,w)∈X, then we express X(m)=w,X(w)=m. Also, the ranking of w in the preference order of m is P m (w), which is called the preference rank of w in m. Similarly, the preference rank of m in w is P w This is expressed as (m).

[0019] In this embodiment, individualistic fairness refers to the idea that those with higher abilities or evaluations will be more likely to achieve what they want. In matching between men and women, a person who tends to be designated as having a higher (lower) preference order by the opposite sex is considered to be a person with a higher evaluation.

[0020] Here, a person is quantitatively evaluated based on the sum of preference rankings from all opposite-sex people, and compared with others of the same sex. For any person a in a match, if the preference ranking of the other person paired with the other person of the same sex b, who is rated lower than person a, is always lower (higher) or equal to the preference ranking of the other person paired with person a, then the match is considered to be individualistically fair.

[0021] For m ∈ M and w ∈ W, G(m) = Σ n i=1 P wi (m) and G(w) = Σ n i=1 P mi Let (w) be the popularity of m and w, respectively. Let R(m) be the rank of m when the set of men M is sorted in ascending order of popularity G(m), and call this the popular rank of m. Similarly, let R(w) be the popularity rank of w when the set of women W is sorted in ascending order of popularity G(w). It should be noted that for a certain member m or w, the smaller the popularity G and popularity ranking R, the more popular the member is with the opposite sex. Here, for a set H and a natural number p∈N, let us define a subset of H whose popularity ranking is smaller than p (highly rated). <p Then, individualistic fairness can be defined as follows:

[0022] Definition 1: For any m∈M and w∈W, (1) For any m′∈M <R(m) About P m′ (X(m′))≦P m(X(m)) and, (2) For any w′∈W <R(w) About P w′ (X(w′))≦P w (X(w)) A matching X is strictly meritocratically fair if

[0023] However, a strictly meritocratically fair matching that satisfies the conditions of Definition 1 does not necessarily exist for any preference ordering. In addition, there may be a matching that satisfies strict meritocratic fairness but significantly impairs global optimality. Therefore, we present a definition of meritocratic fairness based on the following relaxed conditions. Allow same-sex people with a lower popularity ranking than you to be matched with people of the opposite sex who have a lower preference ranking than you. For two people of the same sex, if the difference in preference rankings between their matched partners is within l, it is considered to be 0 and is accepted.

[0024] Definition 2: For any m∈M and w∈W, (1) For any m′∈M <R(m)-k About P m′ (X(m′))≦P m (X(m))+l and, (2) For any w′∈W <R(w)-k About P w′ (X(w′))≦P w (X(w))+l If X satisfies the above, then the matching X is (k, l)-meritocratically fair.

[0025] Next, the functional configuration of the device for determining relaxed meritocratic fairness and the processing algorithm are shown. In addition, strict meritocratic fairness can also be determined using this algorithm, since it is a special case of relaxed (k, l)-meritocratic fairness where k = 0, l = 0.

[0026] Here, the set of men is M={m 1 ,m 2 ,…,m n}, and the set of women is W={w 1 ,w 2 ,…,w n} Let M and W be arrays, and element a of these arrays be a structure having attributes a.pref_rank, a.popularity, and a.pop_rank. a.pref_rank is the preference ranking of a for pair a, i.e., P a (X(a)). Also, a.popularity and a.pop_rank are the popularity and popularity ranking of a, respectively.

[0027] FIG. 1 is a diagram showing the functional configuration of a fairness determination device 1 in this embodiment. The fairness determination device 1 is an information processing device (computer) such as a server device or a personal computer, and includes a control unit 10 and a storage unit 20, as well as input / output devices and communication devices for various data.

[0028] The control unit 10 is a part that controls the entire fairness determination device 1, and realizes each function in this embodiment by appropriately reading and executing various programs stored in the storage unit 20. The control unit 10 may be a CPU.

[0029] The memory unit 20 is a storage area for various programs, including a fairness judgment program for causing a hardware group to function as a fairness judgment device 1, and various data, and may be a ROM, RAM, flash memory, or hard disk drive (HDD), etc.

[0030] The control unit 10 includes a preference ranking acquisition unit 11 , a popularity calculation unit 12 , a popularity ranking calculation unit 13 , a judgment table generation unit 14 , a table-specific judgment unit 15 , and a fairness judgment unit 16 .

[0031] The preference ranking acquisition unit 11 acquires the preference ranking of pairs in each element of each of two mutually prime sets M and W from the preference ranking of the other set in each element of the two sets, and information on pairs matched between these two sets.

[0032] FIG. 2 is a diagram showing an algorithm PreferenceRank with which the preference ranking obtaining unit 11 in this embodiment obtains the preference ranking of pairs. The inputs are an instance of a matching, I, and a matching, X, (Step 1). Note that I is two arrays of length n (=|M|=|W|) whose elements are lists of preference orders of length n.

[0033] The preference ranking acquisition unit 11 performs a loop (step 2) for n elements to obtain the preference ranking P of the pair X(M[i]) for the attribute pref_rank of the i-th element M[i] in the array M. M[i] Store (X(M[i])) (Step 3). Similarly, the preference ranking acquisition unit 11 obtains the preference ranking P of the pair X(W[i]) for the attribute pref_rank of the i-th element W[i] in the array W. W[i] Store (X(W[i])) (step 4).

[0034] The preference ranking acquisition unit 11 outputs arrays M and W in which the preference ranking of pairs for each element is stored in the attribute pref_rank (step 6).

[0035] The popularity calculation unit 12 sums up the preference rankings for each element of the two sets M and W, and calculates the popularity of each element.

[0036] FIG. 3 is a diagram showing the Popularity algorithm used by the popularity calculation unit 12 in this embodiment to calculate the popularity of each element. The inputs are a matching instance I and two arrays M and W (Step 1).

[0037] The popularity calculation unit 12 performs a double loop (steps 2 and 3) for n elements, and adds the preference ranking of M[i] in each element of array W to the attribute popularity of the i-th element M[i] in array M for all elements (step 4). Similarly, the popularity calculation unit 12 adds the preference ranking of W[i] in each element of array M to the attribute popularity of the i-th element W[i] in array W for all elements (step 5).

[0038] The popularity calculation unit 12 outputs arrays M and W in which the popularity of each element is stored in the attribute popularity (step 8).

[0039] The popularity ranking calculation unit 13 assigns a popularity ranking to each of the two sets by sorting the elements in ascending order of popularity. At this time, the popularity ranking calculation unit 13 assigns the same popularity ranking to elements with the same popularity value. Furthermore, the popularity ranking calculation unit 13 may sort the elements in ascending order of popularity and in ascending order of preference ranking of pairs to make the subsequent processing more efficient.

[0040] FIG. 4 is a diagram showing the algorithm PopularRank used by the popularity ranking calculation unit 13 in this embodiment to determine the popularity ranking of each element. The input is an array in which the preference order and popularity are assigned as attributes of each element, and M and W are input in that order.

[0041] First, the popularity ranking calculation unit 13 obtains an array A' by sorting the input array A in ascending order of popularity and preference ranking using the function Sort(A) (step 2). Note that Sort(A) is a function that sorts the input array A in ascending order by the value of the attribute popularity, and in the case of a tie, outputs an array A' that has been further sorted in ascending order by the attribute pref_rank.

[0042] Next, the popularity ranking calculation unit 13 initializes the variables pre_score and next_rank to 0 (steps 3 and 4), and then performs a loop process n times (the number of elements) (step 5).

[0043] In the loop, if the popularity of the i-th element of array A' (score=A'[i].popularity) is different (greater) than pre_score, the popularity ranking calculation unit 13 updates next_rank to i (step 8) and updates pre_score to score (step 9).Then, the popularity ranking calculation unit 13 stores next_rank in the popularity ranking (A'[i].pop_rank) (step 11). That is, if i increases but the popularity remains the same (FALSE in step 7), next_rank is not updated and the same popularity ranking is assigned. On the other hand, if the popularity increases (TRUE in step 7), the increased popularity ranking (=i) is assigned.

[0044] The popularity ranking calculation unit 13 outputs an array A' in which the popularity ranking of each element is stored in the attribute pop_rank (step 13).

[0045] The judgment table generating unit 14 generates a judgment table that stores the minimum and maximum values ​​of the preference ranking for each popularity ranking for each of the two sets.

[0046] FIG. 5 is a diagram showing an algorithm MakeTable by which the decision table generating unit 14 generates a decision table in this embodiment. The input is an array in which the attribute of each element is assigned a preference order, popularity, and popularity order, and the arrays M' and W' sorted by the popularity order calculation unit 13 are input in that order.

[0047] First, the decision table generating unit 14 initializes the minimum value (Table[i].min) and the maximum value (Table[i].max) stored in the decision table to 0 by loop processing the number of elements n times (step 2) (steps 3 and 4). Next, the variables pre_pop_rank, pre_pref_rank, and pre_index are initialized to 0, 0, and 1, respectively (steps 6 to 8).

[0048] Next, during loop processing of n elements (step 9), if the popularity ranking (A[i].pop_rank) of the i-th element of the input array A changes (becomes larger) than pre_pop_rank (step 10), the judgment table generation unit 14 stores A[i].pref_rank in Table[i].min (the minimum value of the preference ranking in the i-th popularity ranking) and pre_pref_rank in Table[pre_index].max (the maximum value of the preference ranking in the previous popularity ranking) in the judgment table (steps 11 and 12). Furthermore, since the decision table generating unit 14 has updated the i-th element (min) of the decision table, it updates pre_index to i (step 13).

[0049] On the other hand, if the popularity ranking (A[i].pop_rank) of the i-th element of array A remains the same as pre_pop_rank (step 10), the judgment table generation unit 14 suspends storage of the value in the judgment table and updates pre_pop_rank to A[i].pop_rank and pre_pref_rank to A[i].pref_rank, respectively (steps 15 and 16).

[0050] The decision table generating unit 14 outputs a decision table Table having the popularity order as an index and the range of preference order (minimum preference order min and maximum preference order max) for each popularity order as an attribute (step 18).

[0051] In addition, since the maximum value A[n].max of the preference ranking at the maximum popularity ranking and the minimum value A[1].min of the preference ranking at the minimum popularity ranking are not referenced in subsequent processing, the judgment table generation unit 14 may omit storing these values.

[0052] The table-by-table judgment unit 15 judges that the condition of meritocratic fairness is satisfied if there is no i in the generated judgment table such that the maximum value of the preference rankings up to the i-th popularity ranking is greater than the minimum value of the preference rankings for the i+k+1th popularity ranking + l, and that the condition is not satisfied if there is such a value.

[0053] FIG. 6 is a diagram showing an algorithm Judge that the table-by-table judgement unit 15 uses in this embodiment to judge meritocratic fairness for each judgement table. The inputs are the decision table Table and constants k and l related to relaxed fairness conditions.

[0054] First, the table-by-table determination unit 15 initializes a variable prefer_max to 0 (step 2).

[0055] Next, the table-specific determination unit 15 compares prefer_max with Table[i].max (step 4) in a loop process (step 3) that changes the index i from 1 to nk-1. If Table[i].max is larger, the table-specific determination unit 15 updates prefer_max (step 5). As a result, the maximum value of the preference ranking in the popularity ranking up to the i-th rank is stored in prefer_max.

[0056] Furthermore, in the loop process (step 3), the table-specific judgment unit 15 compares prefer_max with the minimum value (Table[i+k+1]) of the preference ranking in the (i+k+1)th popularity ranking. If Table[i+k+1] is not 0 and the difference with prefer_max is greater than l, it is judged that the condition of meritocratic fairness is not satisfied (steps 7 to 9). On the other hand, if Table[i+k+1] is 0 for all i or the difference with prefer_max is equal to or less than l, it is judged that the condition of meritocratic fairness is satisfied (step 11).

[0057] The fairness judgment unit 16 judges that the judgment tables generated from both the two sets M and W are meritocratic fair if the table-specific judgment unit 15 judges that the conditions are met, and judges that the judgment tables are not meritocratic fair if the table-specific judgment unit 15 judges that the conditions are not met for either of the judgment tables.

[0058] FIG. 7 is a diagram showing an algorithm, FairJudge, for determining relaxed (k, l)-meritocratic fairness by the fairness determining unit 16 in this embodiment. The inputs are an instance of a matching, I, a matching, X, and constants k and l for the relaxed conditions.

[0059] First, the fairness determination unit 16 uses the preference ranking acquisition unit 11 (algorithm PreferenceRank) to store preference rankings in arrays M and W (step 2). Next, the fairness determination unit 16 uses the popularity calculation unit 12 (algorithm Popularity) to obtain arrays M' and W' that further store the popularity (step 3). Furthermore, the fairness determination unit 16 uses the popularity ranking calculation unit 13 (algorithm PopularRank) to obtain arrays M″ and W″ that store the popularity rankings (steps 4 and 5).

[0060] Next, the fairness determination unit 16 uses the determination table generation unit 14 (algorithm MakeTable) to obtain the determination tables Table_M and Table_W from the arrays M'' and W'', respectively (steps 6 and 7). Next, the fairness determination unit 16 uses the table-specific determination unit 15 (algorithm Judge) to determine whether or not the fairness conditions are satisfied for each of the determination tables Table_M and Table_W (steps 8 and 9). Then, if all of the judgment tables satisfy the fairness conditions (step 10), the fairness judgment unit 16 judges that meritocratic fairness is satisfied as a whole (step 11), and if at least any of the conditions are not satisfied, it judges that meritocratic fairness is not satisfied (step 13).

[0061] According to this embodiment, the fairness determination device 1 generates a determination table that stores the minimum and maximum values ​​of the preference ranking for each popularity ranking for each of the two sets, and determines that the condition is met if there is no i in which the maximum value of the preference ranking up to the i-th popularity ranking is greater than the minimum value+l of the preference ranking for the i+k+1th popularity ranking in this determination table, and determines that the condition is not met if there is such a value. As a result, the fairness determination device 1 determines that meritocratic fairness is met if it is determined that the condition is met for both of the two sets, and determines that meritocratic fairness is not met if it is determined that the condition is not met for either of the sets. As a result, the fairness judgment device 1 can judge meritocratic fairness by performing only one loop process in the algorithm Judge using the judgment table. Therefore, in a judgment method that simply follows the definition of fairness, each element of a set is compared with other elements, which requires O(n 2 ), the amount of calculation is expected to be O(n) in this embodiment. As a result, the processing load required to search for a match that satisfies meritocratic fairness is significantly reduced.

[0062] In addition, the fairness determination device 1 sorts each element of the set in ascending order of popularity and in ascending order of pair preference ranking, thereby making the algorithms MakeTable and Judge more efficient and further reducing the processing load.

[0063] Furthermore, the fairness determination device 1 can improve efficiency by omitting storage of data that is not used in the algorithm Judge in the determination table. Specifically, for each of the two sets, storage of the maximum value of the preference order in the maximum popularity order and / or the minimum value of the preference order in the minimum popularity order may be omitted.

[0064] This will make it possible, for example, to efficiently provide a meritocratic and fair matching service over the Internet, which will contribute to Goal 9 of the United Nations-led Sustainable Development Goals (SDGs), which is to "build resilient infrastructure, promote sustainable industrialization and foster innovation."

[0065] Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments. Furthermore, the effects described in the above-described embodiments are merely a list of the most preferable effects resulting from the present invention, and the effects of the present invention are not limited to those described in the embodiments.

[0066] The fairness determination method by the fairness determination device 1 is realized by software. When realized by software, a program constituting this software is installed in an information processing device (computer). These programs may be recorded on a removable medium such as a CD-ROM and distributed to users, or may be distributed by being downloaded to the user's computer via a network. Furthermore, these programs may be provided to the user's computer as a Web service via a network without being downloaded. [Explanation of symbols]

[0067] 1 Fairness judgment device 10 Control section 11 Preference ranking acquisition part 12 Popularity Calculation Section 13 Popularity Ranking Calculation Section 14. Decision table generation unit 15 Table Judgment Section 16 Fairness Judgment Department 20 Memory section

Claims

1. a preference ranking acquisition unit that acquires preference rankings of pairs in each element of each of two disjoint sets from a preference ranking of the other set in each element of each of the two sets and information on pairs matched between the two sets; a popularity calculation unit that combines the preference rankings for each element of the two sets and calculates the popularity of each element; a popularity ranking calculation unit that sorts each element of each of the two sets in ascending order of the popularity and assigns the same popularity ranking to elements having the same popularity ranking; a judgment table generating unit that generates a judgment table storing the minimum and maximum values ​​of the preference ranking for each of the popularity rankings for each of the two sets; a table-based determination unit that determines that a condition is satisfied when there is no i in the determination table in which the maximum value of the preference ranking up to the i-th popularity ranking is greater than a minimum value+l of the preference ranking for the (i+k+1)th popularity ranking, and that the condition is not satisfied when there is such a i; a fairness determination unit that determines that the system is meritocratic fair if it is determined that the condition is satisfied for both of the two sets, and that the system is not meritocratic fair if it is determined that the condition is not satisfied for either of the sets.

2. 2 . The fairness determination device according to claim 1 , wherein when sorting the elements in ascending order of the popularity, the popularity ranking calculation unit sorts the elements in ascending order of the preference ranking of the pair when the popularity rankings have the same value.

3. 3. The fairness determination device according to claim 1, wherein the determination table generating unit omits storage of the maximum value of the preference ranking in the maximum popularity ranking for each of the two sets.

4. 4. The fairness determination device according to claim 1, wherein the determination table generating section omits storage of the minimum value of the preference order in the minimum popularity order for each of the two sets.

5. a preference ranking acquisition step of acquiring preference rankings of pairs in each element of each of two disjoint sets from the preference rankings of the other set in each element of each of the two sets and information on pairs matched between the two sets; a popularity calculation step of calculating the popularity of each element by combining the preference rankings of each element in each of the two sets; a popularity ranking calculation step of sorting each element of each of the two sets in ascending order of the popularity and assigning the same popularity ranking to elements having the same popularity value; a judgment table generating step of generating a judgment table in which the minimum and maximum values ​​of the preference rankings are stored for each of the popularity rankings for each of the two sets; a table-by-table judging step for judging that a condition is satisfied when there is no i in the judgment table, the maximum value of the preference ranking up to the i-th popularity ranking being greater than the minimum value+l of the preference ranking of the (i+k+1)th popularity ranking, and that the condition is not satisfied when there is such a i; a fairness determination step of determining that the system is meritocratic fair if it is determined that the condition is satisfied for both of the two sets, and determining that the system is not meritocratic fair if it is determined that the condition is not satisfied for either of the two sets.

6. A fairness determination program for causing a computer to function as the fairness determination device according to any one of claims 1 to 4.

Images