Multiwinner Voting with Fairness Constraints
Authors: L. Elisa Celis, Lingxiao Huang, Nisheeth K. Vishnoi
IJCAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case. ... Empirically, we show that existing multiwinner voting rules may introduce bias and that our approach not only ensures fairness, but does so with a score that is close to the (unconstrained) optimal (see Section 7). ... 7 Empirical Results ... We report the mean and the standard deviation of the Gini index, and the mean of the score ratio of 1000 repetitions in Table 3... |
| Researcher Affiliation | Academia | L. Elisa Celis, Lingxiao Huang, Nisheeth K. Vishnoi EPFL, Switzerland first.last@epfl.ch |
| Pseudocode | Yes | Algorithm Degree One. 1. Compute a fractional solution y B by the continuous greedy algorithm in [Calinescu et al., 2011, Section 3.1]. 2. For j [p], iteratively do the following until Pj has at most 1 non-integral coordinate: Arbitrarily select two candidates ci, ci Pj with fractional coordinates yi, yi . Let δ1 = min {1 yi, yi } and δ2 = min {yi, 1 yi }. Let ei = (0, . . . , 0, 1, 0, . . . , 0) {0, 1}m. Construct two vectors y1 = y+δ1(ei ei ) and y2 = y+δ2(ei ei). Let y y1 with probability δ2/δ1+δ2 and y y2 otherwise. 3. W.l.o.g., assume y1, . . . , yγ are the remaining fractional coordinates. Iteratively do the same procedure as in Step 2 until y becomes an integral solution. 4. Output S whose indicator vector is y = 1S. |
| Open Source Code | No | The paper does not provide any specific links or explicit statements about releasing open-source code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data ('We generate 400 voters and 120 candidates...'), but does not provide access information (link, DOI, specific repository, or formal citation with authors/year) for this specific generated dataset to make it publicly available. |
| Dataset Splits | No | The paper does not specify explicit training/validation/test dataset splits with percentages, sample counts, or references to predefined splits for reproduction. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., GPU/CPU models, memory amounts, or cloud instances) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | Yes | We generate 400 voters and 120 candidates where each voter and candidate is represented by a point in the [ 3, 3] [ 3, 3] square. 1/4 of the voters are sampled uniformly at random from each quadrant, and 1/3 of the candidates are sampled uniformly from the first quadrant, 1/4 the second quadrant, 1/6 the third quadrant, and 1/4 the fourth quadrant. As in [Elkind et al., 2017], we use Euclidean preferences; given a pair of candidates ci, cj R2, a voter a R2 prefers ci to cj if d (ci, a) < d (cj, a) where d ( , ) is the Euclidean distance. ... In all cases, we let k = 12 be the size of the desired committee. ... We consider each quadrant to be a different group, and let Pi be the collection of candidates in the i-th quadrant. We compare the performance of three different types of constraints to the unconstrained optimal solution and the random baseline. Proportional w.r.t. voters: the number of winners is proportional to the number of voters in each quadrant. Proportional w.r.t. candidates: The number of winners is proportional to the number of candidates in each quadrant. Relax: The number of winners in each quadrant is allowed to be anywhere in the range between what would be proportional to voters and proportional to candidates. |