Effective complements to human judgment, artificial intelligence techniques have started to aid human decisions in complicated social problems across the world. In the context of United States for instance, automated ML/DL classification models offer complements to human decisions in determining Medicaid eligibility. However, given the limitations in ML/DL model design, these algorithms may fail to leverage various factors for decision making, resulting in improper decisions that allocate resources to individuals who may not be in the most need. In view of such an issue, we propose in this paper the method of fairgroup construction, based on the legal doctrine of disparate impact, to improve the fairness of regressive classifiers. Experiments on American Community Survey dataset demonstrate that our method could be easily adapted to a variety of regressive classification models to boost their fairness in deciding Medicaid Eligibility, while maintaining high levels of classification accuracy.

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Achieving Fairness in Determining Medicaid Eligibility through Fairgroup Construction


Boli Fang0  Miao Jiang0  Jerry Shen0 

footnotetext: 1AUTHORERR: Missing \icmlaffiliation. . Correspondence to: Boli Fang <>.  
Appearing at the International Conference on Machine Learning AI for Social Good Workshop, Long Beach, United States, 2019.

As defined by the United Nations Sustainable Development Goals, social decision problems in equality, fairness, and sustainability are top priorities for developed and developing nations across the world. In particular, proper allocation of health and medical resources are vital for the well-being of citizens across different countries. While the majority of endeavors in previous work centered on the developing world, one cannot ignore the related issues in developed countries. According to the American Community Survey (Bureau, ), millions of American households are regularly receiving governmental assistance in receiving Medicaid, a compensation scheme designated for low-income individuals to receive proper reimbursement for necessary medical treatment. It is noted in the same dataset that over 16 million households in America are living ”below poverty level”, yet a substantial amount of poor households are not yet receiving Medicaid. On the other hand, out of the households that are receiving Medicaid, a highly non-trivial amount - around 56 - of these households do not live under poverty. Such great disparity behooves the researchers to introduce a complementary decision maker that better takes various factors of the problem into consideration, and recent advancements in Machine Learning and Deep Learning algorithms have offered objective insights into these problems (Morse, 2018).

However, given the limitations of ML/DL algorithms, the issue of fairness has also been the focus for a lot of current machine learning research. Taking into consideration aspects of computational actions and socioeconomic context, previous researchers have focused on two subcategories of fairness as benchmarks - outcome fairness and process fairness. Given the nature of most social welfare programs, which are designed to maximize the interests of individuals and households with low socioeconomic status, outcome fairness is often more important than process fairness.

Moreover, some factors are more important than others when discussing fairness. In the context of Medicaid eligibility, for instance, it is important to include as many individuals living under poverty into the program as possible, while minimizing the number of individuals that do not need such assistance so as to allow for the optimal allocation of the finite monetary and health resources.

Thus, given such considerations, we introduce in this paper a novel method for regressive classification algorithm to more fairly distribute Medicaid resources among individuals. Given an agnostic classifier which might produce biased classification results, we construct fairgroups in the testing data set, and proceed to classify the entire testing set by first classifying representatives of fairgroups and then propagating the decision to other data points. Here, the notion of fairness follows that of disparate impact (Feldman et al., 2015), which calls for similar levels of representation for all the groups of people in different decision outcome classes. Our contributions in this work can be summarized as follows:

  1. We introduce a method to help regressive classifiers to better allocate Medicaid resources by constructing fairgroups, and achieves outcome fairness in the Medicaid Decision Problem with respect to the features that we hope to impose fairness on.

  2. Our algorithm also takes into consideration other features not involved in defining fairness while making decisions on fairness, so that individuals with similar features will be classified in similar ways.

  3. The method to achieve fairness in our paper is easily adaptable to other decision making procedures, such as judicial verdicts, acceptance to educational programs and approval of credit card applications.


Previous work on fairness in machine learning can be largely divided into two groups. The first group has centered on the mathematical definition and existence of fairness (Feldman et al., 2015; Zafar et al., 2017; Chierichetti et al., 2017). Along this track, alternative measures such as statistical parity, disparate impact, and individual fairness (Chierichetti et al., 2017) have been produced. Additionally, Grgic-Hlaca et. al. (2016) covers common notions of fairness and introduces methods of measuring fairness such as feature-apriori fairness, feature-accuracy fairness, and feature-disparity fairness. (Kleinberg et al., 2016) suggested that although it’s not possible to achieve some desired properties of fairness at the same time, including ”protected” features in algorithms would increase the equity and efficiency of machine learning models.

The second group has centered on algorithms to achieve fairness. Along the route of disparate impact, (Feldman et al., 2015) has described algorithms to spot the presence of disparate impact through Support Vector Machine, while (Chierichetti et al., 2017) applied the notion of disparate impact to design an algorithm that achieves balance in unsupervised clustering algorithms. (Chierichetti et al., 2017) also introduces the notion of protected and unprotected features, which we have used in our paper.


In this section we present a novel strategy called fair-grouping to achieve fairness in classification results. This strategy adopts the notion of fairness as related to disparate impact (Feldman et al., 2015), where practices based on neutral rules and laws may still more adversely affect individuals with one protected feature than those without.


We first define the terminology to be used in subsequent description. A protected feature is a feature that carries special importance and is of priority when making relevant decisions. An unprotected feature, on the other hand, is of relative minor importance in decision making. Since the problem in our paper primarily focuses on discrete label classification with discrete features, we assume, without loss of generality and for sake of simplicity, that the protected traits are binary and that the classification label class is also binary. Given a protected feature along with the dataset, the balance of the dataset with respect to is defined as

where refers to the case of all data points having the same feature value of , and refers to the case where . A dataset is -fair with respect to feature if the balance of does not go below a certain number . In other words, a dataset is -disparate with respect to if the groups with 2 different values in have a bounded and relative balanced numerical ratio between and . Following the doctrine of disparate impact as stated in (Feldman et al., 2015), we say that a classification is -fair if the group corresponding to label in the classification class is -fair, meaning that the protected feature is fairly represented with balance at least in group .


We provide in this section the details of the algorithms we will use to achieve fairness in classification. Assume that we already have a classifier which yields predictions for data points and might not yield -fair classification results. Overall, our algorithm constructs fair-groups from testing data, and conducts classification on the data points with while taking the properties of the fairgroups into consideration.

The sections below provide more details of our method.


Most of the social decision problems involve different features of varying degrees of relevance and importance to the goal. To achieve this goal, we compute the correlation coefficient between feature and the outcome to determine the contribution of each feature to the final classification outcome:

We then rank all the features by an increasing order of the absolute values of correlation coefficients, because higher correlation values indicate greater statistical significance in either positive or negative directions. Then, we assign to each feature a weight which is equal to the rank by increasing values of the correlation coefficients. The weight reflects the significance of feature in the classifier.

After constructing the relative weight of each feature from the correlation coefficients, we examine the actual values of for each data point , here denoted by . If a feature is positively correlated with , then we rank all data by the decreasing order of the corresponding ’s of the feature , and define as the rank of in the set of all values of ’s. Alternatively, if a feature has negative correlation, the the data is ranked in increasing order of , and ’s are defined accordingly. Intuitively, the rank ’s show how much influence each feature in data point has to the final classification prediction. These ranks are constructed in a way to make sure that the data points with higher values of are given enough consideration, since higher feature values in socialogical datasets are often likely to correspond to special cases requiring extra attention.

Finally, for each attribute in corresponding to data point , we define as the feature importance index, and define as the feature importance vector corresponding to data point . The feature importance vector reveals information about the relative importance of data point , and such information will be used to construct fairgroups for subsequent fair classification.


With each data point now represented in the form of feature importance vectors, we now examine how close these data points are in terms of the influence each data point might exert to the final classification outcome, and how data points with similar features can be grouped together for easier analysis. To achieve these goals, we define a suitable distance between two vectors and consider a clustering problem where similar data points are grouped together.

Notice that each of the entries in the feature importance vectors are integers corresponding to different rankings, and that closer ranks imply similarity in one feature. Thus, we make use of the Manhattan-L1 distance to describe the distance between feature importance vectors :

Here refers to the number of unprotected features.

Afterwards, we consider a -median cluster algorithm to divide the entire dataset into groups, each containing points with similar feature values. Within each cluster, we look at the protected features. Without loss of generality, we assume that the protected feature is binary, and that our goal is to maintain the balance of the protected feature does not go below a certain threshold . Since this requirement implies that the ratio between and falls between and , we match as many and data points as possible on condition that the ratio between and in each match falls between and . A set consisting of data points in such matches is denoted as a fairgroup.


For each fair-group we have thus constructed, we randomly pick a point to be classified by . If the point is labeled as , we apply the same label to all other data points in the group. Alternatively, if the point is labeled as , we need to take into consideration the properties of the protected feature to determine whether other data points in the same fair-group will be given the same label. For instance, in the case of Food Stamp distribution, protected features such as poverty should be treated as a protected feature only in the positive label class, because our primary goal is to ensure that people receiving food stamps are mainly composed of people living under the poverty threshold. On the other hand, for decision problems that favor similar representation of one feature in different label classes, we need to include the feature in both positive and negative classes. While determining admission eligibility for admission into selective schools, for instance, it is important that the odds of being admitted and rejected are roughly the same across different demographic groups to ensure equality.

Moreover, to reduce the negative effect of potential misclassification as much as possible, we construct as many fairgroups as possible by first expressing and as ratios and , where are co-prime integers. Starting from , we iteratively match data points where with data points where (or data points where with data points where ) depending on whether or is smaller than and closer to the ratio of unmatched . These matched points will form a fairgroup, and corresponding numbers of , points will be moved from the unmatched point set. We repeat the procedure until all the points are matched or unmatchable.This procedure ensures that we create maximal numbers of fairgroups, so that even when one fairgroup is misclassified due to the misclassification of the randomly drawn point, the effects on the overall fairness and consistency can be minimal.


To conduct experiments using the model explained above, we use the United States Census American Community Survey data. Consisting over 2 million entries, the individual level microdata displays important features, including status of receiving Medicaid for a specific household.


The feature importance scores have been calculated using the correlation formula in section 3.2 with respect to the training data. Other variables include disability, number of persons in a household, poverty status, locations, etc. The numerical values of these features are listed in table 1. For this experiment, we have selected household income and poverty status as protected variables because they have the highest importance of the model. To make household income an indicator variable, we have set an experimental threshold of $20000, and define those households earning below the threshold as households to be protected.

Feature Feature importance
Age 0.0783
Division 0.00532
Region 0.00132
State 0.00197
Gender 0.00215
Number of Children 0.00306
Hearing Difficulty 0.0121
Vision Difficulty 0.0121
Ambulatory difficulty 0.0121
Self-care difficulty 0.0121
Class of workers 0.127
Household Income 0.398
Interest Income 0.111
Race 0.00587
Poverty Status 0.1747
Table 1: Feature importance of Medicaid Dataset

Here in our experiments, the target variable is the feature which indicates whether a single individual has finally received medicaid or not. This is a binary feature with two options ’yes’ and ’no’.


We have carried out two sets of experiments to show that our algorithm is able to improve the fairness in the predictive results, as compared to pure regressive classifiers such as logistic regression. By the description of our method, we cluster all household data points into 5 clusters by K-median clustering(Zhu & Shi, 2015). In each cluster, we maintain the same ratio for poverty and non-poverty households by setting the balance as between poverty and non-poverty households, so as to impose a 80% poverty percentage among the people receiving MedicAid.

Table 2 and 3 list the experimental results for different regressive classifiers when the protected features are household income and poverty status respectively. We have experimented on Linear Regression, Logistic Regression and Support Vector Machine, three of the most representative regression models, to demonstrate the effectiveness of our method. We notice that for all three models, our fairgroup construction effectively boosts the level of protected features in fairness, increasing the proportion of poverty by 15 to 20 %. At the same time, the classification accuracy of the respective models remains very high and comparable to the original models. This indicates that the clustering step in our algorithm preserves the similarity between data points in classification.

Method % of Poverty Accuracy
Logistic Regression 67.4 92.6
Linear Regression 65.3 90.2
SVM 68.7 91.5
Logistic + Fairgroup 84.3 89.5
Linear Rgression + Fairgroup 82.7 88.1
SVM + Fairgroup 83.1 88.3

Table 2: Experiment results on Medicaid with Household Income as Protected Feature

Method % of Poverty Accuracy
Logistic Regression 67.4 92.6
Linear Regression 65.3 90.2
SVM 68.7 91.5
Logistic + Fairgroup 84.7 89.3
Linear Rgression + Fairgroup 83.4 86.9
SVM + Fairgroup 83.6 88.9
Table 3: Experimental results on Medicaid with Poverty Level as Protected Feature

In this work we present a novel approach to solve the problem of Medicaid Eligibility Determination through classifiers that achieve fairness in outcome. To achieve our goal, we propose the strategy of fair-group construction, to promote representation of households in poverty in the group of people receiving Medicaid. Experiments on the US Census individual level microdata yields results that are more consistent among samples with similar attributes. As a part of our future work. we hope to apply our method to address the current social problems related to inequality and inequity in both the developed and developing world.


  • (1) Bureau, U. C. American community survey 2017 5-year estimate. URL
  • Chierichetti et al. (2017) Chierichetti, F., Kumar, R., Lattanzi, S., and Vassilvitskii, S. Fair clustering through fairlets. In Advances in Neural Information Processing Systems, pp. 5029–5037, 2017.
  • Feldman et al. (2015) Feldman, M., Friedler, S. A., Moeller, J., Scheidegger, C., and Venkatasubramanian, S. Certifying and removing disparate impact. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 259–268. ACM, 2015.
  • Grgic-Hlaca et al. (2016) Grgic-Hlaca, N., Zafar, M. B., Gummadi, K. P., and Weller, A. The case for process fairness in learning: Feature selection for fair decision making. In NIPS Symposium on Machine Learning and the Law, volume 1, pp.  2, 2016.
  • Kleinberg et al. (2016) Kleinberg, J., Mullainathan, S., and Raghavan, M. Inherent trade-offs in the fair determination of risk scores. arXiv preprint arXiv:1609.05807, 2016.
  • Morse (2018) Morse, S. Artificial intelligence helps insurers identify medicare members who also qualify for medicaid, Nov 2018.
  • Zafar et al. (2017) Zafar, M. B., Valera, I., Rogriguez, M. G., and Gummadi, K. P. Fairness Constraints: Mechanisms for Fair Classification. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, pp. 962–970. PMLR, 2017.
  • Zhu & Shi (2015) Zhu, H. and Shi, Y. Brain storm optimization algorithms with k-medians clustering algorithms. In 2015 Seventh International Conference on Advanced Computational Intelligence (ICACI), pp. 107–110. IEEE, 2015.
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