Analysis of top to bottom-kk shuffles

A deck of $n$ cards is shuffled by repeatedly moving the top card to one of the bottom $k_n$ positions uniformly at random. We give upper and lower bounds on the total variation mixing time for this shuffle as $k_n$ ranges from a constant to $n$. We also consider a symmetric variant of this shuffle in which at each step either the top card is randomly inserted into the bottom $k_n$ positions or a random card from the bottom $k_n$ positions is moved to the top. For this reversible shuffle we derive bounds on the $L^2$ mixing time. Finally, we transfer mixing time estimates for the above shuffles to the lazy top to bottom-$k$ walks that move with probability 1/2 at each step.Comment: Published at http://dx.doi.org/10.1214/10505160500000062 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Measure and Mismeasure of Fairness: A Critical Review of Fair Machine Learning

The nascent field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last several years, three formal definitions of fairness have gained prominence: (1) anti-classification, meaning that protected attributes---like race, gender, and their proxies---are not explicitly used to make decisions; (2) classification parity, meaning that common measures of predictive performance (e.g., false positive and false negative rates) are equal across groups defined by the protected attributes; and (3) calibration, meaning that conditional on risk estimates, outcomes are independent of protected attributes. Here we show that all three of these fairness definitions suffer from significant statistical limitations. Requiring anti-classification or classification parity can, perversely, harm the very groups they were designed to protect; and calibration, though generally desirable, provides little guarantee that decisions are equitable. In contrast to these formal fairness criteria, we argue that it is often preferable to treat similarly risky people similarly, based on the most statistically accurate estimates of risk that one can produce. Such a strategy, while not universally applicable, often aligns well with policy objectives; notably, this strategy will typically violate both anti-classification and classification parity. In practice, it requires significant effort to construct suitable risk estimates. One must carefully define and measure the targets of prediction to avoid retrenching biases in the data. But, importantly, one cannot generally address these difficulties by requiring that algorithms satisfy popular mathematical formalizations of fairness. By highlighting these challenges in the foundation of fair machine learning, we hope to help researchers and practitioners productively advance the area

The limits of human predictions of recidivism.

Dressel and Farid recently found that laypeople were as accurate as statistical algorithms in predicting whether a defendant would reoffend, casting doubt on the value of risk assessment tools in the criminal justice system. We report the results of a replication and extension of Dressel and Farid's experiment. Under conditions similar to the original study, we found nearly identical results, with humans and algorithms performing comparably. However, algorithms beat humans in the three other datasets we examined. The performance gap between humans and algorithms was particularly pronounced when, in a departure from the original study, participants were not provided with immediate feedback on the accuracy of their responses. Algorithms also outperformed humans when the information provided for predictions included an enriched (versus restricted) set of risk factors. These results suggest that algorithms can outperform human predictions of recidivism in ecologically valid settings

Herbivore: A Scalable and Efficient Protocol for Anonymous Communication

Anonymity is increasingly important for networked applications amidst concerns over censorship and privacy. In this paper, we describe Herbivore, a peer-to-peer, scalable, tamper-resilient communication system that provides provable anonymity and privacy. Building on dining cryptographer networks, Herbivore scales by partitioning the network into anonymizing cliques. Adversaries able to monitor all network traffic cannot deduce the identity of a sender or receiver beyond an anonymizing clique. In addition to strong anonymity, Herbivore simultaneously provides high efficiency and scalability, distinguishing it from other anonymous communication protocols. Performance measurements from a prototype implementation show that the system can achieve high bandwidths and low latencies when deployed over the Internet

Popular Support for Balancing Equity and Efficiency in Resource Allocation: A Case Study in Online Advertising to Increase Welfare Program Awareness

Algorithmically optimizing the provision of limited resources is commonplace across domains from healthcare to lending. Optimization can lead to efficient resource allocation, but, if deployed without additional scrutiny, can also exacerbate inequality. Little is known about popular preferences regarding acceptable efficiency-equity trade-offs, making it difficult to design algorithms that are responsive to community needs and desires. Here we examine this trade-off and concomitant preferences in the context of GetCalFresh, an online service that streamlines the application process for California's Supplementary Nutrition Assistance Program (SNAP, formerly known as food stamps). GetCalFresh runs online advertisements to raise awareness of their multilingual SNAP application service. We first demonstrate that when ads are optimized to garner the most enrollments per dollar, a disproportionately small number of Spanish speakers enroll due to relatively higher costs of non-English language advertising. Embedding these results in a survey (N = 1,532) of a diverse set of Americans, we find broad popular support for valuing equity in addition to efficiency: respondents generally preferred reducing total enrollments to facilitate increased enrollment of Spanish speakers. These results buttress recent calls to reevaluate the efficiency-centric paradigm popular in algorithmic resource allocation.Comment: This paper will be presented at the 2023 International Conference on Web and Social Media (ICWSM'23

Reevaluating the Role of Race and Ethnicity in Diabetes Screening

There is active debate over whether to consider patient race and ethnicity when estimating disease risk. By accounting for race and ethnicity, it is possible to improve the accuracy of risk predictions, but there is concern that their use may encourage a racialized view of medicine. In diabetes risk models, despite substantial gains in statistical accuracy from using race and ethnicity, the gains in clinical utility are surprisingly modest. These modest clinical gains stem from two empirical patterns: first, the vast majority of individuals receive the same screening recommendation regardless of whether race or ethnicity are included in risk models; and second, for those who do receive different screening recommendations, the difference in utility between screening and not screening is relatively small. Our results are based on broad statistical principles, and so are likely to generalize to many other risk-based clinical decisions.Comment: 11 pages, 4 figure