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Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
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    Adversaries can manipulate rank aggregation by fabricating data during collection. This study proposes sequential manipulation policies, demonstrating their effectiveness even with incomplete knowledge.

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    Area of Science:

    • Social Sciences
    • Computer Science
    • Game Theory

    Background:

    • Rank aggregation using pairwise comparisons is prevalent across various fields like sociology, politics, and economics.
    • The significant social impact of rankings incentivizes adversaries to manipulate them, but existing methods are impractical due to attack constraints.

    Purpose of the Study:

    • To explore the risks of rank manipulation by targeting the data collection process.
    • To model the adversarial scenario as a distributionally robust game and analyze vulnerabilities in sampling algorithms.

    Main Methods:

    • Formulating the confrontation between a manipulator and data controller as a distributionally robust game.
    • Analyzing the vulnerability of sampling algorithms (e.g., Bernoulli, reservoir sampling).
    • Proposing sequential manipulation policies under a Bayesian decision framework and developing a distributionally robust estimator for incomplete knowledge.

    Main Results:

    • Demonstrating that the game equilibrium favors the adversary due to sampling algorithm vulnerabilities.
    • Establishing asymptotic optimality of proposed policies for attackers with complete knowledge.
    • Showing that a distributionally robust estimator improves sequential manipulation success with incomplete knowledge.

    Conclusions:

    • The proposed online attack on data collection is a practical method for manipulating rank aggregation.
    • Sequential manipulation policies are effective, particularly with the developed robust estimator for incomplete information scenarios.
    • Empirical evidence confirms the efficacy of the proposed methods in sequentially manipulating rank aggregation outcomes.