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arXiv 2305.04050cs.CYcs.CR
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风险限制审计的新算法与应用

New Algorithms and Applications for Risk-Limiting Audits

Bar Karov, Moni Naor

AI总结:

本研究提出Batchcomp方法将选票级风险限制审计转换为批次级并应用于以色列议会选举,同时调整ALPHA方法提出适用于人口普查席位分配核查的RLA,拓展了其应用场景。

摘要:

风险限制审计(Risk-Limiting Audits, RLAs)是提升选举结果准确性可信度的重要工具。它由一系列随机算法组成,用于核查选票统计系统上报的选举计票结果是否对应正确的获胜候选人。若初始计票得出了错误的选举获胜者,RLA可保证凭借自身的随机性以高概率识别出该错误。这类审计通过顺序抽样并检查选票来运作,直到能够确认上报的获胜者或识别出真正的获胜者。\n本研究的第一部分提出了一种名为“Batchcomp”的新型通用方法,用于将经典的(选票级)RLA转换为可在批次层面运行的RLA。作为所提方法的具体应用,我们开发了首个适用于以色列议会(Knesset)选举的选票级RLA,并将其转换为批次级运行的版本。我们在第22、23和24届议会选举的结果上运行了所提出的“Batchcomp”流程,分别在存在错误和不存在错误的两种场景下开展了测试。\n本研究的第二部分提出了RLA的一个新用例:验证人口普查是否能将政治权力正确分配给国家的各选区或联邦州。我们对现有的RLA方法ALPHA进行了调整,提出了一种适用于人口普查的方法。我们的人口普查RLA适用于以下国家:议会席位根据一类特定函数(最高均值法)按人口比例分配给各地理区域的国家。该方法同时依赖人口普查数据,以及一项如今许多国家都已开展的额外流程——即事后 enumeration 调查(post-enumeration survey)的数据。

英文摘要:

Risk-limiting audits (RLAs) are a significant tool in increasing confidence in the accuracy of elections. They consist of randomized algorithms which check that an election's vote tally, as reported by a vote tabulation system, corresponds to the correct candidates winning. If an initial vote count leads to the wrong election winner, an RLA guarantees to identify the error with high probability over its own randomness. These audits operate by sequentially sampling and examining ballots until they can either confirm the reported winner or identify the true winner. The first part of this work suggests a new generic method, called ``Batchcomp", for converting classical (ballot-level) RLAs into ones that operate on batches. As a concrete application of the suggested method, we develop the first ballot-level RLA for the Israeli Knesset elections, and convert it to one which operates on batches. We ran the suggested ``Batchcomp" procedure on the results of 22nd, 23rd and 24th Knesset elections, both with and without errors. The second part of this work suggests a new use-case for RLAs: verifying that a population census leads to the correct allocation of political power to a nation's districts or federal-states. We present an adaptation of ALPHA, an existing RLA method, to a method which applies to censuses. Our census-RLA is applicable in nations where parliament seats are allocated to geographical regions in proportion to their population according to a certain class of functions (highest averages). It relies on data from both the census and from an additional procedure which is already conducted in many countries today, called a post-enumeration survey.

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