The repeated insertion model for rankings: Missing link between two subset choice models

Doignon, Jean-Paul; Pekec, Aleksandar; Regenwetter, Michel

doi:10.1007/bf02295838

Cited by 64 publications

(60 citation statements)

References 33 publications

(39 reference statements)

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“…We fix a canonical reference ranking, so the remaining parameters of our synthetic datasets are m, the number of elements, n, the number of rankings, and φ ∈ (0, 1], the dispersion parameter. We use an instance of the repeated insertion model to generate Mallows data [7]. Figure 2 presents empirical error rates on SUSHI and JESTER, for privacy levels of = {.01, .1, 1}.…”

Section: Methodsmentioning

confidence: 99%

Differentially Private Rank Aggregation

Hay

Elagina²,

Miklau

2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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Given a collection of rankings of a set of items, rank aggregation seeks to compute a ranking that can serve as a single best representative of the collection. Rank aggregation is a well-studied problem and a number of effective algorithmic solutions have been proposed in the literature. However, when individuals are asked to contribute a ranking, they may be concerned that their personal preferences will be disclosed inappropriately to others. This acts as a disincentive to individuals to respond honestly in expressing their preferences and impedes data collection and data sharing.We address this problem by investigating rank aggregation under differential privacy, which requires that a released output (here, the aggregate ranking computed from individuals' rankings) remain almost the same if any one individual's ranking is removed from the input. We propose a number of differentially-private rank aggregation algorithms: two are inspired by non-private approximate rank aggregators from the existing literature; another uses a novel rejection sampling method to sample privately from a complex distribution. For all the methods we propose, we quantify, both theoretically and empirically, the "cost" of privacy in terms of the quality of the rank aggregation computed.

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Section: Methodsmentioning

confidence: 99%

Differentially Private Rank Aggregation

Hay

Elagina²,

Miklau

2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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“…For simplicity and to reduce the number of free parameters, we consider uniform mixtures over k Mallows-φ with a shared parameter φ and refer to this as Mallows k-mixtures. Sampling from Mallows-φ (or Mallows mixtures) is conveniently possible by a repeated insertion model (Doignon et al, 2004;Lu and Boutilier, 2011).…”

Section: Stochastic Modelsmentioning

confidence: 99%

On the Discriminative Power of Tournament Solutions

Brandt

Seedig

2016

Operations Research Proceedings

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Tournament solutions constitute an important class of social choice functions that only depend on the pairwise majority comparisons between alternatives. Recent analytical results have shown that several concepts with appealing axiomatic properties such as the Banks set or the minimal covering set tend to not discriminate at all when the tournaments are chosen from the uniform distribution. This is in sharp contrast to empirical studies which have found that real-world preference profiles often exhibit Condorcet winners, i.e., alternatives that all tournament solutions select as the unique winner. In this work, we aim to fill the gap between these extremes by examining the distribution of the number of alternatives returned by common tournament solutions for empirical data as well as data generated according to stochastic preference models such as impartial culture, impartial anonymous culture, Mallows mixtures, spatial models, and Pólya-Eggenberger urn models.

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“…4 show histograms on two real-world data sets: Sushi [7] (10 alternatives and 5000 rankings) and Dublin, voting data from the Dublin North constituency in 2002 (12 candidates and 3662 rankings). 4 With Sushi, we divided the 5000 rankings into 50 voting profile instances, each with n = 100 rankings, and plotted MMR histograms using the same protocol as in Fig. 1 and Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The repeated insertion model (RIM), introduced by Doignon et al [4], is a generative process that can be used to sample from certain distributions over rankings and provides a practical way to sample from a Mallows model. A variant of this model, known as the generalized repeated inseartion model (GRIM), offers more flexibility, including the ability to sample from conditional Mallows models [9].…”

Section: Probabilistic Models Of Population Preferencesmentioning

confidence: 99%

Vote Elicitation with Probabilistic Preference Models: Empirical Estimation and Cost Tradeoffs

Boutilier

2011

Algorithmic Decision Theory

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Abstract. A variety of preference aggregation schemes and voting rules have been developed in social choice to support group decision making. However, the requirement that participants provide full preference information in the form of a complete ranking of alternatives is a severe impediment to their practical deployment. Only recently have incremental elicitation schemes been proposed that allow winners to be determined with partial preferences; however, while minimizing the amount of information provided, these tend to require repeated rounds of interaction from participants. We propose a probabilistic analysis of vote elicitation that combines the advantages of incremental elicitation schemes-namely, minimizing the amount of information revealed-with those of full information schemes-single (or few) rounds of elicitation. We exploit distributional models of preferences to derive the ideal ranking threshold k, or number of top candidates each voter should provide, to ensure that either a winning or a high quality candidate (as measured by max regret) can be found with high probability. Our main contribution is a general empirical methodology, which uses preference profile samples to determine the ideal ranking threshold for many common voting rules. We develop probably approximately correct (PAC) sample complexity results for one-round protocols with any voting rule and demonstrate the efficacy of our approach empirically on one-round protocols with Borda scoring.

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The repeated insertion model for rankings: Missing link between two subset choice models

Abstract: Approval voting, probabilistic choice models, probabilistic ranking models, subset choice,

Cited by 64 publications

References 33 publications

Differentially Private Rank Aggregation

Differentially Private Rank Aggregation

On the Discriminative Power of Tournament Solutions

Vote Elicitation with Probabilistic Preference Models: Empirical Estimation and Cost Tradeoffs

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