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Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties

Sergei Bazylik, Magne Mogstad, Joseph Romano, Azeem Shaikh, Daniel Wilhelm

arXiv 31 Jan 2024 · Econometrics · publishedJournal of Econometrics (2025) · 6 citations (OpenAlex)

arXiv:2402.00192 · PDF · DOI · OpenAlex · Extracted main text

Abstract

It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Mogstad, M., Romano, J. P., Shaikh, A. M. and Wilhelm, D (2024) Inference for ranks with applications to mobility across neighbourhoods and academic achievement across countries self0.97715493%
2Brown, L. D., Cai, T. T. and DasGupta, A (2001) Interval estimation for a binomial proportion0.87452100%
3Klein, M., Wright, T. and Wieczorek, J (2020) A joint confidence region for an overall ranking of populations0.73732100%
4Xie, M., Singh, K. and Zhang, C.-H (2009) Confidence intervals for population ranks in the presence of ties and near ties0.73732100%
5Goldstein, H. and Spiegelhalter, D. J (1996) League tables and their limitations: Statistical issues in comparisons of institutional performance0.64422100%
6Hall, P. and Miller, H (2009) Using the bootstrap to quantify the authority of an empirical ranking0.64422100%
7Lehmann, E. L. and Romano, J. P (2022) Testing Statistical Hypotheses self0.5114225%
8Andrews, I., Kitagawa, T. and McCloskey, A (2018) Inference on winners0.51121100%
9Bean, C., Cameron, S., Gibson, R., Makkai, T., McAllister, I. and Sh… (2019) Australian election study 2019: Voters technical report0.51121100%
10Gu, J. and Koenker, R (2020) Invidious comparisons: Ranking and selection as compound decisions0.51121100%

Showing the top 10 of 17 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference for Rank-Rank Regressions0.40511
2Causal Interpretation of Regressions With Ranks0.40511
3Ranking Treatment Saturations under Clustered Network Interference0.40511