Finite- and large-sample inference for ranks using multinomial data with an application to ranking political parties

Sergei Bazylik, Magne Mogstad, Joseph P. Romano, Azeem Shaikh and Daniel Wilhelm
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Sergei Bazylik: Institute for Fiscal Studies
Joseph P. Romano: Institute for Fiscal Studies and Stanford University

No CWP40/21, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 con?dence sets for the rank of a particular category as well as simultaneous con?dence 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 con?dence 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 ?nd that our finite-sample con?dence 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 con?dence 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 con?dence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.

Date: 2021-11-18
New Economics Papers: this item is included in nep-pol
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Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties (2024)
Working Paper: Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties (2021)
Working Paper: Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties (2021)
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