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

Daniel Wilhelm, Magne Mogstad and Azeem Shaikh

No 2132, RF Berlin - CReAM Discussion Paper Series from Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM)

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.

Keywords: Confidence sets; Multinomial Data; Multiple Testing; Polls; Ranks; Surveys (search for similar items in EconPapers)
JEL-codes: C12 C14 D31 I20 J62 (search for similar items in EconPapers)
Date: 2021-11
New Economics Papers: this item is included in nep-ecm, nep-ore and nep-pol
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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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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