Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties
Social Science Research Network(2024)
摘要
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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关键词
multinomial data,ranking,ranks,political parties,large-sample
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