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Candidate Set Size and Voting Behavior: A Front-Door Approach to Causal Moderation

Masayuki Haruhara

arXiv 21 Aug 2026 · Econometrics

arXiv:2608.20779 · PDF · Extracted main text

Abstract

We study causal moderation when treatment assignment is randomized but the moderator is not. We combine the parallel estimation framework with front-door adjustment to identify an average mediated treatment moderation effect. We apply this approach to 165 municipal assembly elections in Tokyo (1987-2023), where pamphlet positions are assigned by lottery and total pamphlet pages are mechanically determined by candidate set size and fixed municipal rules. One additional candidate increases the front-page effect on winning probability by 0.322 percentage points through the page-count channel, 8.0% of its baseline magnitude, while the back-page effect does not increase significantly.

Citation extraction

44
references
73
in-text mentions
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distinct cited
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self-citations
7,910
main-text words

appendix boundary found by appendix_command · 82% of the source is main text. Read the extracted text to check this.

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
1Haruhara, Masayuki and Haruhara, Miho and Ishii, Yuki and Katayama,… (2026) Unintended Inequality: A Pitfall of Electoral Systems Driven by Information Acquisition Costs self1.00054100%
2Cunow, Saul and Desposato, Scott and Janusz, Andrew and Sells, Cameron (2021) Less is more: The paradox of choice in voting behavior0.87452100%
3Bansak, Kirk (2021) Estimating causal moderation effects with randomized treatments and non-randomized moderators0.81142100%
4Goidel, Spencer and Armstrong, Brenna (2025) Choice overload in crowded primary elections0.81142100%
5Bellemare, Marc F and Bloem, Jeffrey R and Wexler, Noah (2024) The Paper of How: Estimating Treatment Effects Using the Front-Door Criterion0.73732100%
6Pearl, Judea (1995) Causal diagrams for empirical research0.73732100%
7Söderlund, Peter and Von Schoultz, Åsa and Papageorgiou, Achillefs (2021) Coping with complexity: Ballot position effects in the Finnish open-list proportional representation system0.73732100%
8Iyengar, Sheena S and Lepper, Mark R (2000) When choice is demotivating: Can one desire too much of a good thing?0.64422100%
9Meredith, Marc and Salant, Yuval (2013) On the causes and consequences of ballot order effects0.64422100%
10Payne, John W. and Bettman, James R. and Johnson, Eric J (1993) The Adaptive Decision Maker0.64422100%

Showing the top 10 of 44 scored citations.