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Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation

This paper utilizes a causal inference model and double machine learning on North Carolina judicial elections to demonstrate that omitting party designations from ballots causes approximately 12–15% of partisan voters to cast incorrect votes by relying on misleading candidate order cues, an error that disappears when party affiliations are explicitly displayed.

Original authors: Alessandro Arlotto, Alexandre Belloni, Fei Fang, Saša Pekeč

Published 2026-07-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alessandro Arlotto, Alexandre Belloni, Fei Fang, Saša Pekeč

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are at a massive, chaotic party where everyone is trying to pick a team captain. In the world of political science, researchers study how people make these choices. Sometimes, voters are super informed; they know exactly who they like and why. Other times, they are just looking for a quick hint, like a team color on a jersey. One of the most famous hints is "party affiliation"—knowing if a candidate is a Democrat or a Republican. But what happens when the jersey is missing? That's where the science of causal inference comes in. Think of this as a detective's toolkit used to figure out cause and effect. Instead of just guessing that "A caused B," scientists try to isolate A to see if B really happens because of it, ruling out other sneaky suspects. They also look at ballot design, which is simply the layout of the list of candidates. Just like a menu can make you order the first item just because it's at the top, the order of names on a voting sheet can trick your brain into picking the wrong person. This matters because if voters accidentally pick the wrong candidate, the election results don't actually reflect what the people wanted, which can change laws and leaders.

Now, let's zoom in on a specific mystery solved by a team of researchers from Duke University and Yale. They wanted to know: Does the order of names on a ballot trick voters into voting for the wrong party?

In North Carolina, the rules for how judges are listed on the ballot were a bit like a game of chance. For some years, the law said that in races where candidates had their party labels printed (like "Democrat" or "Republican" next to their name), the order was determined by which party was in charge of the governor's office. But for other races—specifically judicial races without party labels—the order was decided by a random drawing, like pulling a letter out of a hat to see who gets listed first. This created a perfect, accidental experiment. Sometimes, the "Democrat" was listed first in the presidential race (with the label), but the "Democrat" judge was listed second in the judicial race (without the label). The researchers call this a "flip."

The team wondered if partisan voters (people who usually vote for their party) would get confused. If a voter sees "Democrat first" for the President, they might assume "Democrat first" for the judge too. If the judge's ballot is flipped, that voter might accidentally pick the Republican judge, thinking they are voting for the Democrat.

To solve this, the researchers didn't just guess; they used a super-smart computer method called Double Machine Learning. Imagine trying to find a single needle in a haystack that is also moving around. This method helps them separate the "needle" (the effect of the flip) from the "haystack" (all the other things that affect voting, like how old people are, how many people turned out, or what other races were on the ballot). They looked at data from over 37,000 voting precincts across four different election years.

Here is what they found: The flip really does happen, and it causes mistakes.

When the order of the judges was flipped compared to the presidential race, the connection between how a town voted for the President and how they voted for the judge got much weaker. It's like if you usually follow a friend's lead, but suddenly your friend is standing on the opposite side of the room, and you end up following the wrong person.

The researchers calculated exactly how many people got it wrong. They estimated that 12.0% of Democratic voters and 15.4% of Republican voters cast their votes incorrectly because of this order swap. That's a lot of people! To put it in perspective, if you have a room of 100 Republican voters who intended to vote for their party's judge, about 15 of them accidentally voted for the other side just because the names were in a different order than they expected.

The team was very careful to make sure this wasn't a fluke. They ran a "placebo test," which is like a control group in a science experiment. They looked at races where the party labels were visible on the ballot. In those cases, the "flip" effect disappeared. This confirmed their theory: people only get confused when the labels are missing and they have to rely on the order of names as a clue. When the clue is there (the label), the trick doesn't work.

So, the paper concludes that ballot design isn't just about aesthetics; it's a powerful force that can accidentally change election outcomes. When voters rely on the order of names to guess a candidate's party, and that order is flipped, a significant chunk of the vote gets misdirected. The authors suggest that if we want elections to truly reflect what people want, we need to be careful about how we arrange the names on the page, especially when we take away the helpful party labels.

Technical Summary: Ballot Design and Electoral Outcomes

Problem Statement
This paper investigates how ballot design influences electoral outcomes, specifically focusing on the impact of omitting party designations (labels) in nonpartisan judicial races. The central hypothesis is that partisan voters, when faced with a nonpartisan ballot lacking party labels, rely on "party-order cues"—the sequence in which parties appear on the ballot in other contests (e.g., the presidential race)—to infer candidate affiliation. If the party order in a nonpartisan judicial race differs from the party order in the concurrent partisan presidential race (a "flip"), these voters may cast their ballots for the wrong candidate. The authors aim to quantify the magnitude of these "partisan-voting mistakes" and the resulting "flip effect" on vote shares.

Methodology
The authors develop a causal inference framework leveraging a quasi-randomized natural experiment within North Carolina (NC) judicial elections.

Data Source: The study utilizes precinct-level data from 13 statewide judicial races (NC Supreme Court and NC Court of Appeals) held during the 2004, 2008, 2012, and 2016 general elections. These races lacked party designations. A placebo sample of 17 races with party designations (2016, 2020, 2024) is used for validation. The dataset comprises 37,690 precinct-level observations for the main sample and 50,804 for the placebo sample, enriched with over 85,000 covariates including demographic data, turnout, and results from concurrent statewide races.
Identification Strategy: The identification relies on the NC General Statute, which historically dictated candidate ordering via random draws (e.g., selecting a starting letter for alphabetical ordering) for nonpartisan races, while partisan races followed different rules (e.g., alphabetical by party or governor's party first). This creates exogenous variation in whether a judicial race's party order is "flipped" relative to the presidential race ( $T_c=1$ ) or aligned ( $T_c=0$ ).
Estimation Technique: To handle the high dimensionality of covariates and allow for flexible functional forms, the authors employ Double Machine Learning (DML).
- Outcome Model: $Y_{cp} = f(X_p)T_c + g(X_p, W_{cp}, Z_c) + \epsilon_{cp}$ , where $Y_{cp}$ is the judicial vote share, $X_p$ is the presidential vote share, and $f(X_p)$ represents the heterogeneous flip effect.
- Treatment Model: The treatment assignment is modeled as a constant mean ( $m_0$ ) due to the quasi-randomized nature of the assignment at the contest level.
- Nuisance Parameter Estimation: The function $g$ is estimated using Elastic Net with cross-validated penalty selection to control for confounders without introducing bias into the treatment effect estimator.
- Inference: The authors compute cluster-robust standard errors to account for intra-contest dependence. They use a multiplier bootstrap procedure to construct simultaneously valid confidence bands for the flip effect across the entire range of presidential vote shares ( $x \in [0, 1]$ ).

Key Contributions

Causal Framework for Ballot Design: The paper establishes a rigorous causal inference model to isolate the effect of party-order flips in the absence of party labels, distinguishing between the net impact on vote shares (flip effect) and the proportion of voters casting incorrect ballots (partisan-voting mistakes).
Methodological Application: It demonstrates the application of Double Machine Learning in an election context with clustered treatment assignment and high-dimensional covariates, utilizing cross-fitting and orthogonality conditions to ensure valid statistical inference.
Quantification of Voting Errors: The study provides specific estimates of the share of partisan voters who vote incorrectly due to ballot design, a metric often difficult to identify in aggregate data.

Results

Flip Effect Heterogeneity: The analysis confirms that the flip effect is heterogeneous with respect to the presidential vote share. The effect is positive when a party's presidential vote share is low and negative when it is high, consistent with the mechanism that voters use the top-of-the-ticket order as a cue.
Magnitude of Mistakes: Using the estimated flip effect at a hypothetical precinct where a party's presidential candidate receives 100% of the vote, the authors estimate that:
- 12.0% (Standard Error: 3.6%) of Democratic partisan voters cast their votes incorrectly due to the party-order flip.
- 15.4% (Standard Error: 4.0%) of Republican partisan voters cast their votes incorrectly due to the flip.
Placebo Test: A placebo test using judicial races with party designations (where affiliation is observable) shows that the flip effect disappears. This confirms that the observed errors in the main sample are driven by the reliance on order cues in the absence of labels, supporting the proposed causal mechanism.
Correlation Evidence: Preliminary analysis shows a significant drop in the correlation between presidential and judicial vote shares in flipped races compared to non-flipped races (e.g., Democratic correlation drops from 0.714 to 0.564), providing descriptive evidence of the disruption in voting patterns.

Significance
The paper claims that its findings are critical for understanding how ballot design can inadvertently distort election outcomes, causing results to diverge from underlying voter preferences. By quantifying the share of partisan-voting mistakes, the study offers concrete evidence that the omission of party labels in nonpartisan contests, combined with specific ordering rules, leads to a non-trivial number of voters casting ballots contrary to their intent. The authors posit that these results have direct policy implications for how ballots should be designed to minimize confusion and ensure that electoral outcomes accurately reflect voter will. The study does not propose specific future legislative changes but highlights the causal mechanism by which current designs may fail partisan voters.

Technical Summary: Ballot Design and Electoral Outcomes

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