Ranked-Choice Tie-Breaking in Elections

ISEF Category: Mathematics

Subcategory: Other  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

A single tie-break rule can change who wins an election. In ranked-choice voting, that tiny choice can ripple through every round. You can study which rules feel fair, which rules break under pressure, and how often they change real outcomes. That makes this a sharp math project with real civic stakes.

What Is It?

Ranked-choice voting, or RCV, lets voters rank candidates instead of picking just one. If no one wins outright, the lowest candidate gets removed and their votes move to the next choice. When two candidates tie, the election system needs a tie-break rule to decide what happens next.

That tie-break rule sounds small, but it can matter a lot. Think of it like a referee’s call in overtime. The game has already been close, so the rule that breaks the tie can decide the final result. In this project, you study tie-break rules with math. You ask which rules satisfy fair-sounding principles, and which ones fail under certain conditions. You can also test real ballot data to see how different tie-break rules change the outcome.

Why This Is a Good Topic

This topic works well because you can study it with clear math, public data, and real consequences. You do not need a wet lab, but you do need careful modeling, logic, and data analysis. The project connects to election fairness, voting rules, and public trust in local government. You can learn how to state axioms, test them against rules, and compare outcomes across simulations.

Research Questions

• How does the choice of tie-break rule change the final winner in San Francisco-style ranked-choice elections?
• What is the effect of using ballot-order tie-breaking versus random tie-breaking on elimination outcomes?
• Does a new family of tie-break rules satisfy more fairness axioms than common election tie-breakers?
• To what extent do tie-break rules change the number of rounds needed to reach a winner?
• Which candidate profiles are most sensitive to tie-breaking in ranked-choice voting?
• How does the frequency of tied elimination rounds vary across public municipal election data?
• What is the effect of different tie-break rules on voter satisfaction scores computed from ranked ballots?

Basic Materials

• Laptop or desktop computer with spreadsheet software.
• Public ranked-choice election datasets from San Francisco election records.
• A statistics notebook or spreadsheet for tracking assumptions and results.
• Python installed through Anaconda or a similar free distribution.
• A text editor for writing definitions, axioms, and proofs.
• Graph paper or a whiteboard for drawing elimination trees.

Advanced Materials

• Laptop or workstation with Python and a scientific computing stack.
• Public San Francisco RCV ballot data and election summaries.
• A symbolic math tool or proof assistant, if your mentor approves it.
• A version control tool such as Git for tracking simulation code.
• Access to a university library database for voting theory papers.
• Optional access to R for cross-checking simulations and summary statistics.

Software & Tools

• Python: Runs simulations of tie-breaking rules and compares election outcomes across many ballot profiles.
• Jupyter Notebook: Keeps code, notes, and results in one place for easy revision.
• pandas: Organizes ballot data and election summary tables for analysis.
• NumPy: Handles fast repeated simulations and random tie-breaking trials.
• GeoPandas: Helps if you want to map results by precinct or district.

Experiment Steps

1. Define the exact election setting you will study, including the kind of tie and the round where it appears.
2. Translate each tie-break rule into a clear algorithm so you can compare rules step by step.
3. Select the fairness axioms or properties you want to test, then write them in plain language and in math form.
4. Build a simulation plan that replays public ballot data under multiple tie-break rules.
5. Compare outcomes with summary statistics, sensitivity counts, and counterexample searches.
6. Check whether your strongest results hold on different elections, not just one dataset.

Common Pitfalls

• Mixing up elimination ties with final-winner ties, which makes the rule analysis inconsistent.
• Using one election dataset and assuming the pattern generalizes to all ranked-choice contests.
• Writing vague fairness claims that you cannot turn into a testable axiom.
• Forgetting that ballot exhaustion can change the active voter set across rounds.
• Comparing rules without fixing the same candidate set, which makes outcome differences hard to interpret.

What Makes This Competitive

A strong version of this project goes beyond simple simulations. You would define a clean axiomatic framework, prove one or more impossibility results, and then test those results on real ballot data. The best projects also look for edge cases, not just average behavior. If you can show where a new tie-break family behaves better or worse than standard methods, you move from a class project to real research territory.

Project Variations

• Study tie-breaking only in municipal elections with three or more rounds, then compare how often ties appear at each stage.
• Test a different ballot dataset, such as another city’s ranked-choice election results, and see whether the same axioms still fail.
• Analyze voter-order or candidate-order tie-breaking as a fairness baseline, then compare it with your new family of rules.

Learn More

• MIT OpenCourseWare, Game Theory and Social Choice: Search the MIT OpenCourseWare site for lectures on voting theory and social choice.
• NBER working papers on voting systems: Search the National Bureau of Economic Research site for ranked-choice voting and election tie-breaking studies.
• PubMed not needed here, so use JSTOR or arXiv search for voting theory papers on tie-breaking and impossibility results.
• City and County of San Francisco Department of Elections: Find public ranked-choice voting data and election reports on the city elections website.
• Stanford Encyclopedia of Philosophy, Social Choice Theory: Read the overview article for definitions, axioms, and classic impossibility theorems.
• Python documentation: Use the official docs to learn pandas, NumPy, and random simulation tools for election analysis.