The Distortion of Approval Voting with Runoff
Bibliographic record
Abstract
Recent work introduces approval with runoff voting, in which voters cast approval ballots, two finalists are selected, and a runoff election is conducted between them to choose the final winner by majority voting. While the more common plurality with runoff voting admits only one reasonable choice of the two finalists (the two candidates with the most plurality votes), the use of approval ballots in the first stage opens up the possibility of using many reasonable ways to choose the two finalists. What is the optimal way to choose the two finalists? In this work, we answer this question using the distortion framework, in which the performance of every voting system is quantitatively measured by its worst-case social welfare approximation ratio, also known as distortion. We prove that the best distortion achievable by approval voting with (majority) runoff is Θ(m2) with deterministic finalist selection and Θ(m) with randomized finalist selection, where m is the number of candidates. This is actually worse than what simple approval voting without any runoff achieves (Θ(m) and Θ(√m), respectively). We pinpoint the use of majority runoff in the second stage as the culprit, propose a candidate proportional runoff system that declares each finalist the winner with probability equal to the fraction of voters who prefer it, and analyze the extent to which it can help curb the distortion.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".