The Wasserstein Bipolarization Index: A New Measure of Public Opinion Polarization, with an Application to Cross-Country Attitudes toward COVID-19 Vaccination Mandates.
Bibliographic record
Abstract
Although the topic of opinion polarization receives much attention from the media, public opinion researchers and political scientists, the phenomenon itself has not been adequately characterized in either the lay or academic literature. To study opinion polarization among the public, researchers compare the distributions of respondents to survey questions or track the distribution of responses to a question over time using ad-hoc methods and measures such as visual comparisons, variances, and bimodality coefficients. To remedy this situation, we build on the axiomatic approach in the economics literature on income bipolarization, specifying key properties a measure of bipolarization should satisfy: in particular, it should increase as the distribution spreads away from a center toward the poles and/or as clustering below or above this center increases. We then show that measures of bipolarization used in public opinion research fail to satisfy one or more of these axioms. Next, we propose a p-Wasserstein polarization index that satisfies the axioms we set forth. Our index measures the dissimilarity between an observed distribution and a distribution with all the mass clustered on the lower and upper endpoints of the scale. We use our index to examine bipolarization in attitudes toward governmental COVID-19 vaccine mandates across 11 countries, finding the U.S and U.K are most polarized, China, France and India the least polarized, while the others (Brazil, Australia, Colombia, Canada, Italy, Spain) occupy an intermediate position.
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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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 source (direct Gemma or distilled Codex), 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".