Equal Opportunity and Luck: Empirical Exploration Using the Canadian Longitudinal Study on Aging
Bibliographic record
Abstract
Abstract Equality of opportunity (EOp) is a broad category of egalitarian theories that has attracted considerable attention in recent decades. Empirical implementations of EOp primarily focus on the explained component of inequality, classifying determinants of the outcome (e.g., health) into effort —legitimate causes of inequality—and circumstance —illegitimate causes of inequality. Largely overlooked is unexplained variation, which in statistical analysis manifests as residuals and is often ignored as a statistical annoyance. The true random component of residuals is now often referred to as luck . In this paper, we propose the playing field framework that serves as a pragmatic test as to whether residuals signal unfairness in empirical EOp analyses and that enables empirical explorations of roles of luck within the EOp framework. Using a large sample of Canadian older adults, our empirical application of the playing field framework shows that distributions of residuals are not always fair, though there is no consistent pattern of unfairness across age-sex groups. The paper’s three main conclusions are: luck matters; luck should be explicitly incorporated in the EOp framework through the brute luck-effort characterization; and residuals are not just an innocuous statistical annoyance but can represent unfair inequality, and ignoring them can underestimate unfair inequality.
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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 | 0.015 | 0.041 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.013 |
| Science and technology studies | 0.008 | 0.003 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".