Constrained Group Balancing: Why Does it Work
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider a problem where a set of objects possessing multiple attributes must be partitioned into a certain number of groups so that the groups are as balanced as possible with respect to the number of objects possessing each attribute. This multi-criteria decision problem arises in a variety of practical applications, ranging from assigning students to study groups to designing level schedules for JIT assembly lines. A direct approach, enforcing balance through hard constraints, may lead to infeasibility, but works well in practice. We analyze this phenomenon from the worst-case and empirical perspectives, as well as through an in-depth analysis of one representative practical application - the design of student groups at the Rotman School of Management, University of Toronto. The goals of the analysis are to understand what classes of balancing problems may contain infeasible instances and how prevalent such instances are within these classes, as well as to synthesize practical managerial insights that a decision maker could follow in order to increase the chances that balanced groups can be found.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it