A Class of Linear Quadratic Collective Discrete Choice Models with Congestion Effects
Bibliographic record
Abstract
This paper introduces a new class of linear quadratic dynamic collective choice models with congestion effects. Agents choose between multiple destinations and cooperate to minimize a collective average cost. To preserve the model’s analytical tractability, we employ a quadratic negative term in the cost function to simulate congestion avoidance. We show that identifying a solution to our model is equivalent to solving a number of linear quadratic regulator problems equal to the number of choices of destinations, followed by an optimal transport problem parameterized by the fraction of agents choosing each destination. This contrasts with the brute-force approach consisting of solving a series of linear quadratic regulator problems whose number increases exponentially with the population size. To further reduce the complexity of the solution search, we also define an appropriate system of limiting equations, whose solution can be used to efficiently approximate the optimal solution as the number of agents increases.
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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 | 0.000 | 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 | 0.000 |
| 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 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".