The Neglected Bi-Threshold Aspect of Human Decision-Making: Equilibrium Analysis
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
Linear threshold models have long served to intuitively capture binary decision-makings in contexts such as vaccination, trading, and innovation, imposing "to take an action if enough fellows do so". Similarly, anti-threshold models have been used in contexts such as following fashion, volunteering, and routing, complying "to take an action if not too many fellows do so". Despite the achieved useful insights, these models are often against the common-sense intuition that human decision-making is a mixture of both: "to take an action if enough but not too many fellows do so". We capture this missing aspect of human perception and introduce the bi- threshold models, where each individual rather than one, has a pair of possibly unique thresholds and takes an action if and only if the number of others doing so is between the two thresholds. We find the equilibria of the resulting population dynamics and perform convergence analysis for homogeneous populations. Our analysis highlights the difference between bi- threshold and single-threshold models. In particular, we show that cooperation may be a rare outcome compared to single- threshold models. This highlights the dramatic difference in estimations of the cooperators using threshold models in critical situations such as taking vaccination in a pandemic.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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 it