The St. Petersburg Paradox: A Fresh Algorithmic Perspective
Bibliographic record
Abstract
The St. Petersburg paradox is a centuries-old puzzle concerning a lottery with infinite expected payoff on which people are only willing to pay a small amount to play. Despite many attempts and several proposals, no generally-accepted resolution is yet at hand. In a recent paper, we show that this paradox can be understood in terms of the mind optimally using its limited computational resources (Nobandegani et al. 2019). Specifically, we show that the St. Petersburg paradox can be accounted for by a variant of normative expected-utility valuation which acknowledges cognitive limitations: sample-based expected utility (Nobandegani et al. 2018). SbEU provides a unified, algorithmic explanation of major experimental findings on this paradox. We conclude by discussing the implications of our work for algorithmically understanding human cognition and for developing human-like artificial intelligence.
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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 | 0.002 | 0.007 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".