Bibliographic record
Abstract
The lottery paradox exposes some tensions in our natural ways of thinking about probabilities, and in how we think about belief itself. This chapter explores the paradox from a psychological angle, arguing that it arises from the flexibility of our cognitive capacities to represent (and reason about) the empirical realm. A better understanding of these capacities can give us a clearer sense of our theoretical options. Ultimately, I take a broad view of the paradox: In my view, it can be triggered not only by discussion of games with stipulated odds but by topics of all sorts. However, it will be simplest to start with an example inspired by Kyburg’s (1961) classic discussion, in which you hold one ticket in a fair lottery, with odds of (let us say) a million to one, in which the draw has been held but the single winner not yet announced. It is very likely that your ticket has lost, but what is the significance of this high likelihood for the rationality of believing that your ticket has lost? If we insist that a threshold of .999999 is not high enough for rational belief, it may seem we are trapping ourselves in skepticism: Surely many of the ordinary things we rationally believe about the world are less certain than logical truths. On the other hand, if we do believe that this ticket has lost, by symmetry we should say the same for any of the other tickets in the lottery, and as long as conjunction of rational beliefs is a rational operation, it seems we would be rational to deduce that all the tickets have lost, in contradiction to our other beliefs about this fair lottery.
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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 | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.041 |
| Scholarly communication | 0.008 | 0.012 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".