The mean, the median, and the St. Petersburg paradox
The St.~Petersburg Paradox is a famous economic and philosophical puzzle that has generated numerous conflicting explanations. To shed empirical light on this phenomenon, we examined subjects' bids for one St.~Petersburg gamble with a real monetary payment. We found that bids were typically low...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2009-06-01
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| Series: | Judgment and Decision Making |
| Subjects: | |
| Online Access: | http://journal.sjdm.org/9226/jdm9226.pdf |
| _version_ | 1797716042854694912 |
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| author | Benjamin Y. Hayden Michael L. Platt |
| author_facet | Benjamin Y. Hayden Michael L. Platt |
| author_sort | Benjamin Y. Hayden |
| collection | DOAJ |
| description | The St.~Petersburg Paradox is a famous economic and philosophical puzzle that has generated numerous conflicting explanations. To shed empirical light on this phenomenon, we examined subjects' bids for one St.~Petersburg gamble with a real monetary payment. We found that bids were typically lower than twice the smallest payoff, and thus much lower than is generally supposed. We also examined bids offered for several hypothetical variants of the St.~Petersburg Paradox. We found that bids were weakly affected by truncating the gamble, were strongly affected by repeats of the gamble, and depended linearly on the initial ``seed'' value of the gamble. One explanation, which we call the extit{median} extit{heuristic}, strongly predicts these data. Subjects following this strategy evaluate a gamble as if they were taking the median rather than the mean of the payoff distribution. Finally, we argue that the distribution of outcomes embodied in the St.~Petersburg paradox is so divergent from the Gaussian form that the statistical mean is a poor estimator of expected value, so that the expected value of the St.~Petersburg gamble is undefined. These results suggest that this classic paradox has a straightforward explanation rooted in the use of a statistical heuristic. |
| first_indexed | 2024-03-12T08:16:43Z |
| format | Article |
| id | doaj.art-48d257f75fb94ef4baeb74d314da7c34 |
| institution | Directory Open Access Journal |
| issn | 1930-2975 |
| language | English |
| last_indexed | 2024-03-12T08:16:43Z |
| publishDate | 2009-06-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Judgment and Decision Making |
| spelling | doaj.art-48d257f75fb94ef4baeb74d314da7c342023-09-02T18:51:42ZengCambridge University PressJudgment and Decision Making1930-29752009-06-0144256272The mean, the median, and the St. Petersburg paradoxBenjamin Y. HaydenMichael L. PlattThe St.~Petersburg Paradox is a famous economic and philosophical puzzle that has generated numerous conflicting explanations. To shed empirical light on this phenomenon, we examined subjects' bids for one St.~Petersburg gamble with a real monetary payment. We found that bids were typically lower than twice the smallest payoff, and thus much lower than is generally supposed. We also examined bids offered for several hypothetical variants of the St.~Petersburg Paradox. We found that bids were weakly affected by truncating the gamble, were strongly affected by repeats of the gamble, and depended linearly on the initial ``seed'' value of the gamble. One explanation, which we call the extit{median} extit{heuristic}, strongly predicts these data. Subjects following this strategy evaluate a gamble as if they were taking the median rather than the mean of the payoff distribution. Finally, we argue that the distribution of outcomes embodied in the St.~Petersburg paradox is so divergent from the Gaussian form that the statistical mean is a poor estimator of expected value, so that the expected value of the St.~Petersburg gamble is undefined. These results suggest that this classic paradox has a straightforward explanation rooted in the use of a statistical heuristic.http://journal.sjdm.org/9226/jdm9226.pdfSt.~Petersburg paradoxriskrisk aversionheuristicsmedian heuristicexpectation heuristic. |
| spellingShingle | Benjamin Y. Hayden Michael L. Platt The mean, the median, and the St. Petersburg paradox Judgment and Decision Making St.~Petersburg paradox risk risk aversion heuristics median heuristic expectation heuristic. |
| title | The mean, the median, and the St. Petersburg paradox |
| title_full | The mean, the median, and the St. Petersburg paradox |
| title_fullStr | The mean, the median, and the St. Petersburg paradox |
| title_full_unstemmed | The mean, the median, and the St. Petersburg paradox |
| title_short | The mean, the median, and the St. Petersburg paradox |
| title_sort | mean the median and the st petersburg paradox |
| topic | St.~Petersburg paradox risk risk aversion heuristics median heuristic expectation heuristic. |
| url | http://journal.sjdm.org/9226/jdm9226.pdf |
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