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The mean, the median, and the St. Petersburg paradox.

ABSTRACT: 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 median 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.

SUBMITTER: Hayden BY

PROVIDER: S-EPMC3811154 | biostudies-literature | 2009 Jun

REPOSITORIES: biostudies-literature

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The mean, the median, and the St. Petersburg paradox.

Hayden Benjamin Y BY Platt Michael L ML

Judgment and decision making 20090601 4

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 wea ...[more]

PMID: 24179560

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Project description:BackgroundFamilial hypercholesterolemia (FH) is a human monogenic disease induced by a variety of mutations with striking genetic diversity. Despite this variability recurrent mutations occur in each population studied, which allows both elucidating prevalent mutations and developing DNA diagnostic tools for the disease. Recent research of FH in St. Petersburg, Moscow and Novosibirsk (major cities in Russia) demonstrates that each megapolis has its own FH mutation spectrum sharing only small part of mutations with other populations in Russia and Europe. In order to optimize molecular-genetic diagnostic protocols for FH in Russia we studied mutation spectrum in other regions including Petrozavodsk, a smaller town in relatively close proximity to St. Petersburg.MethodsThe principal method was automated detection of single-strand conformation polymorphism followed by direct PCR amplified DNA sequencing.ResultsTwelve different mutations of the low density lipoprotein (LDL) receptor gene were detected in the Petrozavodsk sample (80 patients). Out of these twelve mutations, seven have never been described before (c.192_201delinsGGACTTCA, c. 195_196insT, c. 618 T > G, c. 1340C > G, c. 1686_1693delinsT, c. 1936C > A, c. 2191delG). Other five mutations (c. 58G > A, c. 925_931del, c. 1194C > T, c. 1532 T > C, c. 1920C > T) were previously characterized elsewhere. All new mutations are considered to be a probable cause of the FH in their carriers. Direct evidence of the neutral character of c.58G > A or p. (Gly20Arg) is provided for the first time. Each pathogenic mutation was a trait of its own unique pedigree and so far has not been found in other patients.ConclusionsStrikingly, out of twelve mutations characterized in the Petrozavodsk sample only one mutation, c. 925_931del, has previously been found in patients from St. Petersburg and Finland (most closely located studied populations), suggesting some common roots in origin of these populations in the past or limited gene exchange between them nowadays. No recurrent mutations were detected.

Project description:Introduction. Since the detection of the first COVID-19 patient, 2 years have passed, during which more than 287,862,000 people have fallen ill globally, of which about 1.9% died. The implementation of SARS-CoV-2 control programs required efforts from almost all countries. An important direction in the fight against COVID-19 has been the formation of herd immunity, the main tool for managing the pandemic. Study goal. The aim of the study was to assess the seroprevalence of antibodies (Abs) to SARS-CoV-2 nucleocapsid (Nc) and receptor binding domain (RBD) in the St. Petersburg population during the COVID-19 pandemic. Materials and methods. A longitudinal cohort randomized monitoring study of Ab seroprevalence (SARS-CoV-2 Nc, RBD) was organized and conducted according to a unified methodology developed by Rospotrebnadzor with the participation of the St. Petersburg Pasteur Institute. For this purpose, a cohort was formed of 1000 volunteers who participated in all five stages of seromonitoring. The cohort was divided into seven age groups: 1-17; 18-29; 30-39; 40-49; 50-59; 60-69; 70; and older (70+) years. Seropositivity levels (Nc, RBD) were assessed by quantitative and qualitative enzyme immunoassays. During the second year of monitoring, some volunteers were vaccinated with the GamCOVIDVac (84%) or EpiVacCorona (11.6%) vaccines approved in Russia. Statistical processing was carried out using Excel 2010. Confidence intervals for shares and percentages (95% CI) were calculated using the method of A. Wald and J. Wolfowitz with adjustment (A. Agresti, B.A. Coull). The statistical significance of differences was calculated by z-test, using the appropriate online calculator (p < 0.05) unless indicated. Results. There was a trend toward an increase in Nc seropositivity in stages 1-3 of seromonitoring, with a decrease in stages 4-5 among children and adults. The share of RBD seropositive steadily increased during all five stages of seromonitoring. The most frequent finding was low anti-RBD Abs levels (22.6-220 BAU/mL). High Ab levels were recorded statistically significantly less frequently. Asymptomatic forms were observed in 84-88% of SARS-CoV-2 seropositive volunteers. By the fifth stage of monitoring, this indicator significantly decreased to 69.8% (95% CI: 66.1-73.4). The monitoring revealed a statistically significant increase in anti-RBD Abs alongside a statistically significant decrease in the proportion of Nc seropositives. This dynamic was especially characteristic of persons vaccinated with GamCOVIDVac. Conclusion. Prior to the use of specific vaccines, a seroprevalence of anti-Nc Abs was noted. After the introduction of the GamCOVIDVac vaccine in adults, a decrease in the level of anti-Nc Abs was noted due to an increase in the proportion of RBD seropositive persons.

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The mean, the median, and the St. Petersburg paradox.

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The mean, the median, and the St. Petersburg paradox.

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