Let’s limit our attention to the three hypotheses (a) there is no correlation between names and occupations, (b) the Pelham paper is right that Dennises are about 1% more likely to go into dentistry, and (c) the effect is much larger, e.g. Dennises are 100% more likely to go into dentistry. Then Bayes’ theorem says observing a Dennis in dentistry increases the odds ratio P(b)/P(a) by a factor of 1% and the odds ratio P(c)/P(a) by a factor of 100%. You say you consider (a) and (b) to each have prior probability of 50%, which presumably means (c) has negligible prior probability. Applying Bayes’ theorem means (a) has a posterior probability of slightly less than 50%, (b) slightly more than 50%, and (c) still negligible.
So no, observing a Dennis in dentistry does not produce a strong update in favor of the hypothesis that there is a correlation between names and occupations (i.e. the union of (b) and (c)).
Let’s limit our attention to the three hypotheses (a) there is no correlation between names and occupations, (b) the Pelham paper is right that Dennises are about 1% more likely to go into dentistry, and (c) the effect is much larger, e.g. Dennises are 100% more likely to go into dentistry. Then Bayes’ theorem says observing a Dennis in dentistry increases the odds ratio P(b)/P(a) by a factor of 1% and the odds ratio P(c)/P(a) by a factor of 100%. You say you consider (a) and (b) to each have prior probability of 50%, which presumably means (c) has negligible prior probability. Applying Bayes’ theorem means (a) has a posterior probability of slightly less than 50%, (b) slightly more than 50%, and (c) still negligible.
So no, observing a Dennis in dentistry does not produce a strong update in favor of the hypothesis that there is a correlation between names and occupations (i.e. the union of (b) and (c)).