What you're saying is right (in general, but not in reference to the specific analogy), but I'm not sure what it has to do with a frequentist analysis. Rather, it's a simplistic linear analysis of a higher-order system. Instead of multiplying the number of murders (which is an output, not an input), just multiply the number of potential murderers, with some percentage chance of being triggered to desire to murder a particular individual if encountered. If that chance averages 1%, in a town of 101 people you would have a 50% chance of having at least one person who would want to murder you. In a town of 10,001, you would have a 99.5% chance of having at least one person who would want to murder you. [edit: and in a town of 101, there would be no chance of having more than 100 people who wanted to murder you. In a town of 10,001, you'd be as likely as not to have 100 people would would murder you.]
If everyone is exposed to everyone at all times, then everyone is endangered in large groups (seems obvious) even if no one is consistently looking for trouble more than anyone else. If that the qualities that inspire that 1% reaction have a clumpy distribution (either in perpetrator or victim), the experiences that individuals have will be vastly different in an average forum, and when holding the tolerance for danger constant, the least targeted will feel comfortable in far larger towns than the most targeted.
Of course, in real life, the larger the town, the higher the level of anonymity. In the case of internet forums, however, 1) smaller groups are being eliminated in favor of larger groups due to finance and economies of scale and 2) there is a profit motive in de-anonymizing users. There's absolutely no degree of moderation that can make it work. Anonymity simply makes the problem disappear. What you said can be targeted, you yourself cannot be.
Yeah, all of this I agree with. I don't think quality of social interaction depends on identifiability, although FB certainly leveraged its real-name policy as a quality signal from the outset - it made the platform seem more official/professional to the initial target demo.
If everyone is exposed to everyone at all times, then everyone is endangered in large groups (seems obvious) even if no one is consistently looking for trouble more than anyone else. If that the qualities that inspire that 1% reaction have a clumpy distribution (either in perpetrator or victim), the experiences that individuals have will be vastly different in an average forum, and when holding the tolerance for danger constant, the least targeted will feel comfortable in far larger towns than the most targeted.
Of course, in real life, the larger the town, the higher the level of anonymity. In the case of internet forums, however, 1) smaller groups are being eliminated in favor of larger groups due to finance and economies of scale and 2) there is a profit motive in de-anonymizing users. There's absolutely no degree of moderation that can make it work. Anonymity simply makes the problem disappear. What you said can be targeted, you yourself cannot be.