The Stripy Strudel's Journal

Note: This has been initially posted as a comment in a discussion about a recent epidemic of a social virus about a little girl needing blood for transfusion. The fake message has been started by a LiveJournal user, and contained a plea to forward it to as many people as possible.

During the recent epidemic, I've got the message saying that someone needs B group blood dozens of times, and the shocking thing about it was that some of the people I got it from were:

1. Smart people, and I've got no doubt about it. I can warrant that some of the people whom I got the message from are smart, I've been studying together with them and I know them rather well. They are capable of complex mental activity both at work and in private life (so that it's not “common idiocy” when a professional outside of his workplace is helpless and naïve like a child).
2. People we haven't talked with for quite a while. If those people decided to send the message to me, it means they were sending it to everyone in the contact list, and maybe even outside the contact list.

The most scaring is that the first and the second groups have non-empty intersection.

A little analysis.

None of the forwarders tried to change the text or at least add something to it like “Do you think it's true? What if it is?” to express their degree of trust for this information. Does it mean everyone trusted it for 100%? Of course not. Maybe the hoax got them convinced for 60%, and they decided to forward it. But forwarding or not forwarding is discrete, it's either 0 or 100%. This way, 60% is rounded up to 100%, so we end up with stable reproduction of the worm. If every forwarder expressed their degree of trust, after three or four hops the information would “fade out” and turn into a tale that nobody is going to believe. It's this “rounding” that ensures the reproduction of the worm: the forwarded message looks exactly the same as the original. No gossip transferred the traditional way, through mouth and ears, achieves such steady reproduction as an electronic rumor gets nowadays when text can be copied and forwarded without distortion (experiments show that oral rumors, even when the forwarders are actively trying to reproduce the information exactly, get distorted to full loss of content after ten hops, and after three or four they loose half of the meaningful content).

Why does spam about this subject get reproduced the most steadily? One could build a mathematical model of gossip reproduction with the following parameters:

1. Persuasion threshold — the degree of belief necessary for the reader to take the information seriously.
2. Eloquence coefficient — the factor (usually less than one, but may as well be greater) expressing how the persuasiveness of the message changes when it's forwarded once. For electronic messages forwarded by verbatim copying, the factor equals to one.
3. Distribution factor — the number of recipients that a single participant decides to forward the information to when 100% convinced.
4. Connectedness characteristic — a property of the acquaintance graph (the average number of common contacts that two people in contact have).

Because the connectedness characteristic is a property of the medium and doesn't depend on the message content, this leaves us with the remaining three values. All of them affect the process of message distribution. When the persuasion threshold is high, the eloquence factor is low, or the distribution factor is low, the process fades out after some predictable number of links. This is what happens to most of the lucky mails: you usually get them from a contact or two, but no real epidemic begins. However, when the aggregate attenuation factor (the ratio of the number of active forwarders on the current iteration to that number on the previous iteration) that depends on the aforementioned parameters is greater or equal to one, the process doesn't fade out but instead continues until all closely-linked part of the acquaintance graph is informed. In practice, that means informing close to all potential forwarders in the Russian part of the Internet.

The persuasion threshold, the eloquence factor and the distribution factor depend on the message content. What made the aggregate attenuation factor exceed one in this case? The persuasion threshold, as it seems, is lowered for messages of this type because people prefer to be safe than sorry: “I'm only 25% convinced that it's true, but if it is, I could save someone's life by forwarding this”. However, the potential forwarders in LiveJournal are gullible enough already, one just has to remember this: “They're going to make ICQ a paid service. To not let it happen, please forward this to all your friends”. So I don't think it was the persuasion threshold that played the crucial role. The eloquence factor of one is also typical for electronic communication (though in some cases the forwarders decide to retell the message in their own words, which usually makes the eloquence factor less than one). This leaves us with the distribution factor. An indirect confirmation to this is that I received the message from some people I rarely talk to. It's for this specific kind of information that the distributors feel it especially important to maximize the number of recipients by all means because they think that someone's life depends on it. (The latter might not be exactly true. For the most, as it seems to me, it's more important to ease their own conscience than to save the little girl's life, and to ease the conscience, one has to perform the ritual of forwarding the message to everyone possible, so that one can say: “I did for the unfortunate wretch everything I could”.)

По-русски: Факторы воспроизводства социальных вирусов