Computer viruses, herd immunity, and public goods
| Gabriel |
Today Slashdot has a post arguing that anti-virus software has both a private character (your computer works) and positive externalities (you don’t spread the virus to others) and this latter quality implies a public goods character that may make anti-virus software worthy of some kind of subsidy, including the indirect subsidy of a public service propaganda campaign. (I don’t see how much value a “the more you know” PSA would have, given that Windows is already obnoxiously in your face if you fail to install anti-virus software or let your the subscription lapse). Something the article doesn’t mention but is entirely consistent with is that there are subnational units who benefit from widespread immunity as a club good and so almost all corporate and university buy a site license for anti-virus software. This is perfectly rational behavior as they end up capturing most of the private and public (or rather, club) benefits of anti-virus in the form of less IT support as well as avoiding things like lowered productivity, bandwidth siphoned by botnets, and exposure to corporate espionage.
Similarly, Megan McArdle occasionally talks about how parents who refuse to vaccinate their children are not just endangering their own children but creating a public health problem. This is something I take seriously, not only as someone with a professional interest in diffusion but I also have a personal stake given that I have a toddler and autism junk science is very popular in west LA. So basically my daughter has an elevated risk of measles because these crackpots are terrified of a vaccine additive that is a) harmless and b) hasn’t even been in use for over ten years.
Both of these cases rely on the logic of diffusion. The big picture is that in an endogenous growth process the hazard is a function of extant saturation so the more infected there are the more at risk any given uninfected person is and by implication anything that lowers the overall infection rate lowers the hazard. A more complex and more micro version comes from the mixed contagion / threshold diffusion model of the sort that was modeled in Abrahamson and Rosenkopf’s 1997 Organization Science paper. (I’ve mentioned it before, but I really do love that paper). In these models individuals have a frailty level drawn from a random distribution and are exposed to (network) contagion and (generalized) cascades from their environment. When the contagion effect exceeds the individual’s threshold, the individual becomes infected and starts spreading the infection, thereby increasing the cascade and contributing to the social network effect on alters. What immunization does is it raises the individual’s threshold appreciably, but not to infinity. This makes the individual less likely to be infected, and where the public good aspect comes in is that this is especially so if the individual is facing only low to medium contagion pressure from the environment.
Another way to think of it is as the flipside of public goods, the tragedy of the commons. If everyone else in the world but you installed Symantec and got a measles shot, it would actually be very safe for you as an individual to forgo these protections because everyone else is healthy and won’t infect you or your computer. On the other hand if nobody else in the world had this protection you would be constantly bombarded by both corporeal and computer viruses and so personal immunization would be more attractive, though because your threshold is finite even with immunization you would still be much more vulnerable than if immunization were widespread. The irony is that in the high-vaccination and low-vaccination contexts there are very different individual benefits on the margin vs on average.