Saturday, June 18, 2011

The Invisibility Cloak: Bad for Human Rights?

There was some dramatic news last year. Scientists in Germany have apparently been getting very close to making an invisibility cloak. For the first time ever, through innovations in light-bending materials, a small object was made invisible from all angles. Though the technology is not yet usable in a Harry Potter-like fashion, the development of a cloak one could just throw on to become invisible may only be a few years away.
Now before all you sci-fi and fantasy fans go nuts, just ponder the question: what are the possible uses for an invisibility cloak? I think you'll come to the conclusion that an invisibility cloak would mostly be useful for two things: mischief and mayhem. If invisibility cloaks became widely available to the public, the crimes of peeping toms, shoplifters and murderers for example would all become easier to get away with. Which brings me to the subject of human rights. To understand the full ramifications of widespread invisibility, it's useful to become familiar with the idea in law and economics, of a mathematical equation for the "optimal punishment" for a crime. Donald Wittman's excellent textbook on law and economics explains this concept the best. Because not all criminals can be caught, in order to make them face the full costs their crimes bring upon society "...the expected punishment, probability of being punished (P) times the fine (F), is set equal to the harm of the crime. That is PF = H. Thus the lower the probability of being caught, the higher the level of punishment should be." In other words, for the legal system to adequately dissuade people from committing crimes, two things are possible: 1) increasing the probability of catching the criminal, or 2) increasing the punishment. So the necessary punishment F varies inversely with the probability of being caught. So if suddenly it were half as likely for someone to get caught for a particular crime, to maintain optimality, the punishment must become twice as harsh. This seems to explain at least in part why countries without advanced systems of crime detection and law enforcement (low P) may punish small crimes with huge punishments (high F, e.g. cutting off someone's hand for shoplifting, or hanging, drawing and quartering for various crimes in medieval England).

So what does this have to do with invisibility cloaks? Clearly, (no pun intended), if invisibility cloaks became cheap and widely available to criminals,  the probability of getting caught (the P in the optimal punishment equation), for many crimes would decrease. Most crimes would become easier to get away with by use of an invisibility cloak. But not only would it help in the perpetration of crimes, an invisibility cloak would help people resist arrest for any crime, even those not utilizing invisibility, such as cybercrime and fraud perhaps. If the cops came to your door, you could just slip on your invisibility cloak and make a break for it.
So in a world of widespread invisibility crimes, to once again make criminals fully face the costs they bring to society, the legal system could greatly increase F, the punishment, or alternatively attempt to bring P back up to its original levels, perhaps by becoming ever more invasive into peoples lives. Either way an invisibility cloak sounds like bad news, both for the possible victims of invisibility related crimes and for human rights in general. I personally wouldn't want shoplifting a pack of gum to be punishable by years in prison just because pesky invisible people have ruined the legal system for everybody.
Haven't these scientists seen "Hollow Man" or "Predator"?

 Donald Wittman, Economic Foundations of Law and Organization, Cambridge University Press, 2006

Tuesday, June 14, 2011

Party-nomics, Facebook and Positive Network Externalities

Have you ever been party-hopping with friends, found a party or a bar that wasn't highly occupied, and then (maybe due to a unanimous decision, or maybe due to the whining of a few) immediately left to seek a more popular venue? If so, you have helped fulfill a self fulfilling prophesy. In this kind of situation, if more people are willing to stick around at the unpopular venue, it can have had a chance to become popular. But with everyone leaving 5 minutes after getting there, the place will remain, in the parlance of our times, "dead" (as in "dude, this party is dead, let's split"). This phenomenon is very well described by what economists call "positive network externalities". Unlike a good without positive-network externalities such as a banana, where one person's benefit from eating a banana does not depend at all on how many other people eat bananas, a person's benefit from going to a party greatly depends on how many other people go to that particular party. This is because as another person joins the party, benefits (positive externalities) go to all the other partygoers. The more people there are at the party, the more chances there are for exciting social encounters. Therefore there is more benefit both for people already at the party as well as for prospective partygoers. This self-fulfilling prophesy will attract people to the party up to the point when things get overcrowded. After this point, each person's benefit will actually decrease as each additional partygoer arrives. With the number of partygoers on the x axis, and the individual enjoyment of the party on the y axis, a graph of the "total fun" of a party (if we could quantify it) would look something like this:
Note the steep drop-off at a certain point, when the number of partygoers reaches the maximum capacity of the party's physical location. Clearly people like a good party, but no one wants to get squished. As you can see, the appeal of a party is a function of the number of people already there, and this determines how many people will want to join that party in the future. The self fulfilling prophesy is in full effect. Because of this, the success or failure of a party depends largely on the number of people attracted in the initial stages, and this can depend largely on chance. When a party has reached a "tipping point" of popularity through word of mouth, it can fill up to the point of reaching the maximum capacity of the party's physical location. Then there will be spillover to the less popular parties, and a new equilibrium will be reached.
But what about a party with no physical location, other than tiny ones and zeroes occupying a server? Yes I am talking about the internet, and specifically the huge social gatherings that occur 24/7 on social networking sites like Facebook and Twitter. Just like a parties, these sites bring positive network externalities to their users. Meaning, the more people there are on Facebook, the more beneficial it is for a new person to join Facebook. But unlike parties, huge websites do not face the constraints of physical space. So, roughly graphing the benefit of being on a social networking website in response to number of users would look something like this:
Rather than a drop in total fun occurring at the point of some number of users as we saw with the physical party, there is simply a levelling off. There are diminishing marginal returns to fun here, because, for example with Facebook, you can only have so many Facebook friends (5000 as of today I believe, and even fewer you really interact with on a regular basis). But there is no drop-off in benefit, because there is no restriction on capacity. Unlike a real physical party, this party on the internet shows no sign of slowing down. Facebook has become a fixture, and it would be very difficult for another company to come in and compete with it on its own turf. A new site would need to provide amazing new benefits to compete with the massive positive network externalities Facebook has built up through its user base. And why did Facebook build up such a large base of users? Partially because it's a very well designed site, but also because of the initial luck of the draw. Mark Zuckerberg's party got the initial rush of partygoers it needed to sustain itself and grow. Without any capacity restrictions, it seems to be here to stay. Even if there were a better party next door, people would probably ignore it.