When we pay our bills using a plastic card, we are simply authorizing alterations to the information stored in some computers. This is one aspect of the symbiotic relationship that now exists between money and information. The modern financial world is byzantine in its complexity, and mathematics is involved in many ways, not all of them transparently clear.
Fortunately there are some bright spots, such as the fact that it is now possible to measure information. This is the result of the pioneering work of Claude Shannon in the 1940s and 1950s. Shannon’s definitions can be used to prove theorems in a mathematically precise way, and in practice they provide the foundation for the machines which handle the vast amounts of information that are now available to us. However, that is not the end of the story.
In 1738 Daniel Bernoulli pointed out that the mathematical measure of ‘expectation’ did not allow for the fact that different people can value the outcome of an event in different ways. This observation led him to introduce the idea of ‘utility’, which has come to pervade theoretical economics. In fact, Shannon’s measure of information can be thought of as a generalization of expectation, and it leads to similar difficulties. As far as I am aware, academic work on this subject has not yet found applications in practice.
In the absence of a theoretical model, many countries (including the UK) have tried to set up a legal framework for information. First we had the Data Protection Act (1998), intended to prevent the misuse of the large amounts of personal data stored on computers. But it is very loosely worded, and consequently open to many different interpretations. (In one case, a police force believed that the Act prevented them from passing on information about a person whom they suspected of being a serial sex offender. This person then obtained employment elsewhere as a school caretaker, and murdered two pupils.) The next step was the Freedom of Information (FoI) Act (2000), which now seems to be regarded as unsatisfactory – on all sides. Those who see themselves as guardians of our ‘right to know’ are dissatisfied with the wide range of circumstances which can be considered as exceptions. Those who see themselves as guardians of our ‘security’ are concerned that attempts to prevent terrorist activities may be compromised.
We are expected to observe certain rules and regulations about how we use our money, but we are allowed to keep it safe. Will similar rules and regulations about information emerge?
Recently I looked at a question which led me into these muddy waters. The question was a simple instance of a very general one. Suppose a piece of information is only partly revealed to us: it may have been corrupted by transmission through a ‘noisy channel’, or it may have been encrypted, or some important details may have been intentionally withheld. How much useful information can we deduce from the data that we do have?
My example came from the unlikely source of the popular BBC television programme, Strictly Come Dancing. The problem was as follows. In order to determine which contestants should be eliminated from the show, the programme’s creators have devised a complex voting algorithm. First the judges award scores, and these are converted into points. Then the public is invited to vote, and the result is also converted into points. Finally the two sets of points are combined to produce a ranking of all the contestants. But the public points and the final ranking are not revealed on the results show, only the identity of the two lowest contestants. I was able to show that in some circumstances the revealed data can indeed provide a great deal of information about the public vote.
Strictly Come Dancing arouses great passion among its followers, and the lack of transparency of the voting system has led to numerous requests under the FoI Act. Most of these requests have been refused by the BBC, on grounds that appear to be valid in law. It seems that the FoI Act was originally based on some rather idealistic notions. When the Act was passing into law, it had to be converted into a more realistic instrument, and the resulting form of words therefore provides for a large number of exceptions to the general principle. Specifically, the BBC is able to claim that the details of the voting are exempt, because they are being used ‘for the purposes of journalism, art, or literature.’
In my view the FoI Act is simply a shield that deflects attention from the heart of the matter. The public is invited to vote and therefore has good reason to be interested in the mechanics of the voting procedure and its outcome. In addition to details of the method used to combine the public ranking with the judges’ ranking, there are other causes for concern. For example, multiple voting is allowed, and this opens up the possibility of misuse by agents who have a vested interest in a particular contestant.
I began by remarking that there is a close relationship between money and information. We are expected to observe certain rules and regulations about how we use our money, but we are allowed to keep it safe. Will similar rules and regulations about information emerge, and when?
Featured image credit: binary code by Christiaan Colen. CC-BY-SA 2.0 via Flickr.