# Copyright Combinatorics &#8211; exercises in the banal mathematics of EU policy

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Although the creation of the single market has been the primary focus of the European Union for decades, it often seems that for every step forward it takes two back. In that respect it’s often rather interesting to look at the mathematics as they play out in the different directives that come out of Brussels.

After a conversation with Joe McNamee from EDRi a couple of months ago, I took a closer look at the exception clauses in the Copyright Directive. The directive outlines 21 different optional exceptions or limitations to the right of reproduction of copyrighted works. Each country implementing the directive can choose to either include or leave out the exception clause. This gives us 2.097.152 different ways to implement the directive.

But it gets better. After the 21 exception clauses for reproduction rights comes an paragraph stating that where the Member States may provide exceptions or limitations for reproduction, they may provide similarly an exception or limitation to the right of distribtuion.

This can be understood in at least two different ways, with radically different results. On the one hand, if you have an exception on reproduction then you may also have the same exception for distribution, or on the other hand, you may apply the same exception independently of each other. The wording suggests the latter, but at the same time it seems slightly absurd to have an “oh by the way you may also” in a directive; there are other cleaner ways to approach this. There is probably some literature that I’m unaware of about which one they mean, but it’s easier to do the math on both cases than it is to navigate through commission and parliament documentation.

The first case is a three step process where each exception can be either “off”, “on for reproduction” or “on for reproduction and distribution”. This means we get three to the power of twenty-one options, totalling 10.460.353.203.

The second case is a four step process where each exception can be ”off”, “on for reproduction”, “on for distribution”, or “on for reproduction and distribution”. This gives us four to the power of twenty-one options, totalling 4.398.046.511.104.

That’s either ten billion or four trillion ways to implement the copyright directive, depending on how you read article 5, paragraph 4.

Take your pick. It doesn’t matter either way. This back-of-envelope analysis doesn’t even touch on the combinatorical implications of different understandings of the details of articles 5.5, 6 and 7 in particular, and in general the rest of the directive, mostly because they’re less directly quantifiable. Let alone does it distinguish between “exception” and “limitation”, which could easily bring the number up significantly.

These kind of figures boggle the mind. They basically mean that a priori there is a one in three hundred and eighty million chance that any two member states come up with the same implementation, taking the slightly better case. How does that serve the ideal of a single market? It looks like internal dissolution about the specifics of the exception clauses, with each country being difficult in its own little way and no political hardheadedness forcing a teneble solution has yielded a completely useless directive in terms of unification.

While it is true that all the member states could in theory decide on the same exceptions, making this headache go away, the fact that they’re all optional suggests that in each case there was at least some strongly for and some strongly against, unless of course that at some point in blind fury somebody got so tired of debating the exceptions that they just lumped all of them together under optional and decided to let the Member States figure it out. To be fair, I can’t say I blame him.

Either way, what this shows is that the EU is not effectively managing to create a single market, and through its policy on intellectual monopolies may even be pushing the markets further apart. I’m going to allow the question of who stands to gain from this state of affairs as an exercise to the reader, but I’m fairly certain it’s neither the general public nor the creators of creative works.