ENDitorial: Copyright combinatronics

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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.

The EU Copyright 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.

If we imagine this as a set of 21 switches where each has two positions,
then to calculate the number of total possible configurations for these
switches we multiply together the number of options for each one:
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2, or written more concisely,
2^21 (two to the power of twenty-one).

This gives us 2.097.152 different ways to implement the directive.

But it gets better. After the 21 exception clauses for reproduction
rights, there comes a 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 distribution.

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
(meaning we’d have 21 switches with 3 settings each), or on the other
hand, you may apply the same exception independently of each other
(meaning we’d have 42 switches with 2 settings each, or 21 switches with
4 settings – doesn’t matter). 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.
It’s very hard to visualize numbers of this size, but the larger number
is about fifteen times larger than the number of stars in our galaxy.

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 the distinction
between “exception” and “limitation”, which could easily
bring the number up significantly.

This basically means 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 tenable
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. At some point somebody must have gotten
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.

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. The question of who stands to
gain from this state of affairs is left as an exercise to the reader.

(Contribution by Smári McCarthy – International Modern Media Institute)