P2P lawsuits examined with graph theory

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P2P infringement cases are fascinating for several reasons. They are the essence of my argument the intersection of law and technology is going to be a significant one in the future once courts become more widely cognizant of the difference between abstraction and implementation. A case I am keeping tabs on now ACHTE/NEUNTE v DOES 1-2,094 is interesting because of the argument advanced regarding the BitTorrent protocol.

To review, with BitTorrent and most modern P2P protocols an individual offers to share a file. Various users locate files of interest to them. Traditionally, in the BitTorrent model the users locate a torrent file from a search engine or some other source, the torrent file points to a tracker which delivers a list of contacts to the program who have portions of the desired file. The program requests parts of the file from a variety of sources and reassembles the file once all the parts are downloaded.

The ACHTE case is currently arguing over the joining of the various DOES. The plaintiff argues BitTorrent is different than other P2P systems used in the past.

This distributed nature of BitTorrent leads to a rapid viral spreading of a file throughout peer users. As more peers join the swarm, the likelihood of a successful download increases. Because of the nature of a BitTorrent protocol, any seed peer that has downloaded a file prior to the time a subsequent peer downloads the same file is automatically a source for the subsequent peer so long as that first seed peer is online at the time the subsequent peer downloads a file. Essentially, because of the nature of the swarm downloads as described above, every infringer is simultaneously stealing copyrighted material from many ISPs in numerous jurisdictions around the country.

Essentially, the plaintiff is saying each peer automatically begins distributing chunks of the file in question as soon as they receive it. As a corollary, each users is infringing their copyright in each jurisdiction any member of the swarm is in. Therefore, they argue, they should be able to combine all 2,096 anonymous users into one suit in their chosen jurisdiction.

The EFF weights in via amici brief.

Fed. R. Civ. P. 20. Thus, multiple defendants may be joined in a single lawsuit only when three conditions are met: (1) the right to relief must be “asserted against them jointly, severally or in the alternative”; (2) the claim must “aris[e] out of the same transaction, occurrence, or series of transactions or occurrences”; and (3) there must be a common question of fact or law common to all the defendants. Id.

Joinder based on separate but similar behavior by individuals allegedly using the Internet to commit copyright infringement has been rejected by courts across the country. In LaFace Records, LLC v. Does 1-38, No. 5:07-CV-298-BR, 2008 WL 544992 (E.D.N.C. Feb. 27, 2008), the court ordered severance of lawsuit against thirty-eight defendants where each defendant used the same ISP as well as some of the same peer-to-peer (“P2P”) networks to commit the exact same violation of the law in exactly the same way. The court explained: “[M]erely committing the same type of violation in the same way does not link defendants together for purposes of joinder.” LaFace Records, 2008 WL 544992, at *2. In BMG Music v. Does 1-4, No. 3:06-cv- 01579-MHP, 2006 U.S. Dist. LEXIS 53237, at *5-6 (N.D. Cal. July 31, 2006), the court sua sponte severed multiple defendants in action where the only connection between them was allegation they used same ISP to conduct copyright infringement.


Nor does the analysis change because the BitTorrent protocol works by taking small fragments of a work from multiple people in order to assemble a copy. The individual Defendants still have no knowledge of each other, nor do they control how the protocol works, and Plaintiff has made no allegation that any copy of the movie they downloaded came jointly from any of the Doe defendants.

Joining thousands of unrelated defendants in one lawsuit may make litigation less expensive for Plaintiff by enabling it to avoid the separate filing fees required for individual cases and by enabling its counsel to avoid travel, but that does not mean these well-established joinder principles need not be followed here.4 Because this improper joining of these thousands of Doe defendants into this one lawsuit raises serious questions of individual fairness and individual justice, the Court should sever the defendants and “drop” Does 2-4577 from the case. See Fed. R. Civ. P. 21.

The EFF effectively says just because BitTorrent works slightly differently on an implementation level, doesn’t mean the actions and knowledges of the individual users are any different than they would be if the service were Limewire or Kazaa.

I wish to propose a novel thought experiment regarding the technical aspects of the BitTorrent transactions, and the joinder arguments the plaintiff and the EFF discuss in their filings.


(1) There is some user A such that A has a file F to share on the network.

(2) File F can be represented as n chunks f1-fn

(3) Users {U} wish to obtain copies of file F via the BitTorrent protocol

(4) {U} has n members

We can readily deduce for any {U} to have F, A must distribute it in total at least 1 time. Without this first transfer infringement did not occur. This is an iff relationship. The plaintiff argument assumes all {U} will transmit all or some of f1-fn to other users, and assumes also each {U} will receive chunks from multiple other users. While it is most optimal for A to distribute f1-fn to n different user such that each of those users can begin transferring their chunks to each other in a swarm, it is not necessary for the transfer of A to take place. If such optimal transmission did take place you would be able to examine it in a graph-theoretic manner. If, as a basis step, we assumed A could send the entire file in one blast, but did so by distributing the chunks to n users, we would have a directed graph in which A is connected to each {U} – it would resemble a star pattern. In step 2 each individual in {U} would transmit its copy to each other member of {U}. At the conclusion of step 2 {U}’s transfer relationship could be expressed as a K map with nodes {U} and with each node {U} having an A->{U} digraph connection. Under this condition the plaintiff characterization would be correct that each {U} had sent to and received from each other member of {U} thus having both a receive and send event terminating or originating in every jurisdiction containing a member of {U}.

Let us contemplate next, now that all {U} have become seeders with complete copies, what would occur when another user joins the swarm. Given there are n chunks, and at least n+1 users (n users {U} plus A) then at least 1 user in {U} + A will not have contact with the new user. If another user joins after the first new user completes his download, then there will be n+2 users distributing n chunks to the new user leaving 2 users without contact to the new user.

In reality there are going to be more chunks than users, users are going to go on and off line, they are going to join at different times, and a whole host of other complicated timing issues is going to occur. Let us examine another scenario under the 4 assumptions. The prior example assumed a new user would be getting its chunks from as many other users as possible, but this is not the case. Typically a new user connects to a subset of the available swarm, with sufficient participants this easily maxes out the available downstream bandwidth for a given user. Under such a circumstance these second instance transfers are likely as not to never contact the original source A. Even if, as plaintiff argue, all the original users {U} have touched on jurisdictions inhabited by every other member, the jurisdiction of the second instance transfers will only be touched by the subset of {U} they contact.

From what I understand of the issues, the question I see is dependent on how a discrete act of infringement is defined. If each transferred copy is a single discrete act of infringement, than it would be impossible to reasonably believe all 2,096 users were members of the first instance, or that they were all connected in one of the second instance transfers. If, on the other hand, the entire swarm construct is considered one single discrete instance of infringement this would be a reasonable argument, however because they would only be responsible for one discrete act of infringement the consequences would be less severe as it would be spread over 2,096 individuals. I doubt the plaintiff would tolerate treating the incident as if 2,096 individuals had made a single copy of their movie, but without ceding that reading of the situation their argument for joining all the individuals is not supportable from a technical perspective. When you start to contemplate what is infringement, is it one chunk or is there a threshold of transfers, the situation becomes even more difficult to grasp.

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