Twitter has got itself into a tangle. The social network's decision to remove all links to the horrific footage showing the apparent beheading of the photojournalist James Foley is one that most of its users, reasonably, support.

The social network went still further, suspending or banning users who shared the footage or certain stills, following public tweets from the company's CEO, Dick Costolo, that it would take action against such users.

It is hard to think of anyone having a good reason to view or share such barbaric footage, but Twitter's proactive approach reverses a long record of non-intervention.

Twitter has promoted its free speech credentials aggressively since the network's inception. The company's former general counsel once characterised the company as "the free speech wing of the free speech party", an approach characterised by removing content only in extreme situations – when made to by governments in accordance with local law, or through various channels designed to report harassment.

The social network's response to the Foley footage and images is clearly a break from that response: not only did the network respond to reports complaining about posts using the material, they also seem to have proactively sought it out in other instances.

And yet there is not a universal consensus on the use of the images, as was reflected by the New York Post and New York Daily News' decision to use graphic stills from the footage as their front-page splashes. Here begin the problems for Twitter: the network decided not to ban or suspend either outlet for sharing the images – despite banning other users for doing the same.

Twitter has not been nearly as eager to enter the content policing game in other situations. Like many other major companies, Twitter has long insisted it is not a publisher but a platform.

The distinction is an important one: publishers, such as the Guardian, bear a far greater degree of responsibility for what appears on their sites. By remaining a platform, Twitter is absolved of legal responsibility for most of the content of tweets. But by making what is in essence an editorial decision not to host a certain type of content, Twitter is rapidly blurring that line.

The network has not been as quick to involve itself when its users are sharing content far beyond what is even remotely acceptable – even when the profile of the incidents is high.

In the UK, huge attention was drawn to a campaign of malicious abuse and rape threats against Caroline Criado-Perez, a journalist and feminist activist who successfully campaigned for Jane Austen to become the new face of the £10 banknote. The threats – so severe that two people were jailed for their involvement in the abuse – came in so fast and from so many sources that Criado-Perez was unable to keep pace through Twitter's convoluted harassment reporting procedures. Other women who rallied to support Criado-Perez were subjected to similar mass abuse. And this was just one incident among many.

Twitter's strongest, perhaps only, justification for its sluggish and minimal response was that it could only act through its harassment channels, and could not become a curator or editor of content on its site.

With its actions on Tuesday and Wednesday, that facade is eroding: is Twitter saying sharing stills of a murder requires urgent intervention while threatening to rape and mutilate someone does not? What are the criteria for Twitter taking direct action? Why can some users share an image, while others will be banned for doing the same?

Twitter, Facebook and Google have an astonishing, alarming degree of control over what information we can see or share, whether we're a media outlet or a regular user. We have handed them a huge degree of trust, which must be earned and re-earned on a regular basis.

If Twitter has decided to make editorial decisions, even on a limited basis, it is vital that its criteria are clearly and openly stated in advance, and that they are consistently and evenly applied.

Whether you are an ardent First Amendment advocate or a passionate believer that networks must do more to police their backyards, the worst of all possible worlds for the flow of information is one in which we shift from the rule of democratic law to one governed by the arbitrary, inconsistent and perhaps kneejerk rulings of a tiny group of large companies.

Yesterday Twitter was the free speech wing of the free speech party. Today it's a company willing to take action against one particular piece of vile content. What will it be tomorrow?

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