Let us be grateful for small mercies. Thank you Twitter for banning political advertising. Given that such advertising is by its nature biased, tendentious and hard to check, Twitter is behaving as a good publisher should. Politicians may make full use of its outlet. That is democracy. But as the organisation’s chief, Jack Dorsey, points out, with social media awash in “micro-targeting, deepfakes, manipulated videos and misinformation”, those who control it should keep it as clean as possible. Money may not buy truth, but it should not drown fairness.

Facebook disagrees. Its boss, Mark Zuckerberg, declares it “not right for private companies to censor politicians or the news”. He subscribes to the romantic view of social media as the yellow brick road of digital’s global village. The road should not dictate who travels along it, it should just collect the tolls. That includes advertisers, the sustenance of Zuckerberg’s $500bn empire. This argument reruns the celebrated – or notorious – US supreme court ruling on Citizens United in 2010, which overturned restrictions on campaign finance as being an offence against free speech. From then on, lobbyists, corporations, tycoons, anyone with money, could spend what they liked during an election. It declared open season for fake news, targeted ads and dark money “Super Pacs”. That season gave us Donald Trump, and has yet to close.

This presents a regulatory challenge on a scale not seen since the early debates over nuclear weapons

There was some argument for the 2010 decision, as there is in Zuckerberg’s opposition to curbs on advertising. If an ad is mendacious, let the reader judge it as such. Don’t censor the web. If you suppress one form of debate, you shift power to another – in this case editors of the “elitist media”. The democracy of the web should be free to air, come poor and rich. This might have cut ice in digital’s golden age, the nineties and noughties. If you let everything hang out, was the line, global peace would emerge as if from a celestial algorithm. It has not turned out that way. Not a day passes without some new evil being laid at social media’s door, from Instagram’s part in the death of British teenager Molly Russell to the persecution of Britain’s female MPs.

We can all see benefits in the digital revolution. We can also see bad driving out good. As catalogued in Shoshana Zuboff’s tome of our times, The Age of Surveillance Capitalism, we get intrusion, bullying, obscenity and extremism in a thousand devious guises.

Zuckerberg’s oft-repeated claim that he is not a “publisher” is self-serving rubbish. His platforms are devices to project information and opinion into the public realm for profit – as precise a definition of publication as I know. To allow users to do this anonymously and without liability is a licence to mendacity and slander. It pollutes debate and corrupts democracy.

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Free markets are a blessing to human society, but since Adam Smith they have tended towards monopoly and self-interest. Social media are no different. Zuckerberg makes the same claim as America’s gun lobby: Facebook does not kill people, people do. As the Edward Snowden revelations showed, the boundary between social media and mass surveillance, whether by capitalism or the state, is now hopelessly permeable. Like any market, this one must be regulated. It is a poor comment on western democracy that it still is not.

Anyone delving into this realm is easily lost in technology and jargon, but we must try. Wiser heads – including at times Zuckerberg himself – have recognised that things are getting out of hand. Facebook, Google and Twitter this year lobbied the British government to introduce a mechanism for combating “online harm”. They remain reluctant to take that responsibility themselves.

I believe this presents a regulatory challenge on a scale not seen since the early debates over nuclear weapons. We must somehow disentangle the public from the private digital sphere. There must be control over those who trade the identities and behaviour of individual citizens. We must define the concept of causing online harm, as distinct from causing offence. We must place obligation and liability on digital “publishers” for the accuracy and legality of third-party content – as we do on conventional publishers.

As in any public forum, anonymity must end for those expecting the privilege of access to public debate. Facebook and others accept de facto moral liability, by filtering and censoring “unsuitable” content. They accept, at last, that showing teenagers how to take their own lives is not free speech but public menace.

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Now they must accept that regulators should dictate the rules of democracy, or it will degenerate into an online Game of Thrones. Publishers have an obligation not to disseminate lies. One reason for the ongoing popularity of the mainstream media, such as the BBC, the New York Times and this newspaper, is that their information is trusted. Some editor is subjecting their output to some ideal of balance, fairness and accuracy. Material is not spewed out at random, or targeted so as to confirm individual bias. Editors are not, as early web enthusiasts predicted, out of date. They are necessary.

The British press has fought against state regulation, other than over monopoly and laws of libel. I think that is right, not out of principle but because statutory regulation is not justified by press misbehaviour or imbalance – or not yet. Self-regulation sort of works. At present it is not the mainstream media driving decent people out of politics. It is what Zuboff calls the “psychic numbing of strip-search technology”. We have not begun to grasp its potency or its aura of invincibility. Today’s robber barons steal from us not our money but something more important, our privacy and integrity as individuals. They cannot remain unregulated.

• Simon Jenkins is a Guardian columnist