IN 2011, the American historian Rick Perlstein sketched out the anatomy of the beast.

"It takes two things," he wrote, "to make a political lie work: a powerful person or institution willing to utter it, and another set of powerful institutions to amplify it."

Perlstein didn't bother to ask why anyone in politics would want to lie. In the United States, as here, that became self-evident long ago. The risk of public censure is no inhibition when the public are your intended victims. If you have right on your side - and doesn't everyone? - any wrong can be made to sound excusable. The only important thing is not to get caught.

So let's say you've been passed a memo from within the Government. It states that Nicola Sturgeon has told the French ambassador she would prefer David Cameron to "remain" in office. If it's true, it's quite a story. It suggests Sturgeon has been dishonest with voters. How do you discover if this enticing tale stands up? Surely, sooner or later, you question the First Minister and the ambassador. Right?

Last week, the Daily Telegraph's great coup against the SNP leader, less amplified than trumpeted, began to fall apart on first glance. As any half-attentive reader could see, a fundamental piece of journalistic practice had been - let's say - neglected. Why was that? For some of us, it was the paramount question.

Then came the denials from those who had actually been present during the meeting in question. The First Minister said the claim was "100%" false. The French Consul General rebutted the allegation. A spokesman for Sylvie Bermann, the ambassador, stated that Sturgeon "did not touch on her personal political preferences with regard to the future prime minister".

That, you might have thought, was that. In another era the Telegraph might have published a brief apology and privately rued its failure to back a claim with proof. Labour people who had exulted in the tale might have withdrawn quietly - to be fair, a few had the decency to do just that; others deleted embarrassing tweets - and awaited another opportunity. That's not how a political smear works.

First, there was Perlstein's amplifier, the Telegraph. Its reputation as a serious newspaper - such as remains after the HSBC debacle - caused word of the disputed memo to be broadcast far and wide. The document's unnamed author had related the central claim sceptically, but that was no obstacle. Suddenly Sturgeon, according to every outlet, was facing "allegations". To help matters along, some journalists and political enemies began to question the veracity of the French. Without a shred of proof, blunt denials were spurned with: "They would say that."

Then the smear entered its important phase. This was, in all probability, its entire purpose. Sundry individuals in the media and rival parties, each unable or unwilling to substantiate a word, told us they "knew" that another Tory government is the deepest desire of the SNP leadership. Sturgeon could deny it all she liked; not a single piece of evidence would be provided; but hacks of every description chose to trade on their supposed credibility. They "knew". That was all anyone else needed to know.

So a dodgy third-hand memo, composed by someone who was not present, with an allegation denied by those in the room and doubted by the document's author, came to rest on the claimed insider knowledge of those who, in turn, could not or would not back up their assertions. An argument over facts became a shouting match over trust.

Deceit in politics needs helpers, dupes and stooges. All categories were no doubt represented in this little affair. For all that the claim got nowhere, those responsible for conveying a civil servant's note to the Telegraph must have been well satisfied. Get enough reputable types to affirm what they "knew" to be true, ran the calculation, and something would stick in voters' minds. For a day or two, the very absence of proof meant it was Sturgeon's word against a chorus of accusers. Amplification, the foghorn of partisan conviction, was all.

Like all smears, this was more than just a simple lie. As these things often do, it involved a kind of non sequitur. An alleged fact justified previously held beliefs. When the allegation began to dissolve, belief, sufficient unto itself, justified all. The aim, ultimately, was to tarnish Sturgeon's character and to cause her to forfeit the public's trust, and hence their votes.

The risk run by the perpetrators and those amplifying the lie involved public scepticism. When does a journalist ever fail to question the subjects of an allegation? The voters who thought a little more might have reached a more dangerous conclusion as the Telegraph's effort foundered. Is this the best the First Minister's enemies have got? What happened to arguments, evidence, actual facts?

If they have nothing else in common, Ed Miliband and Sturgeon share that question. The Labour leader was another to confront the impossible non sequitur last week when his policy on nuclear defence came under attack. As a pained Miliband tried to point out, there is no actual dispute between himself an his Tory opponents over the renewal of the Trident fleet. Both parties want four useless missile-bearing boats. That fact did not deter Michael Fallon, Tory Defence Secretary.

Availing himself of an article in the Times for his amplifier, he alleged that Miliband was "willing to stab Britain in the back". The alleged reason was a deal with the SNP that is not, in fact, on offer. The purported proof - a remarkable example of the non sequitur - was that Ed Miliband had contested the Labour leadership against his brother David. In Fallon's lurid terms, a man capable of betraying his own brother - by gathering more votes - would not flinch from betraying his country.

So stray facts were distorted, conflated and wielded to prove a falsehood. There is no chance whatever of Miliband straying from the nuclear doctrine obeyed by all Labour leaders. Fallon's real purpose was to plant a seed, to assert - again, without proof - that his victim is not as he seems, that he cannot be trusted, and that his party cannot be trusted. Beyond the world of the smear, the dismal fact is that Labour and the Tories do not differ over the future of the nuclear deterrent. Fallon didn't care.

Behind the political lie is a strange superstition. It holds that character and trust are everything. The belief persists even when we know perfectly well that successful politicians are not necessarily good or trustworthy people. The lie depends, in fact, on a belief in honesty. It counts as irony: the smear is meant to destroy trust despite the fact that most of us wouldn't trust a politician to say "Hello" sincerely. The smear says X is no better, and might be worse, than the rest of us. The rest of us already knew that.

There is nothing new about any of this. In Rome in the first century BC the orator and politician Cicero established a model for the smear campaign that has been studied by political types ever since. Probably his most brilliant campaign of "false rumour" was waged against Mark Antony after the death of Julius Caesar, but Cicero was not above accusing one Publius Servilius Rullus, entirely falsely, of promoting land reform simply to raise a private army. He followed the maxim laid down by his brother Quintus in one of the first handbooks on campaigning: always remind the public "of what scoundrels your opponents are and smear these men at every opportunity".

In the American presidential race of 1828, backers of the revered John Quincy Adams threw all they could at his opponent, Andrew Jackson. Son of a mulatto and a prostitute, husband to a bigamist, a murderer in his own right: Jackson was smeared relentlessly. He still managed to win, however.

That isn't always the case. The Zinoviev letter, so called, might not have hurt the Labour vote by much on its appearance in the Daily Mail four days before the 1924 general election, but it certainly bolstered the Tories. Purporting to show Moscow handing out orders to the Communist Party of Great Britain, it helped Stanley Baldwin to a landslide and did for the old Liberal Party as a bonus. The forgery was a smear of the most brutal sort. Its purpose was to create fear of the Red menace and, yet again, destroy trust.

The Mail, never averse to that brand of fun, returned to the well in 2013. Just before its North British edition made common cause with Scottish Labour in the referendum campaign, the Forger's Gazette - as the late Michael Foot liked to call it - decided to assault Ed Miliband through the memory of his father. It mattered not at all that the late Ralph Miliband had been a distinguished scholar who fought for the country that gave him refuge from Nazism. Those who smear are not sentimental.

As the Mail titled its nasty piece of work: "The man who hated Britain: Red Ed's pledge to bring back socialism is a homage to his Marxist father. So what did Miliband Snr really believe in? The answer should disturb everyone who loves this country ..." As it turned out, a great many were more disturbed by the motives behind the article. The Mail thought it proper, in the 21st century, to smear a man because his father had been a Jewish Marxist? Such is the risk run by all who smear.

As often as not, bullying plays its part. If a politician is both successful and deemed beyond the pale, as in the case of Sturgeon, the smears are almost inevitable. Ken Livingstone was smeared endlessly, so he maintains, from the instant he staged his coup at the old Greater London Council until the day he stepped down as mayor of the city. During the 1983 Bermondsey by-election campaign Labour's candidate, Peter Tatchell, was described routinely by tabloid papers as "Red Pete, the gay rights campaigner". Both facts were treated as indictments.

Scarcely an election of any sort passes without smears or allegations of smears. It is a reminder that, for some, democracy is an unsatisfactory affair. It also tells us, if we needed telling, that journalism has been complicit in dirty tricks for centuries. The distinction between reporting and opinion is as thin as the line between honest campaigning and smear tactics. For those content to cross the divide, social media is these days a gift, a hotbed of gossip, anonymous rumours, and lies passed around like chain letters.

Twitter and the like can also eradicate a smear, as the Telegraph discovered last week. Those boasting of what they "knew" were overwhelmed by those asking hard questions and demanding proof. Social media are providing an interesting test, indeed, for the characters who specialise in the political lie. Any old rubbish can be passed off as fact, but every claim imaginable is challenged almost instantly.

Power, in Perlstein's sense, clings on. Voices of authority can still just about get away with the simple smear. In January 2012, for example, Jeremy Paxman decided to enliven an interview with Alex Salmond by comparing the then First Minister to the Zimbabwean dictator Robert Mugabe and suggesting that an independent Scotland would be a one-party state. Patently, this was in one aspect simply false - Salmond wins votes and loses votes - and in another a prejudice passed off as journalistic inquiry.

Why compare a First Minister to a dictator in waiting? Because Paxman "knew" where the SNP were heading, "knew" what independence must mean, and "knew" the character of the man he was interviewing. No evidence was adduced, but that was of no account to the talking head. The representative of the BBC was simply indulging in a bit of sport for the benefit of viewers who might agree with him. Those who have - you can take your pick - compared Salmond to Mussolini, Milosevic or Hitler have played the same game.

In the end, it says more about them than him. Smear has its neatest echo in the word fear. The tactic emerges from the bag of dirty political tricks as an act of desperation, when all the arguments, promises and blandishments have failed. It is no comfort to the victims, but those who are smeared should know one thing: they must be doing something right.