In 1972, Willy Brandt, the West German chancellor, faced a no-confidence vote tabled by the opposition conservatives. The omens didn’t look good. If all the Christian Democrats voted along party lines Brandt would be out. To his surprise, he scraped in by two votes. The wheels of history turned in his favour. Brandt was able to pursue his policy of detente with Moscow and the communist bloc.

As we now know, someone was giving the wheels a surreptitious push. The Soviet leader, Leonid Brezhnev, wanted Brandt to stay in power. Brezhnev believed that improved relations with the west would help revive the struggling economies of the east. And so the KGB ordered the Stasi, East Germany’s secret police, to rig the vote in Brandt’s favour.

The Stasi set about this task with gusto. It had corrupted two rightwing members of the Bundestag, Julius Steiner and Leo Wagner. The pair had what you might call Trumpian weaknesses: women and money. East Berlin paid them $97,000 so they would abstain. A journalist operative delivered the cash in a brown envelope. CDU leader, Rainer Barzel, should have been chancellor but never was.

In the febrile run up to November’s US presidential election, David Shimer reminds us that foreign interference is nothing new. His debut book Rigged delves into the cold war, when both Washington and Moscow sought to influence the politics of third countries. Their reasons were self-interested and strategic. The CIA wished to keep communist leaders out; the KGB wanted them in.

Beginning in 1947, the CIA expended considerable effort to ensure victory for pro-US candidates. Its first major operation took place in Italy, where the Christian Democrats were in danger of losing to a leftwing front. The agency supplied the party with cash, got Italian Americans to write letters home and worked with the church. The rationale was simple - moulding voters’ minds meant protecting democracy.

This Italian template was used in subsequent covert actions. In the early 1950s, the CIA helped topple leaders in Iran and Guatemala. Its ugliest moment was probably Chile, where the agency worked relentlessly to undermine the charismatic socialist leader, Salvador Allende. It targeted Allende during the 1964 election and destabilised his government, leading to his overthrow and death in a 1973 coup.

Meanwhile, the KGB funnelled cash to Allende and to other Latin American and African leftists. It gave large, under-the-table sums to communist parties in Italy, France and around the world. The USSR extinguished non-communists wherever it could, turning postwar eastern Europe into a zone of junior clone states. And it stuffed ballot boxes, something Shimer says the CIA didn’t do.

One place Soviet Moscow failed to influence was America. This was not for lack of trying. Its goal was to stir up domestic discord and to promote Moscow-friendly candidates. And, of course, to kneecap ones seen as hostile. The KGB got up to all sorts of dirty tricks in the 1960s and 1970s, including disinformation and forgery. Its chief targets – Richard Nixon and Ronald Reagan – won anyway.

Rigged offers a convincing analysis of what changed in the three decades since the cold war and with the arrival in the Kremlin of Vladimir Putin. It says the modern CIA has basically given up on covert electoral interference. The US still promotes democracy, but openly, via not-for-profit organisations. In 2004, George W Bush contemplated meddling in Iraq’s post-Saddam poll but didn’t follow through.

Putin, by contrast, has gone back to cold war practices. More than any other nation, Russia has taken advantage of the digital world to disrupt other people’s elections – new, cheap warfare, as Shimer puts it. The playbook is the same. Moscow’s reach is much greater. Tactics include cyber-hacking by professional spies and troll factories that pump stolen and polarising stuff into voters’ heads, via Facebook and Twitter.

The chapters on the 2016 US presidential election are painful reading. The Obama administration was slow to notice that Russia was working flat out to help Donald Trump and to sabotage Hillary Clinton. Faced with overwhelming evidence of Russian meddling, Obama hesitated. He assumed Clinton would win. The Republicans obstructed his attempts to take bipartisan action and in the end he left it too late.

One troubling question is whether Russian hackers altered voting tallies in Trump’s favour. Most intelligence professionals think they didn’t. But Harry Reid , the senate minority leader in 2016 , tells Shimer there’s “no question” Moscow changed the outcome. “The Russians manipulated the votes. It’s that simple,” he declares. True or not, the full scale of the operation by the GRU – a rival to the KGB – is only likely to be known once Putin has gone.

What will happen this November? One National Security Council official tells Shimer he is disturbed by Trump’s friendliness towards Putin and by the president’s unwillingness to patch flaws in US electoral security. Seemingly, the door is being left ajar in case the hackers return. “I reluctantly concluded, as did many of my [White House] peers, that Trump was doing Russia’s bidding and that Russia had leverage over him,” the official said.

Shimer has assembled a broad collection of expert voices – old CIA hands, senators, Bill Clinton. He interviews Oleg Kalugin, the former head of KGB operations in the US. It’s a shame Shimer doesn’t talk to other Russians; they after all are the biggest losers from Putin’s spy games. Russia’s own elections are routinely fixed in favour of pro-Kremlin candidates; a vote on 1 July to extend Putin’s rule for two more presidential terms is unlikely to be free or fair.

Rigged offers a judicious overview of our unhappy times. Democracy looks fragile; the US, Shimer argues, has become a “corrupt version of itself”. And Putin has succeeded where his Soviet predecessors failed: adroitly exploiting American divisions to pull off one of the most spectacular operations in modern espionage. Moscow’s candidate sits in the White House and you imagine Putin will try and keep him there.

Luke Harding’s Shadow State: Murder, Mayhem and Russia’s Remaking of the West is published by Guardian Faber on 2 July

• Rigged: America, Russia and 100 Years of Covert Electoral Interference by David Shimer is published by HarperCollins (£20). To order a copy go to guardianbookshop.com. Free UK p&p over £15