The three words that stood out in Joe Biden’s powerful inaugural address, if only for the number of times he used them, were “democracy”, “unity” and “truth”. But it was democracy that took centre stage. “This is democracy’s day,” he said, in his first statement after taking the oath of office. “The will of the people has been heard … Democracy has prevailed.”

Is this apparent vindication of democracy enough for unity and truth to prevail as well? The founding fathers of the American republic, whose history and institutions Biden also repeatedly invoked, might have been surprised to hear him run the three together. They believed they were founding a state that was designed to keep democracy at arm’s length. James Madison, one of the authors of The Federalist Papers and a future president, stated that the American constitution he helped to write would mean “the total exclusion of the people, in their collective capacity, from any share [in the government]”.

The founders were as keen on unity and truth as Biden. But they thought too much democracy would put them at risk. They viewed the voting public as notoriously fractious and prone to believe all sorts of nonsense. The point of establishing a republic rather than a democracy was to ensure there were safeguards against populism in all its forms.

Biden clearly meant something different by democracy than the people gone wild. He was invoking a different, and much later tradition, that sees democracy as defined by the peaceful transfer of power. In academic circles this is sometimes called the minimalist theory of democracy. It says that it is sufficient for democracy if incumbents, who control the armed forces, hand over that control to the people who defeat them at the ballot box. The guns change hands when the voters change sides.

The trouble with this view is that it is so minimal, unity and truth are optional extras. There are many places around the world where democracy has failed even this test and defeated incumbents have refused to leave, leading to dictatorship or civil war. But when the test is passed it leaves unresolved most of the questions about how to do politics better.

Coming just two weeks after an attempt to storm the Capitol and prevent the certification of the election result, Biden’s inauguration took place in the shadow of the most serious threat to this minimal definition of democracy in recent American history. The country had come dangerously close to failing the test. What Biden could also have said, but didn’t, was that the founders were in part to blame.

The anger of Trump’s supporters was stoked by the institutions designed to keep the people away from the most important decisions. In strict majoritarian terms Biden won the election comfortably, by a national margin of more than 7 million votes. But the electoral college made it seem much closer, and allowed the defeated president to look for a few thousand votes here or there that might have made the difference. Millions of voters are much harder to conjure out of thin air.

Trump’s resistance to democratic realities also rested its hopes on the other institutions of the republic that were meant to keep the people out. He believed that the supreme court, with three of his appointees on it, should save him. He looked to the Senate, which gives a disproportionate influence to sparsely populated rural states, to have his back. The fact that these hopes were misplaced – and the Senate may yet convict him in an impeachment trial – doesn’t mean that democracy was vindicated. The institutions that quelled popular resistance to the election result were the same ones that inflamed it.

This suggests it is not enough for Biden to fall back on the long history of American democracy in making his case for what should come next. The peaceful transfer of power obscures the ways in which American democracy is at odds with the institutions that achieved it.

There is a choice to be made here. Democracy could be enhanced – and institutions such as the electoral college and the Senate reformed to reflect current demography rather than ancient history. But that is likely to come at the cost of unity. Republicans would resist fiercely. Truth would probably suffer too, if only because we have learned that these days resistance tends to come as an assault on the facts. Any attempt to change the constitution would be challenged not just as unpatriotic, but probably as a foreign plot.

The alternative is to stick with the status quo and hope it is enough to paper over the cracks. In that case, unity will have been prioritised over democracy. It is probably the easier path, and Biden may think he has better things to do than pick a fight on democratic institutional reform. Any bipartisan consensus is unlikely to survive changes that leave one party worse off in electoral terms. Enacting the people’s will can be a deeply divisive enterprise.

One temptation – and Biden would hardly be the first president to succumb to it – is to use the word democracy as a catch-all while avoiding these difficult choices. In the short term, it might enable him to concentrate on tackling the immediate challenges the country faces, from the pandemic to the economy. But it also means that frustration with political elites will continue to build.

Invoking the will of the people while relying on institutions that are designed to stifle it is not a recipe for long-term stability. Yet doing anything about it risks the unity for which Biden stands. He is treating democracy as though it were a panacea, when in truth it is always a fight.

On the day of Biden’s inauguration the people were indeed excluded, but not in the way the founders had intended. Instead, because of the threat from extremists, the crowds were kept away and replaced by military personnel around the podium and flags down the Mall. It was in keeping with an occasion that paid lip service to an idea whose reality is much more contentious.

The peaceful transfer of power, particularly achieved at such a high price, is only the bare minimum of what needs to be done for democracy to prevail. The rest is much less certain and comes with many risks.

It was the riskiness of democracy that made the founders nervous, but that is its point: the dynamism of people’s politics has always gone with a dangerous unpredictability. But there are other risks too. Keeping democracy at bay for the sake of unity does not guarantee a peaceful life. The danger is that it comes to seem less like democracy fulfilled, and more like democracy endlessly deferred.