Widespread rioting and violence has again engulfed Egypt following the July 3 overthrow of the Muslim Brotherhood government; Tunisia just suffered this year’s second political assassination; Libya continues unraveling and Syria’s civil war rages on unabated. As the Middle East descends toward chaos, Arab rulers friendly to America must be wondering if their turn is coming.

Egypt is now the main focus, and the central question is whether the Muslim Brotherhood truly qualifies as a democratic political party.

In 2011’s Arab Spring, Hosni Mubarak’s secular opponents proclaimed (and too many in the West believed) that authoritarianism was dead and democracy was at hand. That was the first mistake.

Too late, pro-democracy advocates realized that defining “democracy” simplistically and mechanically — holding elections and counting votes — could produce profoundly anti-democratic results. Quick elections only benefited the best-organized, most-cohesive groups, namely the Brotherhood and the even more radical Salafists. Coptic Christians saw what was coming; scores of thousands fled the country.

After the first wave of elections, the Muslim Brotherhood and its outliers controlled nearly three-quarters of Parliament, and its candidate, Mohammed Morsi, was elected president. The Brotherhood then started to do precisely what it always wanted: create an Egyptian state based on its own harsh, politicized form of radical Islam, a theocracy with numerous authoritarian aspects. To stop the Brotherhood’s creeping coup, Egyptians returned to the streets and soon the Army ended Morsi’s presidency.

Some argue that the military’s action wasn’t really a “coup” because there was widespread popular support. Here’s a secret: Military coups often enjoy extensive popular backing, because citizens faced with radical upheavals often yearn more for safety and stability than they do for abstractions.

Indeed, “democracy” alone is the wrong icon. “Liberty,” “free and open society,” call it what you will, the real objective should have been the more comprehensive, civilizational objective: a way of life, not an adding machine.

Today, the Western media and elites, including President Obama, are pressing Egypt’s interim government to release Morsi from jail, stop using force to repress the Muslim Brotherhood and find a path to a new round of elections.

But this approach will almost certainly lead to the Brotherhood again becoming Egypt’s dominant political force. And it ignores the fundamental problem: The Brotherhood is not a democratic institution, it doesn’t want a democratic society and it uses democratic mechanisms only to achieve its own theocratic objectives.

Allowing the Brotherhood to participate again in Egypt’s elections will prove we and the Egyptians learned nothing from the recent deadly past.

In the United States, faced with a totalitarian political movement dedicated to overthrowing our representative form of government, we acted decisively by outlawing the Communist Party in 1954. Sponsored initially by flawlessly liberal Sen. Hubert Humphrey (supported by Sens. John Kennedy and Lyndon Johnson), the statute paraphrased language first used by Supreme Court Justice Robert Jackson in a famous opinion.

Jackson wrote that the Communists “assert as against our Government all of the constitutional rights and immunities of individuals, and at the same time exercise over their followers much of the authority which they deny to the Government.” His conclusion: “The Communist Party realistically is a state within a state, an authoritarian dictatorship within a republic.”

The Brotherhood is no clone of the Communist Party, but its authoritarian organization, its indoctrination of its followers, their rabid loyalty and its intolerance of dissent all add up to a similar threat to a free society.

Mubarak often predicted that if he fell the Brotherhood would surely follow, and he never hesitated to use repression to protect his regime. Perhaps today’s Egyptian military has belatedly concluded that Mubarak had it right.

Egypt now faces a supremely difficult choice. If Brotherhood supporters among the general public are to be permitted to participate in politics, they must be required to act completely separately from the leadership structures of the Brotherhood itself. Just as guerrillas and paramilitaries must give up their weapons (“put them beyond use,” in the words the IRA finally agreed to in Northern Ireland), so too must Brotherhood adherents renounce the organization itself.

This is a monumental task, and ultimately may not be achievable. The separation cannot simply be pro forma, or it is no solution at all. Those who voted for the Brotherhood must act separately as a genuine political party, not a conspiracy.

Tough medicine, for sure. But absent better ideas, look forward to a radicalized Egypt under the Brotherhood or more violence as far as the eye can see.

John Bolton is a former US ambassador to the United Nations.