To understand the cruel calculus of voter ID laws, voter purges and other election law mutations one political party has turned into an obsession (second only to their fever for passing laws designed to corner women into giving birth) you have to understand what these laws would actually prevent, if they worked as advertised.

Imagine legions of people turning up at polling places pretending to be someone else. Voter John is really disqualified Juan or Keyshaun.

And why would Juan/Keyshaun be disqualified? Maybe he’s an ex-felon, which in some former Confederate states means you lose your civil rights, permanently. Or maybe he’s . . . an illegal immigrant! Or maybe his name sounds similar to a felon or undocumented immigrant, which somehow is almost exactly the same thing . . .

And so, our Juan/Keyshaun signs the identity affidavit as John under pain of prison and a $10,000 fine, and casts exactly one ballot. Fraudy mission accomplished!

But since one ballot won’t swing even a Florida election, our scenario has to play out hundreds, or thousands, even tens of thousands of times. And if we delve deeper into the darkest recesses of the conservative imagination, Juan/Keyshaun isn’t acting alone. He’s fraud-voting at the behest of nefarious union “thugs” — who may even be paying him, using George Soros’ so-much-more-evil-than Koch-brothers’ money.

So now, we need to believe that our union thugs (who are also Saul Alinsky radical Islamists — hey, this is a conservative imagination we’re borrowing . . . ) are willing to spend, what? $20, $50, even $100 per faker in order to swing a statewide election. Rather than maximizing their resources buying television and radio ads, sending direct mail or just registering more voters — our conspirators pay tens of thousands of people to risk jail time and fines of up to 100 times the bounty paid to Juan/Keyshaun to cast a single vote.

The roots of the Republican obsession with voter fraud can be traced to the 1960 presidential election, which in GOP folklore was stolen from Dick Nixon for John F. Kennedy by Chicago Mayor Richard Daley.

As the legend goes, Daley’s notorious Democratic machine swung Illinois’ 27 electoral votes in Kennedy’s direction through massive fraud (Republicans at the time actually claimed 11 states, including Texas and New Jersey, were stolen). This allegedly involved stuffed ballot boxes, armies of zombie voters and people bribed to pull the lever for JFK with free lunches and drawings for baked hams.

Trouble is, none of the 31 state voter ID laws in place today would have helped Tricky Dick get into the White House and on to Watergate sooner.

Asking voters to show ID wouldn’t stop someone accepting a ham in exchange for his or her vote.

It wouldn’t stop a determined fraudster from stuffing a ballot box or stuffing the box into the back of a car.

Voter ID laws wouldn’t stop flyers or robocalls telling people to show up to the polls on the wrong day, or not to show if they’ve missed a utility payment, or that if they signed a petition, they’ve already voted — real voter suppression schemes perpetrated mainly against minority voters in recent elections, including in Wisconsin’s recent recalls.

And they’d do nothing to combat the much more realistic threat of falsified voting applications; claiming an address or voting in a state where a person isn’t really a resident (hello, Ann Coulter!) or mailing in falsified absentee ballots. Those kinds of fraud actually happen in more than infinitesimal numbers. But they remain untouched by voter ID laws, perhaps because absentee voting happens to be particularly popular among Republicans.

But these laws could have a disproportionately negative impact on the kinds of voters who prefer Democrats: young people and students, whose IDs are just not good enough in swing states like Wisconsin and Texas, and minorities, one in 10 who lack government-issued IDs, along with the elderly.

Kennedy beat Nixon in Illinois by just under 9,000 votes, but he won Cook County, which contains Chicago, by more than 300,000. If the Daley machine paid off that many people, they should have stashed their cash in a Mitt Romney-style Swiss bank account instead. Except for Eisenhower, Illinois at that time had voted Democratic in every presidential race since 1932.

Clearly it’s unpalatable for Republicans to admit that a majority of voters simply preferred Kennedy in 1960, as they did Obama in 2008.

They should ask themselves why that is, rather than pushing to keep Juan and Keyshaun from voting.