The Obama campaign would like voters to believe that Paul Ryan’s Medicare plan would “end Medicare as we know it” — privatizing the whole system and costing seniors more than $6,000 extra a year.

But the campaign, even before Ryan was selected as Mitt Romney’s running mate, has effectively been running against the wrong Ryan plan.

The president’s accusations largely refer to Ryan’s 2011 plan, ignoring the fact that the House Budget Committee chairman rolled out a different version in 2012 — taking into account Democratic critiques. Though the 2012 plan is more moderate, Obama and his surrogates have all but ignored the newer version as they amp up their accusations against the Romney-Ryan ticket.

Most glaringly, the campaign has omitted a key point.

While Ryan’s 2011 plan proposes to give seniors a government payment to buy private insurance, his 2012 plan offers seniors a choice.

Under the blueprint, seniors could use the payment to buy private insurance or stay in traditional Medicare.

This distinction rarely comes up at Obama campaign events.

Last week in Davenport, Iowa, Obama again accused Romney-Ryan of wanting to “voucherize the Medicare system.”

“They want to turn Medicare into a voucher system,” he said. “That means seniors would no longer have the guarantee of Medicare — they’d get a voucher to buy private insurance. And if it doesn’t keep up with costs, well, that’s the seniors’ problem.”

Obama neglected to mention the traditional Medicare option. Under the plan, the two-tiered system would kick in a decade from now.

Another distinction the campaign has chosen not to make is over the average cost to seniors. For months, Obama has cited an estimate that the Republican budget plan would cost Medicare seniors $6,400.

The campaign repeated that claim in a new TV ad released Friday called “Fact.”

The ad says: “And experts say his voucher plan could raise future retirees’ costs more than $6,000. … Get the facts.”

But that estimate is from early 2011, and refers to Ryan’s outdated plan from the same year. Sharp-eyed viewers would see in the latest Obama ad the fine print that attributes the estimate to “Center on Budget and Policy Priorities, 4/8/11.”

The liberal-leaning Center on Budget and Policy Priorities indeed estimated the old plan could cost seniors $6,400. The nonpartisan Congressional Budget Office reached a similar conclusion.

However, the CBO this year said it “does not have the capability” to estimate the individual impact of the latest Ryan plan, though it cautioned “beneficiaries might face higher costs.”

Still, Obama has continued to campaign off the outdated $6,400 figure.