Where Wisconsin Gov. Scott Walker (R) wants to take his state, Virginia has already been: It is one of a handful of states that prohibit collective bargaining for public employees in state and local government.

Given that, you’d think the state’s retirement program would look a lot like those offered by private employers, right?

You’d be wrong.

The state has steadfastly maintained a defined benefit plan for the vast majority of its employees, a stable perk increasingly rare in the private sector.

Despite having no unions, Virginia has been one of four states where employees have, for almost 30 years, paid nothing each year toward their retirement.

And its union-free status has hardly spared the state pension woes. Gov. Robert F. Mc­Don­nell (R) has warned that the plan will become insolvent over time if lawmakers do not address $17.6 billion in unfunded liabilities.

Virginia helps illustrate a reality that complicates the political rhetoric for both sides in the debate over public employee unionization: When it comes to retirement plans, there seems to be little correlation between union membership rates and either the generosity of states as employers or the financial stability of their systems.

The reality suggests that, if more states went the way of Virginia and eliminated collective bargaining, it could be that neither union members’ worst fears nor many Republicans’ best predictions for retirement benefits would come true.

“It was a surprise to me,” said Sylvester J. Schieber, former chairman of the Social Security Advisory Board and author of a recent study comparing the generosity of state pension plans.

Schieber’s work shows that states with few union members are typically no more stingy when it comes to employee retirement than those with many union members, he said.

Schieber’s study, which looked at the percentage of an employee’s working wages that pension systems are designed to replace in retirement, found that Virginia offers a middling plan — 32 states are more generous, 17 less so. But its plan offers workers nearly the same as that of Maryland, which has a strong union presence.

Another recent study, by an economist at North Carolina State University, showed the same thing: Although states with strong unions offered better benefits in the 1970s and early ’80s, that advantage had dissipated by 2005.

“It’s hard to explain why some states have done one thing or another,” study author Robert Clark said. “It’s certainly true that states that had relatively little unionization were also increasing benefits.”

In Virginia, the General Assembly agreed last year to make changes to its pension program but only for new hires. Those hired after July 1 will now have to contribute 5 percent of their salary to the plan each year, and they will have to work longer before becoming eligible for retirement.

But when Mc­Don­nell this year proposed extending some of those changes to Virginia’s 87,000 current state employees and offering localities the option to do the same for about 140,000 teachers, the legislature largely balked.

Legislators declined to start a new, optional defined-contribution program. And although they decided to ask employees for a 5 percent contribution to the plan, they also authorized 5 percent pay raises, meaning employees essentially pay nothing and the state’s costs rise by $15 million.

In an interview, Mc­Don­nell said the lack of an employee contribution — originally adopted in 1983 as part of a deal with workers in a year when pay was frozen — was a sign that the state didn’t need a union to be a good employer.

“We don’t need negotiations of a union in order to do the right thing,” he said.

In his role as vice chairman of the Republican Governors Association, Mc­Don­nell has been one of Walker’s most avid cheerleaders, appearing on national television to argue the Wisconsin governor’s case as protesters swarmed Madison.

Without unions, Mc­Don­nell says, it’s been easier for Virginia to slash costs and balance the budget during the economic downturn. State employees went four years without a pay raise. Thousands of state and local employees have been fired or furloughed to make ends meet.

“We didn’t have to go and sit down and negotiate with a number of unions about how we were going to do that,” Mc­Don­nell said. “We just did it.”

But he acknowledges that the state’s ban on collective bargaining has not given him an entirely free hand when in comes to pensions, in part because voluntary associations that employees join still wield political power.

“They’re well organized, and they do represent very large groups of voters and constituents,” he said. “And so they do speak with a fairly loud voice.”

Virginia’s hostility to public sector unions is long-standing, dating at least to 1946, when Gov. Bill Tuck (D) delivered a harangue against unionization in his annual State of the Commonwealth Address to the General Assembly, calling it “utterly incompatible with sound and orderly government.”

In 1977, the Virginia Supreme Court ruled that collective bargaining by local governments was illegal, and the General Assembly codified its long-standing prohibition against the practice in the state workforce in 1993.

The two leading voluntary associations that represent Virginia workers differ in their assessments of the effect of having no unions.

Ron Jordan, executive director of the Virginia Governmental Employees Association, which represents about 20 percent of state employees, said he thinks the lack of an adversarial union has improved how the state treats its employees.

Robley Jones, a lobbyist for the Virginia Education Association, whose members include about half of state teachers, said the lack of a union helps explain why Virginia spends less on education — both in teacher pay and in per pupil spending — than other states, though it is comparatively wealthy.

But both agree that the pension system is neither overly generous nor terribly underfunded.

Various studies have shown that Virginia has done a better job of keeping up with its pension obligations than many states — but a worse job than others, including some union states.

Only five times in the past two decades did the Virginia General Assembly agree to fully fund pension rates recommended by the trustees of the Virginia Retirement System. That is one reason that VRS has said that the state employee plan is only 74 percent funded, and the plan for teachers is 69 percent funded.

But the General Assembly and VRS differ on the correct formula to use to determine how much the state should contribute each year. The legislature has failed to deposit the amount recommended by its own number crunchers only once, in 2010, when legislators agreed to borrow more than $600 million from the pension fund to help close a budget shortfall.

Jones said that if Mc­Don­nell thinks the pension fund is troubled, the solution is easy — persuade the General Assembly to fund the plan as recommended by its trustees.

“If there’s a problem,” he said, “union or non-union has nothing to do with it.”