Former Virginia Delegate Joe May talks with potential voters at AOL headquarters. (Jahi Chikwendiu/Washington Post)

In a race that could determine control of the Virginia Senate, in a bellwether county of a purple state, in a party that is split ideologically, Joe T. May is the man in the middle.

Between a Republican lauded by the party’s right flank and a Democrat backed by her side’s leadership, May is trying to shoot the gap in Tuesday’s special election to succeed Attorney General Mark R. Herring in the state Senate.

The Senate was split 20-20 before Herring and Lt. Gov. Ralph S. Northam, both Democrats, won in November. A recount is set to begin in the special election for Northam’s seat; if Republicans win either that race or Tuesday’s contest, they will take the majority.

May is running as an independent, just days after his service as a longtime Republican member of the House of Delegates came to an unexpected end . As he tries to lure support from Democrat Jennifer Wexton and Republican John Whitbeck, May hopes to persuade voters to ignore party labels and choose him — a grandfatherly engineer and veteran legislator who lost his House seat last year in a primary against a more conservative Republican.

“There are three of us in this race,” May explained to a roomful of AOL employees Thursday, “and we have somebody who’s relatively far right and somebody who’s relatively far left and quite frankly, they’re pretty much paralyzed by partisan politics. One of the nice things about being an independent is that you have a great deal more latitude in doing what you think is the right thing.”

May visited AOL’s office in Sterling as part of a tour of businesses in the 33rd District , which is split roughly 70-30 between Loudoun and Fairfax counties. Before he spoke, May was introduced as “somebody who transcends politics.”

The 76-year-old May said he’s always been a Republican and expects to caucus with the GOP if he wins — which would give the party control of the Senate. “But I’ve also been pretty darn independent,” May said.

May is the founder and chairman of EIT , a Sterling-based electronics manufacturer. He holds several patents, including one for the instrument that measures the octane rating of gasoline (when the pump at the gas station says 87 or 89, it’s because of May’s invention). NFL playoff viewers can also cheer for May: He designed the equipment that projects the yellow first-down line onto the field during televised football games.

After 20 years as a delegate, May lost his House seat last June, when the more conservative David LaRock bested him in a low-turnout Republican primary, 57 to 43 percent. LaRock won in part by casting May as too moderate on social issues and by reminding conservative voters of May’s support of the landmark transportation funding bill.

Now, the very stances that contributed to May’s loss could help him in the Senate contest this year — but only if enough moderates and independent voters show up Tuesday.

“Philosophically, Wexton and I are pretty far apart,” he said. “She’s totally pro-choice, and she doesn’t place the same emphasis on the economic well-being of Northern Virginia, between transportation, education and jobs.”

As for Whitbeck, “John’s answer to almost everything is ‘no’ ” — particularly when it comes to raising money for transportation, May said.

Mark Rozell, a professor of public policy at George Mason University, said May is helped by the fact that he is well known, “but in the end, typically most voters believe that voting for a third-party candidate is effectively throwing away a vote.

“These off-cycle elections tend to have relatively low or extremely low turnouts,” Rozell said. “And who turns out? The really hard-core partisan activists in each party.”

The district gave President Obama 59 percent support in 2012, but that doesn’t make it safe for Democrats. Loudoun has an especially committed corps of GOP voters, and the county’s entire Board of Supervisors is Republican. Election results swing dramatically from cycle to cycle here, depending on who’s on the ballot and who turns out.

The three candidates’ differing strategies are clear in their ads — Wexton and Whitbeck hope to fire up their respective bases, and May is aiming for the middle.

Wexton, a former Loudoun prosecutor, has sparked controversy with an ad featuring her in a courtroom discussing her fights on behalf of rape victims. “In the Virginia Senate, I’ll fight just as hard against tea party Republicans who would take away a woman’s health care and her right to choose, even in cases of rape and incest,” she says.

Whitbeck, a lawyer who heads the 10th Congressional District Republican Committee, has aired an ad saying there’s “not a dime’s worth of difference” between May and Wexton, calling both “liberal politicians with risky agendas” who support higher taxes.

May’s tone is a bit lighter.

“Legends of the game! Joe Namath. Joe Gibbs. Joe May?” asks the narrator of a May ad — before noting his role in designing the first-down line.

“That’s cool, but kinda nerdy,” says a woman pictured on-screen. The ad concludes with the narrator urging, “On Jan. 21, vote for the nerd.”

Unlike Wexton and Whitbeck, May has decided not to spend much time raising money. He has given his campaign $100,000 from this own pocket and transferred another $43,000 from his old campaign account. Through Jan. 10, he had taken in only $27,000 from outside donors, though he believes he has enough money to win.

“One of the nice things at this point in my career — I don’t need the job,” May told the AOL employees. “I’ll take that back. I want the job, but I don’t have to sell myself for a vote.”