MORE THAN a quarter of Virginia’s electorate considers itself Republican, which translates to almost 1 million voters. Of that number, about 8,000 — less than 1 percent — showed up at the party’s convention in Richmond over the weekend to choose the GOP candidates in this November’s races for governor, lieutenant governor and attorney general.

That, in addition to the party’s overall rightward tilt, helps explain how, in one of the nation’s most centrist states, Republicans came to choose a slate of hard-right conservatives.

It’s possible that Attorney General Ken Cuccinelli II, whom the convention nominated for governor, could have won in an open primary, in which 10 times more Republicans might have taken part. But it’s far from certain.

That’s why Mr. Cuccinelli’s partisans, with a major push from tea party activists, fought against a primary and prevailed in an internal party power struggle against his somewhat more moderate rival, Lt. Gov. Bill Bolling, who hoped for a primary. Mr. Bolling elected not to attend the convention, an extraordinary symbolic statement for a prominent incumbent.

As for E. W. Jackson, the convention’s pick for lieutenant governor, it’s almost inconceivable that he could have won an open party primary.

Mr. Jackson, a pastor, was until now a fringe figure whose views have proven deeply embarrassing to the Republican Party’s own leadership. A survey of his rhetorical greatest hits includes assertions that Democrats are peddling the antichrist’s agenda; that Planned Parenthood has done more damage to African Americans than the Ku Klux Klan; that homosexuals are “frankly very sick people psychologically, mentally and emotionally”; and that President Obama sees the world “from a Muslim perspective.”

As lieutenant governor, should he win, Mr. Jackson would be empowered to cast the tie-breaking vote on critical issues for at least the next two years in the state Senate, which is evenly split between Democrats and Republicans.

The GOP nominee for attorney general, state Sen. Mark D. Obenshain, is more cautious in his public utterances, if no less conservative. In the legislature, he has been a champion of the GOP push for more restrictive voter ID laws, which would reduce access for poor and minority voters. (There is zero evidence of voters misrepresenting their identity at the Virginia polls, the ostensible justification for such laws.)

A few years ago, Mr. Obenshain proposed legislation that would have required women to report their miscarriages to police or risk prison time. In the ensuing firestorm of controversy, he withdrew the bill.

Mr. Cuccinelli’s record also is far to the right. He has used his office to crusade against abortion clinics, climate change scientists and Obamacare; on his resume there also has been a hostility to gay rights and a brief flirtation with birtherism. (To Mr. Cuccinelli, it once didn’t seem “beyond the realm of possibility” that the president was born in Kenya.)

Lately, he has tried to redirect his campaign toward economics, while reassuring his supporters that his essential nature hasn’t changed. After the convention, he declined to renounce even Mr. Jackson’s most incendiary comments.

Some Republicans are wringing their hands at what many Virginia independent voters will regard as the extremist cast of the GOP slate. By electing to choose candidates in a closed convention, the GOP precluded the possibility of a broader internal contest of ideas and of candidates.