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Mr. Barr was locked in a dead heat with Miss Ruwart after the fifth ballot, but then announced that he would support Mr. Root, who was the third-place candidate, as his running mate.

The move appeared to swing many of Mr. Root’s delegates to the Barr camp, giving him the support he needed to overcome Miss Ruwart’s challenge.

According to party rules, the vice-presidential candidate is chosen by the convention delegates. Five candidates, including Mr. Root, were in the running.

Earlier, Mr. Root made an impassioned plea for the vice presidency after losing on the fifth ballot, saying he wanted to spend the next few years “learning from the master” in a Barr administration.

Supporters began to chant, “Barr-Root,” after Mr. Barr’s nomination was announced.

Eliminated in a previous round was former Sen. Mike Gravel of Alaska, who ran for the Democratic presidential nomination this year before switching to the Libertarian Party in March.

After his defeat, Mr. Gravel, 78, announced his retirement from politics, a career that spanned more than 50 years and included two terms in the U.S. Senate. A longtime antiwar activist, Mr. Gravel might be best known for reading the Pentagon Papers into the Senate record in 1971.

“I started out in politics when I was 15, and this is the end of my political career,” said Mr. Gravel, adding that he will continue to write and lecture on his pet causes.

This article is based in part on wire service reports.