Olson -- commander of a growing group called the Alaska Citizens Militia -- says he accepted the candidacy last week under the assumption he would be campaigning with Republican Bill Walker as the AIP's pick for governor on the November ballot.
The party was not represented by any lieutenant governor candidate in the August primary.
Olson says he changed his mind about running after party leaders spoke with Walker, then decided to stick with the AIP candidate for governor, Don Wright, over Walker.
Walker, who finished second to Gov. Sean Parnell in the Aug. 24 Republican primary, has been looking for ways to continue his campaign.
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