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Such inconsistencies can get in the way of a carefully calibrated political campaign, the studies found.

“Even when voters perceive that the celebrity is trustworthy, the equation changes when they weigh in on politics,” Mr. Cobb said.

But he doesn’t discount the fame factor altogether. While the impact of a celebrity endorsement is “minimal,” there are circumstances — political rallies, for example — when such an endorsement may be helpful to a candidate.

“Are you more likely to attend a political event if the candidate is slated to appear by him- or herself, or if the candidate is going to appear with Madonna?” Mr. Cobb asked.

“Endorsements may also help candidates distinguish themselves from a crowded field during primaries,” he added.