The North West CruiseShip Association and other groups appealed to the Supreme Court after a state Superior Court judge ruled against them and in favor of the Alaska Division of Elections, which was charged with certifying a petition for the ballot initiative.
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The groups challenged some signatures and claimed the Division of Elections failed to follow its rules in certifying that signatures were valid.
Some people did not put a date next to their signature, making it impossible to verify that they were qualified voters when they signed the petition, the groups' attorneys claimed.
The Supreme Court six months ago rejected that legal challenge. Alaska voters passed the cruise tax initiative in August. The new law imposes taxes and environmental and consumer disclosure rules on large cruise ships that bring nearly 1 million tourists to Alaska each year.
Justices issued a 12-page written opinion Friday.
Justices said the Division of Elections "struck a careful balance" in certifying the ballot petition, retaining signatures that were valid and correctly discarding others that were not.
The justices said they interpret liberally the state's procedures to allow Alaskans to vote and express their will in ballot initiatives.
The justices pointed out previous rulings on ballot initiatives in which their court used the same principle.
Several appellants in the case, including the Alaska Hotel and Lodging Association, had not read the Supreme Court opinion on Monday and would not comment.