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The state Office of Elections will change how it calculates the number of ballots needed at individual polling places and consider keeping reserve ballots on hand at precincts after an Election Day failure that had 70 polling places on Oahu running short or running out of paper ballots and hundreds of frustrated voters waiting hours to vote.

Chief Election Officer Scott Nago appeared before reporters Wednesday, looking somewhat shaken, and apologized for the problem that caused long lines, hours-long waits and flaring tempers, as people queued up at the single electronic voting machine at each polling place.

"We acknowledge that the wrong amount of ballots were ordered for this election," Nago said. "This will not happen again."

In all, 24 polling places on Oahu ran out of ballots Tuesday. One on Kauai and two on Hawaii island also ran short.

Officials said the problem didn’t appear to be one of not enough ballots, but not enough ballots in the right places.

Nago said the state determined how many ballots would be needed using the same calculation it has used for years: The total number of registered voters at each precinct, minus absentee voters, plus 25 percent.

Nago said 274,885 paper ballots were printed for the general election on Oahu, not counting absentee ballots.

In whole numbers that would have been plenty as 160,415 people islandwide voted at a polling place on Tuesday.

But an analysis of voter turnout shows that at the polling sites that ran out of ballots, the number of people casting votes for Hono­lulu mayor was 20 to 50 percent higher than in the primary election.

Precinct officials, voters and observers also say several problems may have contributed to the scope of the voting headaches:

» Reports from polling places that ballots were running low started rolling in around 10 a.m., but there didn’t appear to be an efficient way of getting reserve ballots from the state Capitol building where they’re stored, said Beppie Shapiro, president of the League of Women Voters-Hawaii.

Shapiro, who was an election volunteer at the Capitol Tuesday, said throughout the day precinct officials were calling to ask for extra ballots and were being met with little help.

"They were calling repeatedly, with greater desperation," she said.

» It took hours, in some cases, for extra ballots to arrive at polling sites that had run out.

Mike Gallagher, 61, who helped run the Kainalu Elementary polling place, said paper ballots ran out at 1 p.m. and reserves took about five hours to arrive.

Gallagher said at one point he even volunteered to go pick up ballots, but was told the ballots would be delivered.

"We were constantly on the phone with headquarters," he said. "It shouldn’t have happened, and the response was totally inappropriate. They hung everybody out to dry."

» The call center that precinct officials used to report problems had extraordinarily long waits during the worst of the problems. Some officials were on hold for 45 minutes to an hour, only to be told someone would call them back.

» At Hokulani Elementary extra ballots arrived, but officials soon realized they were for the wrong precinct.

A few voters apparently used the incorrect ballots, but it’s unclear if those voters filled out new ballots. Nago said those ballots would not have been accepted by the electronic reader at the polling place.

» Precinct officials appeared to be trying anything to shorten lines. Several allowed English speakers to use foreign-language ballots. But that suggestion was not passed on to other polling places.

Nago said that most polling places that ran out of ballots were able to get replenishments, but those reserves in some cases came late in the evening. Moanalua High was the last to get reserves — at 6 p.m.

The last polling place to close was Waimanalo Elementary and Middle School, at 8:45 p.m., nearly three hours behind schedule.

Some worry that the election problems will reduce voter turnout in Hawaii, which has historically been low.

Overall, voter turnout Tuesday declined from the presidential election four years ago.

About 62 percent of Hawaii registered voters — or about 436,000 people — cast ballots, according to the state Office of Elections, compared with 66 percent in 2008, or about 456,000 people.

Shapiro said the League of Women Voters plans to ask for a full investigation of the problems, and also wants the Legislature to look at the issue.

She and others suspect that many people got to polling places, saw the long lines and opted to leave without casting a ballot.

"The major concern of the league is of the discouraging effect on people who tried to vote and found the process so inconvenient they gave up," she said. "I so fear voters who gave up won’t come back."

Nago said his office will be conducting an internal investigation to figure out what went wrong — and how to prevent it from happening again.

He said the state will have to come up with a better calculation of how many ballots will be needed.

"The bottom line is we miscalculated," he said.

Nago also noted that this year there was a change to the ballots themselves which did not allow polling places in the same vicinity to share if they ran low. Instead, each polling place had a unique ballot.

Nago said where reserves are stored might also change, but he noted that the elections office also wants to make sure extra ballots are secured.

Tuesday’s vote was also the first general election after reapportionment, which takes place every 10 years. About one-third of voters statewide were assigned a different polling place because of reapportionment, and there were nine fewer polling places statewide compared with 2010.

The Oahu general election problems dwarf those seen during the primary election in Hawaii County, when 13 precincts opened late.

State election officials took over operations after losing confidence in County Clerk Jamae Kawa­uchi.

But Tuesday, there didn’t appear to be any big problems in Hawaii County.