Logan, who took office Jan. 4, acknowledges that the ballot created confusion among voters and says the county will abandon the double-bubble design and have a new ballot design in time for the June primary. It is unclear what the additional cost would be.
Logan also is investigating whether any of the 50,000 votes can be counted.
"It's not a good ballot style," Logan said. "It is difficult to discuss this without sounding defensive, but I want this fixed more than anyone."
Some voters believe the uncounted votes might favor Sen. Barack Obama over Sen. Hillary Rodham Clinton in the Democratic primary.
But Logan and Democratic Party officials say the margins in the race are so large that the votes are not likely to affect the statewide outcome or the county allocation of delegates.
Los Angeles County, the only county in the state to use this ballot design, first adopted it for the March 2002 primary. Keeping costs down was a major factor in the decision, Logan said, as was a desire to minimize the number of different ballots and keep things simple for poll workers.
For election officials, running an election in Los Angeles County is a daunting logistical exercise.
With nearly 4 million registered voters in 4,379 precincts, the county is the largest single voting district in the nation.
The Feb. 5 election alone cost the county about $30 million.
Election officials say that a primary is the most complex kind of election. The number of political parties -- six on Feb. 5 -- means a multiplicity of ballots. Crossover voting that allows nonpartisans to vote in certain party primaries can make organizing the vote even more complicated.
"Election officials will tell you they despise these elections," said former L.A. County Registrar Conny McCormack, who retired in January, a month before the vote. "Voters don't understand them, and poll workers don't understand them."
There are other peculiarities about L.A. County's election system that set it apart.
It is the only county in California to use the InkaVote Plus system, in which voters darken bubbles on their ballot with a special InkaVote pen.
The names of the candidates are listed in the "vote recorder" book in the polling booth but are not printed on the ballot itself. The ballot contains only numbers representing the candidates and the bubbles where voters mark their choices.
