1.   But Democrats complain that a badly designed ballot in Palm Beach County caused thousands of voters to have their ballots discarded when they meant to vote for Gore.

2.   But there were questions about how many ballots were actually discarded as the charges and counter-charges escalated.

3.   If two or more corners of the chad remain attached, the ballot must be discarded.

4.   If Toyota prevails in its challenge, the ballots may be discarded, according to Ron Lebi, the labor board solicitor overseeing the election.

5.   In other cases, legitimate ballots were discarded by machines because their sides were mangled or they were otherwise unable to be fed properly.

6.   Others finally voted only to learn that many ballots had been discarded because of faulty machines or confusing instructions.

7.   Some completed ballots are discarded, such as those to which no name is signed and those that contain votes for only one or two places.

8.   The Times asked Dr. Gary King, a Harvard expert on voting patterns and statistical models, what would have happened had the flawed ballots been discarded.

9.   The vote-counting machines detected two votes for one office and naturally discarded the ballots.

10.   Their ballots were discarded as invalid.