In New York?
In New York, candidates are allowed to run on multiple lines. It does not always work out that the Democratic candidate runs on the Liberal line and the Replublican candidate on the Conservative line. Rudy Gulliani, for example ran as a Republican/Liberal.
That being said, it doesn’t matter to the candidate — he gets the vote regardless of which line you use. The party, on the other hand, cares very much. In order to continue to have a guaranteed spot on the ballot, the party has to receive a certain percentage of votes (I forget the percentage off the top of my head). If they fail to get that percentage, then they have to petition to get on the ballot (like a brand new party) the next year.
In addition, after the Dems/Repubs, the parties are ranked on the ballot in order of how well they did the previous year. So, for example, if the Conservative Party gets the most votes in this election from among all the third parties, they will have line “C” on next year’s ballot.
The Wolf