Should they be allowed to vote twice?

[W brad]

I was reading this article: US civil rights group NAACP challenges Louisiana voter purge after Hurricane Katrina and am wondering why anyone objects to having people choose only one place to be registered to vote.

To quote the article:
"On June 15, Secretary of State Jay Dardenne announced that his agency was mailing notices to 53,554 voters saying they must give up their registration in other states or risk losing the right to vote in Louisiana. Dardenne said the state had compared Louisiana voter roles with those of other states and identified people with identical names and dates of birth."

That seems fair. What is the basis for a lawsuit here other than giving a bunch of people two votes in two states?