French-based Paulsson chaired the Court of Arbitration for Sport panel that acquitted rider Inigo Landaluze due to a procedural error during his own positive doping test, although at the time CAS said the decision was not a declaration of the Spaniard's innocence.
The court's rules allow each party in an appeals case to choose one arbitrator each from a list supplied by CAS, with the court itself then selecting the chairman of the panel.
CAS general secretary Mathieu Reeb said the case was unlikely to be heard before March 2008, with a final verdict coming as late as May.
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"The parties will have until around the end of January to submit their statements, so it is very unlikely that the hearing can proceed before March," Reeb said.
The United States Anti-Doping Agency, who are defending the appeal, have selected New York lawyer David Rivkin, whose previous cases include the controversial stripping of Alain Baxter's alpine skiing bronze medal from the 2002 Olympics.
Briton Baxter's explanation that he had failed a doping test after using a common nasal inhaler was accepted by the court but his appeal was rejected in accordance with the International Olympic Committee's strict liability rules.
New Zealand-based lawyer David Williams will chair the panel.
Landis was banned from cycling for two years after a French laboratory reported traces of synthetic testosterone in a sample provided during the 2006 Tour.
The American became the first rider to be stripped of a Tour de France title but his lawyers argue the laboratory made mistakes in the handling of the sample.
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