The Publican political party is a party that believes in fair voting, a right to a fair trail, rights to own a firearm, and self defense laws.
It was popularized by PaperLand Leader Pencil to counter the Loyalist party so she could combat the unfair practices the Loyalists wanted.
The primary intention of the Publican party is to counter Loyalists on multiple points (mainly done by Pencil in Paperland):
Leader's word is law
The party wanted a more fair method of deciding people's fate in court, so they ensured a right to a fair trial by a Publican. This popularized the Paperland DOJ.
The party also introduced a Senate like system into the PaperLand government, forcing laws to go through both Publicans and Loyalists in order to pass.
No Free Speech
The Publican party aimed to allow all citizens to have the right to say what they please within Paperland without worrying about a fine or arrest. In Paperland this was achived the first day in office.