Independent TDs Catherine Murphy and Finian McGrath will take their battle to have constituency boundaries redrawn to the High Court today.
Ms Murphy, TD for Kildare North, and Mr McGrath, TD for Dublin North Central, said the Government is in breach of Article 16.2.4 of the Constitution. The pair claims 11 of the 43 electoral areas are not being represented correctly.
"Democracy is supposed to mean equality, but with five constituencies having too many and six having too few TDs proportionate to their respective populations the voting power of all Irish people is decidedly unequal," Ms Murphy said. "This simply must be fixed immediately.
"Growing populations in commuter belts around greater Dublin and neighbouring counties combined with movement of people have led to claims that some areas are now being under-represented and over-represented," the TDs said.
Boundaries should have been redrawn to ensure a ratio of not less than one TD for every 30,000 people and no more than one TD for every 20,000 people, they added.