 For the 1985 parliamentary election, he was the only member of the Progress Party who openly challenged a sitting Member of Parliament, namely Bjørn Erling Ytterhorn in Hordaland.Although Albrektsen had support from party chairman Carl I. Hagen, he lost the nomination for first candidate in the county, and declined an offer of running as second candidate, stating that "if I am not trusted as the first candidate, I have nothing there to do".Albrektsen resigned as deputy chairman of the party the same year and left politics.