When his grandfather Minamoto no Yorimasa and father Nakatsuna mobilized the troops following Prince Mochihito and both died in battle in 1180, Aritsuna was in safety because he was staying in Izu Province, which was the chigyo-koku (provincial fiefdom) of Yorimasa.
治承4年（1180年）、祖父・源頼政、父・仲綱らが以仁王を擁して挙兵し敗死した際には、有綱は頼政の知行国であった伊豆国にあり難を逃れた。