All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no harm in voting for a woman running for Parliament or a Municipal Council since there is no text in Sharia forbidding that. Moreover, the ruling of Sharia on running for parliamentary elections and voting rests on the candidate`s characteristics which qualify them to shoulder this big responsibility in terms of keenness on the best interest of the people and the country, loyalty in delivering services and consciousness in making laws. A candidate should also have a strong character, the ability to perform the duties and responsibilities of an MP and the audacity to oversee the performance of the government. Allah, The Almighty, Said (What means): "truly the best of men for thee to employ is the (man) who is strong and trusty" {Al-Qasa, 26}.
Abu Dharr (May Allah be pleased with him) reported: I said to Messenger of Allah (PBUH): "Why do you not appoint me to an (official) position?" He (PBUH) patted me on the shoulder with his hand and said, "O Abu Dharr, you are a weak man and it is a trust and it will be a cause of disgrace and remorse on the Day of Resurrection except for the one who takes it up with a full sense of responsibility and fulfills what is entrusted to him (discharges its obligations efficiently)." {Muslim}. Once the afore requirements and conditions are met, the gender of the candidate becomes insignificant since Prophet Mohammad {PBUH} said: "Women are counterpart of men" {Abu Dawud}. Indeed, the opinion of a wise woman is important and useful for improving laws and regulations pertaining to family and women in addition to other affairs. However, the Hadith mentioned in the above question: " A people who make a woman their ruler will never be successful, " had a certain occasion and reason but not in this very context.
The Messenger of Allah (PBUH) used to consult the Mothers of the Believers about public affairs, and this is sufficient proof that women have what it takes in terms of knowledge, trust and righteousness to run for parliament. And Allah knows best.