The High Court has already ruled One Nation party member and Senate crossbencher Malcolm Roberts was still a British citizen at the time of the 2016 federal election, after being born in India to a Welsh father and an Australian mother.
Walters argued that the country of one's birth and one's parents' citizenship constituted "primary facts" that should prompt inquiries about one's citizenship.
As soon as they found out, they took all reasonable steps required to sever their foreign ties.
But the Greens' proposed test was immediately doubted by the chief justice, Susan Kiefel.
That's because they were both born overseas, he says.
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"You can not heed a call you can not hear", he said.
Australia's 116-year-old constitution states that a "subject or citizen of a foreign power" is not eligible to be elected to parliament.
Section 44 aims to "reinforce confidence" in the Australian Parliament by ensuring it is occupied "by Australians and only by Australians", he said.
Mr Bennett told the High Court there was a possibility that Senator Canavan was not an Italian citizen because expert advice was that conferring the citizenship could be in breach of the Italian constitution.
Walters conceded that his own clients did not take "reasonable steps" to investigate their citizenship because Ludlam, who was naturalised as an Australian at age 19, knew he was New Zealander before that, and Waters, who was born in Canada but left at 11 months of age, did not investigate whether she was Canadian.
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Bret Walker SC, representing Mr Joyce and Senator Nash, said neither of them knew until recently they were dual citizens of New Zealand and Britain respectively.
The court will hear submissions from the seven politicians, the government, and an independent challenger, former MP Tony Windsor.
He gave the example of a dual Greek-Australian citizen conscripted into military service in Greece despite ignorance of their foreign citizenship.
Solicitor-general Stephen Donaghue said: "If a person is not aware either that they are a dual citizen or of a significant prospect that they are, in our submission by definition that person can not have a split allegiance".
The dual citizenship rule was originally inserted into the 1901 constitution to ensure parliamentarians were loyal exclusively to Australia.
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Mr Bennett said "the better view" was that it was a conditional citizenship, which did not apply automatically, and a person would then need to take steps to become an Italian citizen.