Visa Cancellation and the Presumption of Innocence

How broad are the Minister's powers to cancel a visa under section 501(3) of the Migration Act?
And how difficult is it to challenge a decision of the Minister? Even where the visa holder has not actually been convicted of any criminal offences, and the cancellation is based on a finding that the visa holder has had a past association with a group or organisation that has been involved in criminal activity? Even where that association was apparently many years in the past?
The unsurprising answer to all of these questions, as illustrated by a decision of the Full Court of the Federal Court that was handed down in February, Taulahi v Minister for Immigration and Border Protection (2018) FCAFC 22 (19 February 2018) , is that it is "very" or "extremely" hard to challenge a visa cancellation on character grounds, even in the described above.
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