In a media release at the time, he said: "It is with the utmost reluctance that I have taken this possibly unprecedented step."
His petition contains the claim that Mr Williams' conduct during the election was biased in favour of Mrs Chadwick and some incumbent councillors and was "therefore unfair on the other candidates". It claims Mr Williams' actions affected the result of the election.
In the seven-page petition, Dr Macpherson states Mr Williams had a duty to act fairly and without bias.
It refers to the council-commissioned Community Satisfaction Survey 2016 dated June 30, which was released publicly by the council on October 26 - after the election.
The petition claims the survey findings were adverse to the interests of the mayor and "the incumbent power bloc councillors" - who he lists as Dave Donaldson, Merepeka Raukawa-Tait, Karen Hunt, Janet Wepa, Charles Sturt, Trevor Maxwell and Tania Tapsell.
"The effect of Mr Williams withholding the release of this report until after the election was that the RDRR candidates were deprived of the opportunity to use the report in support of their campaign," the petition states.
It also alleges bias by Mr Williams in publishing positive advertorials during the election campaign that it alleges ignored the findings of the survey.
Dr Macpherson claims both these factors show the bias by Mr Williams was unfair on the other candidates and breached the Local Electoral Act.
Mr Williams previously stated: "We will await the outcome of the process".
Mrs Chadwick did not wish to comment.
