In a media release today Macpherson said: "It is with the utmost reluctance that I have taken this possibly unprecedented step."
His petition contains the claim that Williams' conduct during the election was biased in favour of Chadwick and some incumbent councillors and was "therefore unfair on the other candidates". It claims Williams' actions affected the result of the election.
Macpherson was endorsed as mayoral candidate by the Rotorua District Residents and Ratepayers (RDRR) group, of which he was a founding member and is secretary.
However RDRR chairwoman Glenys Searancke told the Rotorua Daily Post Macpherson's legal challenge had not been sanctioned by the group.
"As an independent person he has every right to challenge as he sees fit.
"This has nothing to do with the RDRR and we as an association have not discussed this challenge," she said.
"I will be interested in hearing what the district court has to say."
In the seven-page petition, Macpherson states Williams had a duty to act fairly and without bias.
It refers to the council-commissioned Community Satisfaction Survey 2016 dated June 30, which the council released 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" - whom 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 Williams in publishing positive advertorials during the election campaign that ignored the findings of the survey.
Macpherson claims these factors show the bias by Williams was unfair on the other candidates and breached the Local Electoral Act.
"It materially affected the outcome of the election by enabling a number of the incumbent councillors to be re-elected by very slim margins."
In his media release, Macpherson said: "I know I have the support of many in the community."
"At the same time I am disappointed that the Rotorua ratepayers may have to pay for and be inconvenienced by another election."
When asked for comment by the Rotorua Daily Post, Williams stated: "We will await the outcome of the process."
Chadwick did not wish to comment.