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Ms Butler yesterday withdrew her application to have about 34,000 voting papers rechecked, telling the Dunedin District Court she was "unable to bear the prospect of punitive costs".
Earlier, she filed an affidavit in which she said the council could decide whether it should seek costs and that seeking "considerable" costs could taint the electoral process.
If the council refused to "withdraw the threat of seeking considerable costs" it would remove the democratic right of a recount for most future local body candidates.
"Recounts for local body candidates in Dunedin would then only be accessible for those with wealth and influence. This strikes at the heart of democracy."
Ms Butler declined to be interviewed yesterday, but Mayor Dave Cull said the council had not threatened costs, punitive or otherwise.
"I'm not sure where the term threat of punitive costs comes from. The council has never threatened anything," Mr Cull said.
Last week, he said the issue of costs was up to the court.
"My position is that it is not the council that has the say on this, it is the court, and it is the court's discretion to award costs."
Ms Butler polled 43 votes behind the lowest-polling successful candidate Colin Weatherall in this month's local government election.
In part, she sought a recount based on there being so few votes between them and concerns about the robustness of the count.
Judge Stephen Coyle granted the recount last week, but refused her request for an assurance there would be no costs above a $750 deposit she had already made.
Judge Coyle noted she might have to pay costs if the recount was unsuccessful.
Evidence suggested the recount could cost between $60,000 and $70,000.
He gave her until noon yesterday to "reflect as to whether she wishes to proceed".
Ms Butler withdrew her application just before 11am, soon after filing an affidavit in which she pointed out she was not backed by a party and did not think it was her "responsibility to shoulder the burden of potentially considerable costs - up to $70,000 (maybe more) - because of a tenuous voting outcome that has eventuated under such a complex system".
The council could decide whether to seek costs and she asked it "through the judiciary, to uphold the democratic right for a legitimate case for a recount under the complex STV voting system ... without the fear of personally damaging financial costs held over the candidate".
She did not believe the recount would be a direct cost on rates, and asked why the council could have unbudgeted spending on Forsyth Barr Stadium land, on Dunedin Venues Management activities, and buying out the lease of the Hungry Frenchman Restaurant, and be so reluctant to pay costs for something that struck at the heart of democracy.
She was unaware of any precedent for a candidate in an STV election to face costs when requesting a recount and asked Judge Coyle to clarify why a precedent looked likely to be set.
In a note forwarded to Ms Butler, Judge Coyle suggested the affidavit appeared to ask him to predetermine and/or revisit the issue of costs, even though he said in his judgement last week that it was improper for him to do so.
It was also not proper for him to give Ms Butler legal advice as to the potential costs.
She should have consulted a lawyer it that was what she wanted, Judge Coyle said.
In an emailed response to the note, Ms Butler said she was not asking Judge Coyle to revisit costs, she was asking the council, through the court, to withdraw its "threat of punitive costs".
She withdrew her application saying she would "leave it to the wider public to debate the democratic merits, or otherwise, of the 'Catch 22' situation that I was placed under".