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Ms Arnold claims Mr Shadbolt defamed her in four newspaper opinion columns. They talked about her stance on various council projects including a proposed kakapo chick and tuatara display house at the Southland Museum & Art Gallery.
Mr Shadbolt counterclaimed over a letter to the editor written by Ms Arnold but later dropped his action.
After a hearing in February to discuss a series of preliminary applications from Ms Arnold, Justice Denis Clifford declined all but one and ordered her to pay costs of $5908 to Fairfax and $5167.50 to Mr Shadbolt.
Ms Arnold appealed his decision and a hearing was scheduled for the middle of next month. However, she confirmed yesterday she had abandoned the appeal.
She said she and her lawyer had been waiting for another defamation judgement on similar issues to be released. That had happened about two weeks ago and after reading it, they had decided "on balance'' not to pursue the appeal.
However, the defamation action was still proceeding, Ms Arnold said.
"We were going down a path and the appeal was like having to step off to one side. Now we are on the path again.''
When contacted yesterday, Mr Shadbolt said he was "saddened'' by the defamation action because it distracted from the good work the council was doing.
"Defamation is the pinnacle of division. This is going to make [councillors] look very divided, and we're not.''