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And that one member is "most likely"" to be Sir Tim, a new report"s findings say.
Governance research was carried out with the mayor and 11 of the 12 councillors in March to assess the Invercargill City Council"s progress and help highlight ongoing governance challenges, after the Department of Internal Affairs raised concerns in 2020.
The findings of the survey will be presented at the council"s project governance group meeting today.
Among the key observations was that elected members felt there had been less notable progress from July last year to March this year than in the previous six months.
In the previous survey, 53% of respondents believed there had been "significant progress"" towards having strong and unified governance and leadership in the past six months.
In the latest survey, that figure dropped to 41%.
Asked if they had "confidence that the mayor is on top of key council issues"", 92% of respondents answered they "strongly disagree"".
"It must be noted that the mayor himself is one of the survey respondents and most likely represents the remaining 8%,"" the findings stated.
Elected members felt the relationship between councillors, chief executive Clare Hadley and executive staff had improved compared with the previous six months.
However, the mayor"s working relationship with his deputy mayor and committee leaders had got worse, and with councillors it "remains similarly poor"".
One respondent felt the survey was full of loaded questions which presented a skewed analysis of governance, the report said.
That respondent had commented, "In reality, councillors are not free to express their honest opinions because there is a clear hierarchy in place where they may be stripped of power for not towing the line.""
The Otago Daily Times was unable to reach Sir Tim yesterday for comment.
-- Luisa Girao