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Wellington is tweaking their ordinances to make it easier to dismiss an appointed board member by the council person who appointed them, if it is not an at large seat. This story got a lot of attention at the time. Click title for link. From the article:

Current village ordinance states an appointed board member can be removed only by a majority vote of council.
By comparison, the proposal going before council Tuesday would allow a council member to remove their own appointee “without cause” and “no vote by the Wellington Council shall be required for such removal.” Members appointed at-large by the council would still require a majority vote to be removed.
Vice-Mayor John Greene said he also supports the ordinance change because board appointees are supposed to be “a reflection of an individual council member.”
“We like to think we have a like-minded view when we appoint somebody,” Greene said. “Should there be some break in that mindset, a council member should have the opportunity to make a change in that appointment.”