The balloting took place at the Cardiff Labour group's annual general meeting at County Hall.
BBC: Cardiff council leader Heather Joyce survives challenge
They showed a man walking around Norfolk County Hall, in Martineau Lane, while it was closed.
BBC: Norfolk County Hall: New security measures after trespass
Some residents have stuck posters in their windows that read: "County Hall - neighbour from hell".
No planning permission has been granted for redevelopment of the County Hall building itself.
County Hall said it hoped work will start in February and be finished in September.
Campaigners marched from Fairfield car park in Dorchester to County Hall from 1100 GMT.
One Independent councillor in 2009 found the daggers drawn at county hall in Truro an unedifying spectacle.
Bus companies were discussing proposed cuts to subsidies for concessionary passes at a meeting in County Hall.
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At a meeting in County Hall, Truro, the cabinet deferred a decision over increased charges until February.
Cliff Jordan, cabinet member for efficiency, said retaining County Hall was "the most practical and affordable solution".
The Glen Parva Action Group has already handed over a 1, 400-signature petition to officials at Leicester's County Hall.
The decision to award the contract will examined by the cabinet scrutiny committee at County Hall on Tuesday.
Jonathan Dunning, branch secretary of UNISON at county hall, said social workers were facing increasing workloads and declining resources.
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Northamptonshire County Council said it wants to build new offices on derelict land at the back of County Hall.
He said council chambers would remain at County Hall, and that the new office was for "back office staff".
The award will be presented at a regional road safety conference held at County Hall in Durham on Tuesday.
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Coroner Dr Elizabeth Earland recorded a verdict of accidental death at the inquest held at County Hall in Exeter.
Council leader Adrian Hardman said it would be "principally backroom jobs" that will go at County Hall in Worcester.
BBC: Worcestershire County Council is to cut another 650 jobs
Adam Simmonds was quizzed by a member of the public, Patricia Masters, at his first panel meeting at County Hall.
Council tax will also be frozen for the fourth consecutive year, since the Conservatives came to office at county hall.
To help pay for the work, all council staff are to be brought back to County Hall building in Norwich.
The hearing at Dorchester County Hall heard the family were crossing the road near the Swannery Bridge when the accident happened.
New security measures have been introduced at Norfolk County Hall after an intruder's film of the council headquarters appeared on the internet.
BBC: Norfolk County Hall: New security measures after trespass
The site behind County Hall is currently a council staff car park.
Protesters marched to the hospital after the rally at the county hall.
It is also expected that office premises in Chelston in Somerset and County Hall in Exeter, Newton Abbot and Barnstaple will be retained.
The residents, who live opposite County Hall, have begun a petition to ask Leicestershire County Council to make the area a no-parking zone.
The hearing at Kendal County Hall had earlier been told that the former nightclub doorman had taken a designer drug known as Madcat.
BBC: Dale Burns inquest: hospital staff 'did all they could'
The Conservative-run council would look to move out of buildings including John Dryden House, parts of the current County Hall, Riverside House and Century House.
He said the problem started three years ago when the authority decided to move its staff from other offices to County Hall to save money.
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