None would have chosen it this way, of course, given the conventional demands of party-political name calling; but, in 1989, the voters of Avon returned a hung council of 36 Labour, 33 Tories and seven Liberal Democrats. The expedient response of the Avon Ladies was to sit down and talk. Endlessly.
What emerged was a scheme designed to take some of the partisan sting out of county hall politics and open the decision-making process to wide public debate. Old-style committee chairmen were replaced by 'chairs' who lost the traditional power of the casting vote; committees had spokesmen (or persons) elected from each of the three parties; each group was consulted by council officers on policy.
Members of the public were encouraged to attend committees and even to join in the debates. Annual budget time involved talks on an heroic scale with the pressure groups and voters of industrial Bristol, Georgian Bath and broad swathes of prosperous rural England, the Cotswolds and Mendips.
The new deal required a lot of selling to some Labour members, deeply suspicious as they were of a Liberal Democrat party which had spent several years before 1989 hopping in and out of bed with the county's Tories. 'We saw it as a hard-headed solution in a hung council,' Mrs Davey says. 'We simply couldn't go on winning the arguments and losing the vote. Maureen, to give her her due, worked very hard on this. We're three women but we're three women of very different character.
'It's not an ideal system. It can be very frustrating, very hard work for officers and members alike. To be a bit cynical about it, one of the reasons we've got three women running it is that all of us work virtually full-time, unpaid, as councillors, which most men wouldn't tolerate or be able to do. Men prefer to be in power, they like to give orders.'
Pat Hockey - a mother of seven and, like Mrs Davey, a former teacher - is, understandably, enthusiastic about a system which has benefited her small group of Liberal Democrats. She says: 'I've sent a little document out to candidates this time saying we honestly don't think we could have achieved any more if we'd been operating in overall control. I wouldn't be very surprised if Labour won but I do think that if the Tories lose seats they're more likely to go to us rather than Labour. With their poor performance nationally, especially in rural areas, it's us that'll pick up the Conservative vote. Hopefully we'd still hold the balance of power, but with more of us to do it.
'On a personal level I get on very well with Val; with Maureen, I wouldn't say there's animosity, but she does have a lot of Tory tendencies which I can't relate to . . . She's got a bit of a born-to-rule attitude.'
Mrs Wheadon takes a dim view these days of the alliance. Her group enraged Labour in 1990 by getting the county's budget rate- capped. She is under pressure from her own party. Her deputy, John Portch, a big name in office equipment in Bristol, has already challenged her once for the leadership and may do so again if the Avon Tories do badly this week.
'I did feel, when we initiated this system four years ago, that it was the best set of working practices that we could have devised with a hung council,' she says. 'But I have to say it's proved even more frustrating than we'd expected. We think the committee system and the consultation is extremely expensive and time-wasting. The district auditor has said the cost of democracy is getting too high. He's estimated that formal committee meetings cost pounds 2m last year.
'In the last 12 months we've had a system when the public can speak at committee meetings. It's supposed to take half an hour but quite frequently it takes longer.
'We had one planning committee which started at 2.15pm and was abandoned at 9pm with 12 items still to go. I think also that this business of calling it chair rather than chairman, which I think should apply even to lady Tories, diminishes the office in the public's eye. When we get a majority, we'll stop all these silly practices.'
The Local Government Commission is expected to abolish Avon in its two-tier form - along with other county authorities like Derbyshire - by 1996. With it will go the Avon Ladies' dream that local politics deserved something better than the self-interested wheedling of party politicians.