"My nice dream is where I see Halifax having converted to a plc and every member takes their money or shares next year and moves their savings to Nationwide because of our better rates," Mr Davis says.
The nightmare scenario, he concedes, is that his society might be forced to follow the others and de-mutualise.
"The bad dream is that short-termism might take over. That members might say, 'Well, look, we would rather have the pounds 500. We don't really care about building societies or the long term'. If that were to happen it would be a great shame."
Mr Davis's dreams, good and bad, encapsulate the dilemma facing the building societies movement, of which Nationwide is poised to become the largest member once Halifax de-mutualises next year.
Building societies dominated the home loans market as recently as 1994. But control of mortgage lending in the UK is set to pass into the hands of the banking sector, perhaps within the next 18 months. The radical transformation of the market will not be the product of a stand-up, knock- down fight between banks and building societies. Rather, nearly all the UK's top 10 societies are themselves crossing over to the other side.
The stampede to de-mutualise, signalled by Abbey National in 1989, accelerated two years ago when Cheltenham & Gloucester announced it would be taken over by Lloyds Bank.
Since then, Halifax, Leeds Permanent, Woolwich and Alliance & Leicester have all announced that they too will make the change.
National & Provincial has been swallowed up by Abbey National, while Bristol & West has also thrown in the towel and plans to be taken over by Bank of Ireland.
In the process, more than 16 million society members are to share in a free cash-and-shares bonanza worth up to pounds 20bn.
The challenges ahead have special meaning for Nationwide, and even greater poignancy for Mr Davis himself, as he prepares to become chairman of the Building Society Associations, which holds its annual conference in Birmingham from Wednesday.
The Nationwide chief's emergence as a leading defender of mutuality strikes some observers as surprising. Certainly there is little in his background to suggest he would become a dyed-in-the-wool mutalist. A scientist by training, he earned a doctorate in a rocket-fuel technology. He spent his early working life at Esso, gradually moving up the oil company's management ladder before joining Nationwide in 1986 as general manager in charge of technology.
His promotion to chief executive followed the departure of Tim Melville- Ross, who left to head the Institute of Directors.
Mr Davis has not always been so pro-mutuality. Nationwide was pipped by Abbey National in the race to take over N&P last year. Had the two societies merged, they would have announced their own plans to convert to a bank, Mr Davis admits.
The irony, Mr Davis says, is that the experience of talking to N&P confirmed Nationwide's decision to stay mutual. "We learnt a lot more about what conversion entails. I had to say that I think it has worked out the right way and we are happy to stay the way we are."
Since then, Nationwide has moved to assert the benefits of mutuality by handing back more than pounds 200m of annual profits to members in the form of mortgage rate cuts and savings rate increases. At 6.74 per cent, the society's variable lending rate is half a percentage point cheaper than all the "wannabe" banks, cutting up to pounds 40 a month off the cost of an average pounds 50,000 mortgage.
Mr Davis dismisses claims by competitors that Nationwide's rates are a short-term headline-grabbing stunt. Nor does he accept the argument that flotation and the disciplines of shareholder democracy are the key to a well-run institution.
"That is one of the things people talk about. But we have improved our efficiency year on year for seven or eight years without the disciplines of the City. We don't need to go through the two-year pain and the expense of giving pounds 100m to merchant banks to discover that discipline," he says.
In any event, he believes any handicaps societies may have faced in the past will soon be overcome by the new Building Societies Act, aimed at enabling them to widen the services they provide. He intends to use his year at the helm of the BSA to promote the passage of the Bill through Parliament.