This could of course just be politeness: the courtesy of showing interest in the visitor's home. But I think it is something more. There seems to be a real desire to learn how a government coming from somewhere other than the right might soften the edges of the market revolution, so that economic efficiency can be combined with a greater element of social justice.
Why look to Britain? Well, consider this: every one of those countries has higher, and in most cases significantly higher, unemployment than either the US or the UK. A set of economic policies developed in both countries through the 1980s is now being applied universally. These are the policies of the market: cuts in top tax rates, privatisation, growth of stock market finance and so on. But if other countries are applying these market policies, they are deeply concerned at the social costs. Here the US is seen as having little to offer: it is just too different, too prepared to allow the weak to fall by the wayside to be an appropriate model. A Blair government might just be able to develop a middle path.
And so in Sweden they were profoundly worried about the need to pull the less-skilled into the work-force and wondered what a Blair government might do to stimulate growth in private sector employment. In France and in Portugal people asked me about the future of the privatisation programme, for both countries are seeking to increase political support for privatisation.
As for Argentina, well, there seemed to be genuine relief when I assured people that there would be a change of government. The country has recently carried out radical reforms, pegging the currency to the dollar, cutting inflation close to zero and privatising everything possible. Maybe the people I was meeting tended to come from the centre-left rather than the right, but there seemed to be a real thirst for a non-US model for the market economy. The American version of market capitalism, peddled by Harvard economists and expensive investment bankers, was just too brutal. Maybe there was no alternative path of reform, but if there was, well, they would like to hear about it. "It really matters to us that Blair wins the election," I was told by the head of a large mutual financial institution, and he was not thinking about whether Blair would be a soft touch on the Falklands.
Who knows what the intellectual exports of a Blair government might prove to be? You certainly cannot tell from the election rhetoric. Remember that privatisation, perhaps Britain's greatest intellectual export of the last three decades, was not in the 1979 Tory programme. It was around as an idea, for Denis Healey had sold off a chunk of BP, but it was buried. And so I can see from these conversations some ideas, similarly buried in New Labour ideology, that might play well in places a diverse as Stockholm and Buenos Aires.
One example would be a rebalancing of the duties of the state towards the individual and the obligations of the individual towards the state as far as employment is concerned. Thus the state has a duty to make training available so that people out of work are not excluded from work by lack of skills. But individuals have an obligation to apply themselves to that training and then accept jobs if offered.
Another would be attitudes to crime. If a new government were able to deliver a policy that delivered lower crime levels because it was "tough on crime and tough on the causes of crime" then the world would beat a path to its door. If that is just a cute slogan and nothing more, it will not just be Britons who will be disappointed.
Yet another would be a lead on the problems of coping with an ageing population: appropriate health-care and affordable pensions of course, but also ways of using older people in the work-force. There are some very interesting ideas about pension provision pioneered by people like Frank Field. If Labour pushes those forward, it will get huge interest abroad.
But perhaps the big idea that would generate the greatest resonance overseas would be the emphasis on morality that comes from people like Jack Straw and indeed Tony Blair himself. Politicians who talk in moral terms are open to ridicule - come to think of it, morality does not play too well when it comes from journalists, either. But there is clearly a global shift in the expected acceptable behaviour of politicians. The Tories have suffered from sleaze but the shift is universal: look at what is happening in the US, or France, or Japan.
This matters in economic as well as political terms. The market economy is an open system in the sense that any country can have it. Information is universal. So the world is operating on pretty much a level economic playing field. Competition, therefore, will come to be more and more in people's behaviour. If people can combine order and creativity, and live in societies with low crime and stable families, then those societies will be able to increase their living standards, and care better for their old. If, on the other hand, economic growth is dissipated on police and lawyers, and cross-subsidies between in-work and out-of-work, in-family and in-care, then it will be much harder to increase overall wealth.
It is a tall order for any new government to ask it for messages not just for the country but for the world. But at least the world is interested, and that is a start.