Almost invariably, the white man present unsuccessfully tries to pass the pipe on, is forced to draw on it and gags painfully as a result.
John Carter is not one to splutter over the pipe of peace. As someone who has proudly spent all his working life in the insurance industry, the newly-appointed chairman of the Association of British Insurers does not see the post as any kind of a poisoned chalice.
Far from it. The calm and measured tone he adopts when discussing the industry seems so reasonable that any criticisms of it sound childish and extreme.
The ordinary consumer views the insurance industry in terms of the dodgy salesman with his foot in the door, selling expensive and inappropriate products. For John Carter, putting the problem into context is key to assessing it.
"There are real issues behind what people feel about the industry at the moment," Mr Carter says carefully. "What we must understand, however, is that we have one of the most developed insurance markets in the world. We are third in the world in terms of life products and fifth on the non- life side."
He argues that the British economy as a whole has seen the need for insurance. We are a big contributor to the economy in terms of overseas earnings. The insurance sector is one of our most successful international businesses and we are a key worldwide marketplace.
"There is not a particular dislike of the insurance sector as such. Indeed, there are many in Europe who wish they had an industry quite as well developed as us."
The issues he sees the ABI confronting include the extension of a partnership between the state and the industry in providing benefits to the public.
As part of this, Mr Carter also wants to improve the tax breaks available for long-term savings products. "The claims on the state are so great that it cannot afford to meet them any longer.
"On the pensions side, we are quite well advanced, certainly compared with our European neighbours. But in others, such as long-term care, this is not the case. The playing field is skewed against long-term savings."
He admits that the industry is clouded by problems on the life side. "Now, there is no doubt that the industry did sell very aggressively at the end of the bull-market in the late 1980s. There was a very real need for people to take out personal pensions and we were strongly encouraged by the Government to win new business. Nor is there any doubt that there was some mis-selling and this is something that the industry has to face." But he wants this kept in context.
"My own personal view, however, is that the scale of the problem is probably not as great as is sometimes predicted. The consumer's impression of the industry has been damaged but for every one person who has a legitimate claim that he was mis-sold a product, there will be 999 others who have no problem and do not need to make a claim."
Mr Carter's methodical - and curiously effective - defence of the industry owes much to the approach he takes in all his business affairs. After National Service in the RAF and a mathematics degree at Oxford, he joined Commercial Union. Thirty-four years later, Mr Carter is CU's chief executive. In his time at the company, he spent the first 15 years rising to the top in CU's UK life side before transferring to management of the company's general operations internationally.
Mr Carter was one of those responsible in the 1980s for CU's new strategy of diversification and expansion. "We decided to expand our life business internationally, principally because the life market has a high growth rate. It also has a more secure profit profile and tends to be more stable. It therefore offsets volatility of general insurance cycles." Since the mid-1980s, CU's life operations worldwide have doubled and now account for 40 per cent of its business. Complementing, the life operation is CU's move into asset management.
Mr Carter places great emphasis on strategy as a way of ensuring success: "I have found that if you can agree a very clear strategy in terms of what you want to achieve and then get the highest-quality management team that you can find, things fall into place thereafter."
This is something he wants to continue at the ABI. "The chairman has to provide leadership and support and get involved on a regular basis with ministers, opposition parties, civil servants and other parts of the City."
Through it all, Mr Carter intends to be the serious, responsible ambassador for what he believes is a much-maligned industry. It may be too soon to tell whether the pipe of peace is shared between consumers and the world of insurance. But if the new ABI chairman has his analytical way, it will be.