The vested interest we can see in this scene is selling the company's product. This works by trying to find the perfect advertising in the one throught lying and relating the cigarette with healthy habits, people get to think that tobacco does not kill.
Peter's idea is rejected because in his slogan he states that if you smoke you will die and if you don't you will die too. It is rejected because the adversting they were looking for involved not associating it with death or something negative. Don's idea is accepted because looked for the way of presenting the product so as to make it different from the same products of the different countries. Moreover, he doesn't mention death, which is crucial in this types of advertising.
Then we had to analyse an old tobacco advertisement in terms of vested interest and distortion of the truth.
In this advertisement we can clearly see that the company is lying so as to sell the product as much as they can. The phrase "To keep a slender figure no one can deny" is fake since cigarrettes might reduce your weight as it reduces anxiety but it causes other health problems that are even worse and might lead to death. Furthermore, by showing someone thin and with good aspect people directly relate it with good health and admirable phyiscal state. Additionally, as in the case Mad Men, it says "it's toasted" to differ it from other companies, so people who don't know the 'secrets' of the cigarrette production cannot realize if its something exclusively from this company or everyone does it.