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Vilfredo Pareto is not a household name so I should start by saying a few things about his life. An Italian, he was born in Paris in 1848 to an aristocratic family of exiled liberals.

Returning to Italy after the wars of unification, he graduated from an engineering school in Turin and became a civil engineer, but soon extended his interests to practically all academic

pursuits, including economics, sociology, political science and philosophy. In 1893, at the age of 45, he became Professor of Political Economy at the University of Lausanne and thereafter

remained in Switzerland, where he died in 1923. His ideas have been subject to many sophisticated mathematical analyses, but some can be easily understood without resorting to any

mathematics. He is best known for the Pareto principle. This states that 80 per cent of the effects come from 20 per cent of the causes. He first applied this principle to wealth

distribution, claiming that in general 80 per cent of the wealth of a country is owned by 20 per cent of the population. The Pareto principle has since been extended to dozens of activities,

e.g. 80 per cent of the revenue in a company comes from 20 per cent of the customers, or 80 per cent of the accidents are caused by 20 per cent of the drivers. My aim is here to concentrate

on another of his ideas: Pareto efficiency, widely used in welfare economics. For a given set of resources a distribution is Pareto optimal if nobody can be made better off without making

at least one member of the set worse off. My interest is in a closely-related rule, often called Pareto comparison. It can be used to assess the relative standing of two individuals

according to a given set of criteria. We can say that person A is (in this sense) superior to person B if person A has a higher score in at least one of the criteria and has no lower score

in any of the other criteria. The most popular manifestation of Pareto comparison is the song in _Annie get your gun_: “Anything you can do, I can do better.” In Pareto language this means

that person A scores higher than person B in respect of all relevant criteria. I shall give below a few other examples of Pareto behaviour. Mr Robinson has a house. It has n bedrooms, m

bathrooms and a garden of area A where, say, n = 3, m = 1 and A is a tenth of an acre, so A = 0.1, measured in acres. Now he decides to move. Once the decision is made, most people aim to

look for a house that on the basis of a Pareto comparison scores higher. What kind of house would that be? Taking into account only those three criteria (bedrooms, bathrooms, garden area),

Mr Robinson would be better off if at least one of the 3 indicative figures is higher and the others are no smaller. I give here three examples: Example 1, n = 4; m = 1; A = 0.1;  Example 2,

n = 3; m = 2; A = 0.1; Example 3, n = 3; m = 1; A= 0.12. Note that in all these cases, one of the indicative figures is higher and the other two are identical. Let us now look at a further

example: Example 4, n = 4, m =2, A = 0.02, i.e. Mr. Robinson is considering buying a house which has one more bedroom and one more bathroom than those of his present one. Unfortunately, it

has a much smaller garden. Two indicative figures are higher and one is lower. Pareto comparison is inapplicable. Mr Robinson has now a dilemma. He might argue: “It is nice to have a fourth

bedroom (now Suzie and Lucy can have separate bedrooms), it is nice to have one more bathroom (Clare and I, we can at last have our own bathroom), but what about young Jimmy wanting to play

football in the garden? Our present garden is so big that he can happily play football or any other ball game. The house on offer has a much smaller garden. Will Jimmy be grumpy? What will

Suzie and Lucy say?” The simple conclusion is that when Pareto comparison fails one must resort to some other measure. Would an extra bedroom and an extra bathroom outweigh the disadvantage

of having a smaller garden? Jimmy might say, no. Suzy and Lucy might say yes. There is no obvious answer, unless one is prepared to assign numerical values to each of the attributes and look

at the total score (economists call this process optimising a utility function). If a bedroom is worth 6 units, a bathroom 4 units and an acre of land 100 units, then the existing house has

a utility of 3 x 6 + 4  + 0.1 x 100 = 32 units and a house in Example 4 has a utility of 4 x 6 + 2 x 4 + 0.02 x 100 = 34. The new house has a higher utility. Suzie and Lucy will be happy.

Jimmy will protest: “You cannot make such a big decision on a difference between 32 and 34.” (Remainers would argue that you cannot make a big decision on the basis of a difference between

48 and 52.) Jimmy will further argue that the family has attributed too low value to the garden. Jimmy proposes a value of 200 to be more suitable for one acre of land. In that case the old

house is valued at 42 and the new house comes out at 36. Jimmy does not think it would be worth moving. The above story is a digression showing how one can make a decision when Pareto

comparison is _not_ applicable. However, I want to return to my original aim and discuss Pareto comparison in a social context. Let us look first at people who are _nouveau riche_ (sorry to

choose the male gender, the conclusions surely apply equally to those who are _nouvelle riche_). Let’s start with the most profound desire of our newly rich couple. They hanker after social

respectability. They choose carefully a society to which they would like to belong.  A typical member of that society has chauffeur-driven cars, a ten-bedroom house, holidays three times a

year on the French Riviera, children go to elite schools, wife wears the most beautiful mink coat and she has a 3-carat diamond ring. These are six attributes which the couple we discuss

should match. What they are aiming at is Pareto equivalence, not Pareto superiority. There would be no point in acquiring a fifteen-bedroom house. That would make assimilation to that

particular society more difficult. Next apply Pareto comparison to some average couple. I think most of them loathe Pareto comparison. Why? Let us assume that two freshly married couples,

named Smith and Jones, land as neighbours in two adjoining semi-detached houses. They have identical gardens and identical Renault Clios. Shortly after they moved into their respective

houses, Mr Jones decides to upgrade to a Renault Scenic. Mr Jones has apparently more money. He can afford a Renault Scenic. Should Mr Smith keep up with the Joneses? Should he buy a Scenic,

or an even more elegant car? He thinks not. Not even if he had the money. If Pareto comparison is applicable then there is always the chance that he will lose, that in all attributes he

will have a lower score. But once he rejects Pareto comparison, he is O.K. He wants at least one attribute (say the beauty of the back garden) in which his score will be much higher, and

decides not to care about lower scores in some others. He can always say to his in-laws, “Yes, the Joneses have a nicer car but our garden is vastly superior to theirs.”