Students of economics will hear about "Pareto efficiency" very early in Econ 101. It's a tool to compare outcomes. Sadly, poor Pareto now has his name attached to a disastrously misunderstood concept - Pareto efficiency is everywhere used and frequently abused.
From a biography of the man himself, Vilfredo Pareto:
"Like Irving Fisher (1892), Pareto stumbled on the idea that cardinal utility could be dispensed with. Preferences were the primitive datum, and utility a mere representation of preference-ordering. With this, Pareto not only inaugurated modern microeconomics, but he also demolished the "unholy alliance" of economics and utilitarianism. In its stead, he introduced the notion of Pareto-optimality, the idea that a society is enjoying maximum ophelimity when no one can be made better off without making someone else worse off."
Two reasons to be cheerful: apart from featuring the excellent word "ophelimity" (n., economic satisfaction), this could not be clearer on the definition of Pareto optimality (now synonymous with Pareto efficiency). A situation is Pareto optimal if no one can be made better off without making someone else worse off.
Why, then, is this type of statement easily the most common mistake in economics (not intended to pick on the source, which is certainly not unique):
"There is no connection between Pareto efficiency and equity! In particular, a Pareto efficient outcome may be very inequitable. For example, the outcome in which I have all the goods in the world is Pareto efficient (since there is no way to make someone better off without making me worse off)." [Emphasis mine]
To get the cheapest criticism out of the way first, saying "there is no connection between Pareto efficiency and equity" is a bit like saying "there is no connection between Pareto efficiency and the color of my shoes"; why should there be? It's just a definition. It is, or it isn't. The criticism that's actually important is that the bit in bold is a logical falsehood.
The true statement would be "the outcome in which I have all the goods in the world can be Pareto efficient". In fact, equally true: "outcome _____ can be Pareto efficient". Why? The missing link is that Pareto efficient is, inherently, a concept built on utility. The "better off" part implies that our test of Pareto efficiency centers on the relative satisfaction enjoyed under alternative outcomes. This is, again, not the same as the relative levels of income, consumption or stuff enjoyed under alternative outcomes.
A simple proof by contradiction: I have all the goods in the world. I am also ascetic and thus get more satisfaction from having less goods. You always like more goods. The outcome in which I have all the goods in the world is Pareto inefficient.
Simple, no? Again, it's a case of confusing utility with goods or money, a case that would probably have irritated Pareto himself. The hidden assumption in the mistake quotation is the assumption on what the preferences of the person with all the goods are. We can imagine many ways in which that person's preferences would result in the falsehood of the assertion of Pareto optimality, yet we are anyway confronted with this manifestation of the prejudice that the concepts used by economists to compare outcomes are evil manifestations of an imagined money-centric, capitalist doctrine.
So is Pareto efficiency a normatively loaded term? Is the concept of Pareto efficiency part of positive economics or normative economics? Those who would argue that the boundary between the two is fuzzy frequently point to the Pareto efficiency tool as evidence. It's a concept that is, however, firmly positive, at least up to the scale of the interpretation of language. It either is raining, or it isn't. An outcome either is Pareto efficient, or it isn't. This cannot be a normative statement.
Perhaps the problem arises because, like all concepts that rely on assessing utility or satisfaction, Pareto efficiency might be inherently untestable. Unless it's actually possible to know or deduce preferences, we can't make physically true statements about Pareto efficiency or the like; the best we can do is to say "if these people have these preferences, this outcome is or is not Pareto efficient". To do better than conditional truth we somehow have to know preferences, and whether that's possible is, to me, a huge open question. Pareto efficiency might then seem normatively loaded because the assumption on what preferences people hold is folded into the statement of Pareto efficiency, as in the mistake above that omitted "if people only care about their own material possessions".
The irony is that Pareto, the man, for whom "Preferences were the primitive datum, and utility a mere representation of preference-ordering", might perhaps be the first to object to the misuse of his most famous concept.