In discussing the idea of market failure, in class and in public talks, I usually start by pointing out that technical terms often sound self-explanatory and aren't; the theory of relativity, for instance, is not the theory that everything is relative. I go on to explain that "market failure" is an example of that problem. It does not describe all ways in which markets can fail and it is not limited to markets.
As I define it, market failure describes a situation where individual rationality does not lead to group rationality. Non-market examples include the game of prisoner's dilemma, where each defendant makes the correct decision for himself (confess and betray his co-defendant) even though both would be better off if both made the alternative decision, situations where an army runs away and is slaughtered because each soldier is better off running although all are better off if they all stand, and traffic congestion at an intersection that keeps jamming because drivers, trying to cross before the light changes and failing to make it, block the intersection. In each of these cases, each actor is making the correct decision for himself but every actor would be better off, at least on average, if they all made a different decision.
I have just been redoing the argument as a chapter for the third edition of my first book, The Machinery of Freedom. In doing so, it occurred to me to wonder in what sense what I have been saying is true. I am describing how I use a technical term in my field. Can I legitimately claim that others, including other economists, who use it differently are wrong?
There is no central authority to determine how technical terms are defined, and if there was I would not be it. I made no attempt, before pontificating on the subject, to research the usage of other economists; a recent google suggested that what I regard as the incorrect usage is quite common. I should not have been surprised, given that, a year or so back, I emailed the author of a very successful textbook to try to persuade him to change the way in which he used the term. I got back a courteous reply, saying that he would consider the matter.
I concluded that, in writing the chapter, I should be a little more careful in what I claimed. My definition is not what the term means—meaning is defined by use, and lots of people use it differently. My definition is what the term ought to mean.
Technical terms are tools for thinking and communicating. My definition of market failure makes it a better tool for those purposes than an alternative such as "a situation where the market does not allocate resources efficiently." The latter lumps together similar effects from unrelated causes—the market might produce the wrong allocation because the information to deduce the right allocation did not exist when the relevant decisions were made. It fails to identify situations where the same logic is functioning in the same way in different contexts—rational ignorance in voting as an example of the public good problem, prisoners betraying each other as an example of an inefficiently large output (of confessions) due to a negative externality.
I will continue to argue that my definition is the correct one. I will merely be a little more careful to explain what that means.