Idly surfing the web and crawling around on the Huffington Post yesterday, I stumbled on this picture of a lovely beach, to which was appended the following comment: "Navagio has been called the prettiest beach in all of Greece, which, if we can all agree is one of the prettiest places in all the world, then this beach is the prettiest beach in the whole wide world. Logic works for us."
As I am sure you will all understand, I immediately thought of Amartya Sen, who has an elegant discussion of the logical fallacy embedded in this picture caption. To see intuitively why it is a fallacy, consider the following formally identical argument: "Jones is the richest person in America, and America is the richest nation on earth, so Jones must be the richest person on earth." [I was going to say, "Tell that to Carlos Slim!" but Forbes says that this year Bill Gates has edged him out. Oh well.]
Anyway, I decided to write a little blog post about this logical error, so I pulled Sen's Collective Choice and Social Welfare off my shelf and started paging through it, looking for the passage I was sure was there. For those of you who do not know it, Sen's 1970 book is one of the loveliest works of formal logic ever written. It is breathtakingly brilliant, very clear, and full of surprising and important results. [Not just my opinion -- Sen won the Nobel Prize for it.] Among other things, the book contains Sen's announcement of the necessary and sufficient conditions for majority rule to yield consistent social choice. This is an important extension of Kenneth Arrow's major result, the General Impossibility Theorem [for which Arrow won the Nobel Prize.]
Well, an hour later, I gave up, empty-handed. I know it is there somewhere, but I just cannot find it. I even looked through Sen's short book, On Economic Inequality, but I could not find it there either. Can anyone point me in the right direction?