Coming Soon:

The following books by Robert Paul Wolff are available on Amazon.com as e-books: KANT'S THEORY OF MENTAL ACTIVITY, THE AUTONOMY OF REASON, UNDERSTANDING MARX, UNDERSTANDING RAWLS, THE POVERTY OF LIBERALISM, A LIFE IN THE ACADEMY, MONEYBAGS MUST BE SO LUCKY, AN INTRODUCTION TO THE USE OF FORMAL METHODS IN POLITICAL PHILOSOPHY.
Now Available: Volumes I, II, III, and IV of the Collected Published and Unpublished Papers.

NOW AVAILABLE ON YOUTUBE: LECTURES ON KANT'S CRITIQUE OF PURE REASON
LECTURE ONE: https://www.youtube.com/watch?v=d__In2PQS60
LECTURE TWO: https://www.youtube.com/watch?v=Al7O2puvdDA

ALSO AVAILABLE ON YOUTUBE: LECTURES ONE THROUGH TEN ON IDEOLOGICAL CRITIQUE



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Saturday, March 15, 2014

COLLECTIVE CHOICE THEORY, GET-AWAY BEACHES, AND THE LIZARD BRAIN

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?

2 comments:

Kent Schenkel said...

Unfortunately, I cannot help you with the Sen reference. That caption comment on HuffPo, though, struck me as tongue-in-cheekish so I think the writer might agree understand the logical error.

On another note, congrats on your "How to Do History" blog entry being selected a finalist in the 3QuarksDaily blog contest:

http://www.3quarksdaily.com/3quarksdaily/2014/03/3qd-politics-social-science-prize-finalists-2014.html



Robert Paul Wolff said...

Good grief. Who knew? Is this my fifteen minutes of fame? If I win, do I get something I can eat? [I am on a diet]