Required for next week: April 9, 1996

In the Globe and Mail this week

I didn't have so much luck with the G&M this week, so I've reprinted the entries from last week, with typos and other inconsistencies corrected (I hope). The first three items are new; the remaining are repeats.

Technical Note: voting paradoxes

There are references in both of the articles for today to Arrow's Theorem. It is discussed in another article in A Mathematician Reads the Newspaper(p.~153--155), and also in another book by J.A.~Paulos called Beyond Numeracy. Here is a quote from BN, (p.264):
The mathematical economist Kenneth J. Arrow has demonstrated that there
is never a foolproof way to derive group preferences from
individual preferences that can be absolutely guaranteed to satisfy
these four minimal conditions: 
  1. if the group prefers X to Y and Y to Z then it prefers X to Z;
  2. the preferences (both individual and group) must be restricted to available alternatives;
  3. if every individual prefers X to Y, then the group does too;
  4. and no individual's preferences dictatorially determine the group preferences.
And from MRTN,(p.~156):
Recent polls provide an instance of a related mathematical problem,
that of preserving coherence when moving from a small set of statements
to a larger one. ... The general mathematical question of determining
when a large set of statements is jointly  consistent is a most
intractable one.

These and other principles and ideas may be somewhat abstract and unappealing, but
there are no alternatives if we're to have any hope of scaling up our understanding
without buckling under the mental strain.  As news services
and cable news take over some of the transcriptional aspects of reporting,
there is room in newspapers for more analytic, comprehensive
accounts to supplement (but
certainly not replace) the parochial fights, intrigues, and drama that make
up the bulk of the news.