[EM] Seven +/- Two

Buddha Buck bmbuck at 14850.com
Mon Sep 10 20:22:04 PDT 2001

A message on another list reminded me of something -- an old,
well-established psychology paper entitled "The Magical Number Seven,
Plus or Minus Two: Some Limits on Our Capacity for Processing
Information" by George A. Miller (The Psychology Review, 1956, vol 63,
pp. 81-97, republished at http://www.well.com/user/smalin/miller.html
by permission of author, address checked 2001-09-10).  

What the article talks about is the ability of people to perceive and
distinguish stimulae accurately.  To a very large degree, Miller noted
that most people can easily distinguish things into about 7 plus or
minus two groups -- we can identify 7 plus/minus two shades of grey, 7
tones, 7 time intervals, etc.  Given multiple dimensions to
distinguish, we can do better -- we can easily distinguish things into
25 partitions of a square, 30 combinations of tones on a variety of
instruments, etc -- as long as the amount of information for each
variable is still about 7 +/- 2.  

I believe, because of this paper, and the research along those same
lines that has followed it, that any attempt to try to get more than
3-4 bits of information from the voter per candidate is likely to
result in lots of noise and voter error.  CR, while theoretically nice
(perhaps epecially when done on a -100 to 100 scale), may run afoul of
too much noise if the range of cardinalities greatly exceeds seven +/-
two.  Rankings above 5 or 6 candidates becomes difficult. And so

The ballot proposed by Forest (I believe) involving grading candidates
A, B, C, D, and F (as in school grades) seems to me to have about the
right information content to record the opinions of the voter with
reasonable accuracy and precision.  Approval's ballot is simpler, and
seems to provide enough information to make a good decision.

Just something I was thinking about.


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