[EM] Seven +/- Two

Forest Simmons fsimmons at pcc.edu
Fri Sep 14 11:41:44 PDT 2001

It is true that any ballot proposed for public consumption should not be
much more complicated than the five slot ballot.

Keep in mind, however, that not all ballots (let alone methods of
evaluating them) discussed on this list are to be considered as public

First of all, voting methods have many scientific decision making
applications outside of politics, for example in robotics and other
control systems.

But more to the point for the case in question is the following

It is surprising to many folks that theoretical considerations often have
practical implications. 

This fact has been dubbed by philosophers of science as "The Unreasonable
Effectiveness of Mathematics."

Here's my explanation.

Suppose that your college applies to the legislature for some money to
remodel and upgrade your facilities. You submit your wish list. On that
list the sky is the limit. It gives a vision of the ideal. But budget
limitations pare down the list to realistic improvements.

In mathematics, the theoretical can help us identify the ideal. Then
practical considerations pare this down to the realistic level of the
application. The practical is an approximation to the ideal.  Without the
ideal it isn't clear what we are trying to approximate.

I agree that a CR scale of zero to 100 is probably too much resolution for
a public proposal, although I don't consider it harder to deal with than a
preference ballot with fifteen or twenty candidates to be ranked.

But if we can figure out the ideal use of a high resolution CR ballot,
then we have a better chance of knowing how to get the most out of our
five slot ballot. 

I'm still waiting for ideas on how to infer strength of preference
from the high resolution CR ballots, and how to use the strength of
preference information to best advantage.

I'm saving my ideas along these lines to keep from prejudicing others.

One more thought on the relative ease of rating twenty candidates in
contrast to ranking them; rate them as follows:

First rank them, but with equalities allowed for cases of indecision.

[This feature makes ranking easier, especially for people that have
psychological problems with coin tossing while performing their civic

Then allow the voting machine to assign preliminary ratings by converting
the ranks to percentages.

Finally, if the resulting ratings do not seem quite acceptable, adjust the
gap sizes to roughly correspond to strength of preference. 

The preliminary ranking can easily be accomplished interactively by
responding to (the order of)  n*log(n)  questions of preference, where n
is the number of candidates. 


On Tue, 11 Sep 2001, Dave Ketchum wrote:

> This one makes MUCH sense to me.
> One thing it says is it may not be worth while to provide for any one
> voter listing more than 6 or 7 candidates in preference voting.
> It also leads me to question again the scheme that lets voters say
> something about ranking with >>>>>>> - I have not worked up any
> enthusiasm for understanding what that is about, let alone how to
> explain it to voters in a way that would let them get any good from it.
> Dave Ketchum
> On 10 Sep 2001 23:22:04 -0400 Buddha Buck wrote:
> > 
> > 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
> > forth.
> > 
> > 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.
> > 
> > Later,
> >   Buddha

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