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From: Doug
To: kenji
Subject: Re: Chapter 4
----

I see you are drawn to the combinatorial optimization aspects of this team business, Kenji. I myself can't imagine a single measure of effectiveness of a team formation plan. Personally I just look to see how many teams have to "reach" for some modes, a rough criterion used in the Ch. 4 discussion of the evaluation of team formation plans (p. 8). I also think any measure of effectiveness should be based on cognitive modes rather the MB variables.

A technical point: the transformation from MB 4-space to modal 4-space is "homogeneous" rather than "affine" because the origins map to each other. By the way, the transformation is "orthogonal" but not "normal". Length, which has no meaning anyway in this context, is NOT preserved under the transformation, so the transformation is not even Euclidean. I stumbled on this point when I put together the earlier theory that MM made into a web site for ME310. I had the site withdrawn when I realized the error, but I'm afraid YS did use the MM site in his research. I hope I talked him into correcting things.

Keep on truckin�,

Quoting kenji:

> Thanks Doug,
>
> By the way, because the I-E, P-J, S-N, T-F
> characterization has only 4 degrees of freedom from
> the pairing, each individual is represented by a
> point in 4-space. Then the mapping to the ES-IN,
> EN-IS, ET-IF, EF-IT space (which is also a 4-space)
> is an affine transformation.
>
> When we call the 4 axes in the original space I, P,
> S, T, then the goal is to group all the points in
> groups of 4 points so that for each group,
> Imin * Imax < 0
> Pmin * Pmax < 0
> Smin * Smax < 0
> Tmin * Tmax < 0
>
> This ensures all the eight characters have a member
> with a positive component. We also try to form the
> groups so that,
> Abs(Sum(positive I's))
> Abs(Sum(negative I's)) (=Abs(Sum(positive E's)))
> Abs(Sum(positive P's))
> Abs(Sum(negative P's))
> Abs(Sum(positive S's))
> Abs(Sum(negative S's))
> Abs(Sum(positive T's))
> Abs(Sum(negative T's))
>
> are all fairly big. If we were to find the group
> that maximizes say the multiple of these 8 numbers,
> it is easy. The difficulty is in grouping all
> points so that each group has a good share of
> these 8 quantities.
>
> There is a finite number of combinations, so if we
> can find an evaluation function, then the computer
> can handle the grouping.
>
> The evaluation function will depend on the
> organization policy. For schools it is probably the
> grouping with the smallest difference between the
> minimum and maximum of each of the above 8 numbers,
> across all groups. For F-1 racing, the goal is to
> find the champion team that has the largest
> combination of the above 8 numbers.
>
> Please correct me if I am wrong.
>
> Sincerely,
> * kenji
>
> Doug wrote:
>
> > Ahoy (Team) Mates!
> >
> > Here at last is Ch. 4 on actually forming "great" teams.
> > If you'vedigested the earlier chapters, you'll plunge
> > right in, or have your students make their own teams
> > after you've put them in "affinity groups". If you're
> > still leery of cognitive modes you can form teams by
> > "quick-and-dirty" sorting on the MBTI letters, a section
> > near the end of the chapter.
> >
> > * D *

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