At 10:36 AM 9/16/2014, Stephen Kent wrote:
I like Dave's suggestion i.e., reduce the per-company NOMcom appointment
limit to 1 from 2.
It's not a perfect solution, but it's clear, simple to implement, and
the intent is obvious.
Steve
As I said, I did take a look at that approach, and it is *better* than the
current process for some value of *better". But it still has the
characteristic that by overloading the volunteer pool, a company can pretty
much guarantee its representation on the Nomcom.
The formula is basically "P = 1-(1-n)^10" where P is the probability of
having a member and "n" is the proportion the company has of the volunteer
pool. E.g. A company with 15% of the volunteer pool has an 80% chance of
having a member of the nomcom.
Turning the formula around to how many volunteers you need to get a specific
result, you get "n = 1-ROOT (1-P, 10)"
So to have a 95% chance of having a member, you need about a 26% share of the
Nomcom volunteer pool.
If you cap the share of the volunteer pool (by doing the two stage selection
process I mentioned or something similar), you can set the numbers any way you
want. For example, if you cap the share at 10%, and you're selecting at max
one member per company, a company has about a 65% chance of having a member.
If you use the same 10% cap on the pool, but allow a max of two nomcom members,
a company has about a 33% chance of no member, 33% chance of 1 and 33% chance
of two.
I'm not sure what the right numbers are, but I would like to set things up so
that overloading the nomcom pool is no longer a viable strategy (or at least
has a lower payoff).
Changing the cap to 1 member will reduce, but not eliminate, over
representation of large companies on the Nomcom. If the change is made, then
year to year 2-4 companies will provide about 30% (guesstimate based on what I
remember of past volunteer pools) of the nomcom members; down from what I would
guess is currently close to 50%. The question is whether that number is still
too high or not?
Later, Mike
Note: This is all binomial distribution probability stuff. In excel, the
probability pulling exactly N black balls (nomcom positions) out of Y pulls (10
nomcom slots) given a P percentage of black balls (nomcom volunteers) in the
pool is =BINOMDIST (N, Y, P, FALSE). When you're doing Y pulls, and you cap
successes at N, then the result is the sum of N to Y of that function (e.g. the
probability of pulling at least 2 black balls is the sum of the probabilities
of pulling 2, 3, 4...10 black balls).
I used that to play around with various scenarios.
For instance, assume that 4 companies collectively have a 50% share of the
volunteer pool and that each individual company is capped at 1 member. The
numbers work out to about an 82% chance the companies will share 4 members, a
12% chance of 3, 5% of 2 and 1% of 1. That goes to looking at the nomcom
representation on a longer term basis than year to year. If the cap is 2 (as
it has been in years past), that gives you a 27% chance of 0-3members, a 20%
chance of 4, a 25% chance of 5, a 20% chance of 6, 12% chance of 7 and a 5.5%
chance of 8.