Mike, while I completely agree, I am also thinking about how much bigger we would need to make the pool to overcome the number of volunteers from that company, i.e., to make their fraction of the volunteers small enough relative to the total to significantly reduce the chances of their ending up with two Nomcom members.
Here's the table. If you have 10% of the pool, you have a 65%
chance of having at least 1 member, and a 26.4% chance of having
2. That's a pool of 410 people given 41 volunteers from a single
group.
Given 41 volunteers from a single group, you'd have to have something like 612 volunteers to get below a 50% chance of 1 member or more. (e.g. about 6.7% of the pool).
Note, the values in the table don't change based on total
volunteers, only on proportion of the volunteer pool. Making the
pool larger and keeping the proportions of the components the same
will not materially change the results.
The current model is biased to select most of the Nomcom from
larger organizations. You'd probably need to move to a 2 stage
model to change the bias.
| Number of Nomcom Members | |||||||||||||
| Percent of Volunteer Pool | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | >= 2 | >=1 |
| 1.0% | 90.4% | 9.1% | 0.4% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.4% | 9.6% |
| 5.0% | 59.9% | 31.5% | 7.5% | 1.0% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 8.6% | 40.1% |
| 10.0% | 34.9% | 38.7% | 19.4% | 5.7% | 1.1% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 26.4% | 65.1% |
| 15.0% | 19.7% | 34.7% | 27.6% | 13.0% | 4.0% | 0.8% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% | 45.6% | 80.3% |
| 20.0% | 10.7% | 26.8% | 30.2% | 20.1% | 8.8% | 2.6% | 0.6% | 0.1% | 0.0% | 0.0% | 0.0% | 62.4% | 89.3% |
| 25.0% | 5.6% | 18.8% | 28.2% | 25.0% | 14.6% | 5.8% | 1.6% | 0.3% | 0.0% | 0.0% | 0.0% | 75.6% | 94.4% |
| 30.0% | 2.8% | 12.1% | 23.3% | 26.7% | 20.0% | 10.3% | 3.7% | 0.9% | 0.1% | 0.0% | 0.0% | 85.1% | 97.2% |
| 35.0% | 1.3% | 7.2% | 17.6% | 25.2% | 23.8% | 15.4% | 6.9% | 2.1% | 0.4% | 0.1% | 0.0% | 91.4% | 98.7% |
