Hi all, 

I am trying to build a statistical model for improvements to my 
building. My goal is to look at suggestions from a few residents and 
then pick the one that is most popular - statistically speaking. 


Think of the problem as a filtering or a funnelling system, there a lot 
of ideas at the top and then you keep on filtering till you reach a 
winning idea. 


The process can be broken down in the following steps: 


Step 1: Run a survey with 20 residents, asking them to suggest 1 
improvement to the  building. I am expecting 1-20 unique improvement 
ideas from this survey. 


Step 2: Feed the ideas from Step 1 to another set of 20 residents, and 
have them pick the top 3 that they like. Say Improvement # 7, 8 & 9 
were picked the most. 


Step 3: Feed the ideas from Step 2 to another set of 20 residents, and 
have then pick the top 1 improvement. Say improvement # 7 was picked 
the most. That would be our winner improvement. 


If there is a tie, in any of these steps, I can either re-run that 
entire step OR re-run that step with just the 2 tie results till I can 
find the winning improvement idea. So, as you can see the number of 
steps can grow quite long. 


How can I build this model correctly? Is this problem similar to any 
other statistical problem? I have the flexibility to change the number 
of residents or the logic to pick results or the number of solicited 
improvements. But, I have some ground rules & assumptions that are 
outlined below: 


1. The responders at any step can never be more than 20 but they can be 
less. 
2. The winning improvement must be reached sometime within 6 steps. 
3. No resident can contribute twice to the survey results. 
4. There are infinitely large number of residents in the community. 


One more concern: Is it good enough to just pick the most frequently 
picked improvements at every step -- the MODE -- I mean it sounds
logical when I say that #7, 8 & 9 were picked the most in Step 2, and
therefore they
go to the Step 3 for further review, but I'm wondering if there is a 
more statistical approach to pick the winners at each step. 

Thanks, 
-Anil

Sounds like a good system.  Who is paying?  Is it your building?  If
it is, I would drop from the list any suggestions in the first round
that you don't agree with or that are too expensive.
And I think that you should be careful not to raise hopes too high for
those participating, telling that it is all a theoretical exercise.

Anil,

The problem I see is that if your population is infinitely large, a
maximum sample size of 20 would not give a good representation of the
most desired improvement for the building.  Is there any flexibility
in your sample size or can you redefine your population?

Herkdrvr