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Math Help - Best city choice based on non-normalized demographic parameters

  1. #1
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    Best city choice based on non-normalized demographic parameters

    This is my first time posting and I really don't know if this is the best place for this question. It's worded like something you would read in a text book but I made it up as an example. My ambition is to solve the general case given a large variety of real data sets and make a web based application users can get value out of. (The data below is from the US gov census website.)

    Suppose I have data on 3 cities, Ft. Collins, CO, Denver, CO and Santa Barbara, CA and I want to live in the best city based on my preferences for these 5 parameters:
    1. Persons reporting 2 or more races
    2. Bachelor's degree or higher
    3. Mean travel time to work
    4. Persons per square mile
    5. Home ownership rate


    Parameters 1, 2, and 4 I'd like to maximize. Parameters 3 and 5 I'd like to minimize. All parameters have the same degree of preference.


    Ft. Collins
    1. 2.5%
    2. 48.4%
    3. 18.4 minutes
    4. 2549.5
    5. 57%


    Denver
    1. 3.7%
    2. 34.5%
    3. 24.5 minutes
    4. 3616.8
    5. 52.5


    Santa Barbara
    1. 3.8%
    2. 39.6%
    3. 16.7 minutes
    4. 4864.3
    5. 42%
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  2. #2
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    Quote Originally Posted by kstus View Post
    This is my first time posting and I really don't know if this is the best place for this question. It's worded like something you would read in a text book but I made it up as an example. My ambition is to solve the general case given a large variety of real data sets and make a web based application users can get value out of. (The data below is from the US gov census website.)

    Suppose I have data on 3 cities, Ft. Collins, CO, Denver, CO and Santa Barbara, CA and I want to live in the best city based on my preferences for these 5 parameters:
    1. Persons reporting 2 or more races
    2. Bachelor's degree or higher
    3. Mean travel time to work
    4. Persons per square mile
    5. Home ownership rate


    Parameters 1, 2, and 4 I'd like to maximize. Parameters 3 and 5 I'd like to minimize. All parameters have the same degree of preference.
    Then the best thing to do is to MULTIPLY the parameters you want to maximize and divide by the parameters you want to minimize. That keeps the "units" from conficting. That is: (1)(2)(4)/(3)(5). The city that gives the largest value for that is the "best". but why would you want to maximize "population density" (4) and minimize "home ownership"? I would think it would be the other way around!



    Ft. Collins
    1. 2.5%
    2. 48.4%
    3. 18.4 minutes
    4. 2549.5
    5. 57%
    [FONT=Helvetica]
    [/FONT

    Denver
    1. 3.7%
    2. 34.5%
    3. 24.5 minutes
    4. 3616.8
    5. 52.5
    [FONT=Helvetica]
    [/FONT

    Santa Barbara
    1. 3.8%
    2. 39.6%
    3. 16.7 minutes
    4. 4864.3
    5. 42%
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by kstus View Post
    This is my first time posting and I really don't know if this is the best place for this question. It's worded like something you would read in a text book but I made it up as an example. My ambition is to solve the general case given a large variety of real data sets and make a web based application users can get value out of. (The data below is from the US gov census website.)

    Suppose I have data on 3 cities, Ft. Collins, CO, Denver, CO and Santa Barbara, CA and I want to live in the best city based on my preferences for these 5 parameters:
    1. Persons reporting 2 or more races
    2. Bachelor's degree or higher
    3. Mean travel time to work
    4. Persons per square mile
    5. Home ownership rate


    Parameters 1, 2, and 4 I'd like to maximize. Parameters 3 and 5 I'd like to minimize. All parameters have the same degree of preference.


    Ft. Collins
    1. 2.5%
    2. 48.4%
    3. 18.4 minutes
    4. 2549.5
    5. 57%


    Denver
    1. 3.7%
    2. 34.5%
    3. 24.5 minutes
    4. 3616.8
    5. 52.5


    Santa Barbara
    1. 3.8%
    2. 39.6%
    3. 16.7 minutes
    4. 4864.3
    5. 42%

    You cannot simultaneously maximise (minimise) more than one thing, so in practice you must form a single composite objective to optimise. HallsofIvy suggests one way of doing this, there are many more and which you choose depends how you rate the importance of the factors.

    CB
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  4. #4
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    Thanks for the reply. I google (and Scholar Google) for HallsofIvy and I didn't see anything. Could you elaborate on the reference? I don't even know what this sort of problem is called.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by kstus View Post
    Thanks for the reply. I google (and Scholar Google) for HallsofIvy and I didn't see anything. Could you elaborate on the reference? I don't even know what this sort of problem is called.
    Post #2 in this thread.

    CB
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  6. #6
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    Oh, Ok, I didn't see that post. Completely overlooked it.

    So I think the biggest problem with the above suggestions is that one parameter can dominate the solution. In the example above the persons per square mile dictates the solution proposed by HallsofIvy. That's not desirable.

    I picked these parameters to illustrate the problem of mixing %, minutes and persons per area and also big numbers with small numbers.

    Any other suggestions? I've tried normalizing the parameters which aren't given in % but this still leads to domination of one parameter.
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