A Mathematical Way to Rank Your Offers of Admission?

[HyacinthMacaw]

Hey folks,

I've been trying to develop a way to rank offers of admission that incorporates weights for different criteria. Important criteria might be research fit and financial aid, while less important criteria might be the attractiveness of the campus, nightlife, etc. I've attached a method below that I've just hammered out, but I don't have a quantitative background and welcome comments and suggestions.

What first occurred to me is that we can't simply add the ranks of each school for each criterion; this assumes that each criterion is weighted equally. What also occurred to me is that the intervals between the criterion ranks may not be equal. For instance, research fit may be the most important criterion, followed by financial aid and then nightlife, but the interval between research fit and financial aid may be much smaller than the interval between financial aid and nightlife.

I think the method I outline here solves these problems, but I doubt I've explained it coherently. It involves summing the criterion ranks and distributing shares of the rank sum for each criterion. So if I were ranking three criteria, the rank sum would be 1+2+3=6. If my three criteria were research fit, financial aid, and nightlife, I would ask myself, "How much do these criteria account for my decision?" Let's say that research fit accounts for 50% of your decision, financial aid accounts for 40%, and nightlife accounts for 10%. So then the share of the rank sum for research fit would be 50% of 6 = 3; the share for financial aid would be 40% of 6 = 2.4; and the share for nightlife would be 10% of 6 = 0.6.

Then all we have to do is multiply these weights by the rank of each school for each criterion. Highest ranks will have the highest number. If we are deciding between 2 schools, A and B, and School B has the best research fit, its raw score will be 2, but its weighted score will be the raw score multiplied by the weight for research fit, which is 3. So 2 x 3 = 6. This is the weighted score of School B for research fit. Likewise, School A will have a raw score of 1 and a weighted score of 1 x 3 = 3.

In this manner, schools earn higher scores for having high rankings on important criteria. And schools will be penalized less harshly for low rankings on less important criteria.

Add the weighted criterion scores to obtain a total weighted score. The school with the highest total weighted score may be the best match.

Comments/suggestions are definitely appreciated, especially if I'm violating some mathematical principle that renders all this work moot. Thanks, and all the best to everyone!

And P.S.: I hope it's clear I don't want to be presumptuous--I don't have any offers to weigh would be lucky to receive even one. This was just a fun exercise while waiting to hear back from admissions committees.

[newms]

I think that's a good model you have there. I would personally consider location as a factor as well - which would comprise things like the weather, how easy/affordable will it be to visit family, big city vs small town. I would also factor in the reputation of the programs as well. Your maths look good - here's hoping you get multiple offers and a chance to use your model!

[was1984]

This is why I could never be a social scientist. Arbitrarily assigning values to things gives me the heebie-jeebies.

[HyacinthMacaw]

I think that's a good model you have there. I would personally consider location as a factor as well - which would comprise things like the weather, how easy/affordable will it be to visit family, big city vs small town. I would also factor in the reputation of the programs as well. Your maths look good - here's hoping you get multiple offers and a chance to use your model!

Thanks! I don't think there's any limit to the number of criteria you can use. The examples I gave were just for simplicity's sake. Most likely people weigh half a dozen or more factors in their decision (factors that are probably not all equally important).

Come to think of it, this ranking system could work for any comparison where decision criteria are not equally weighted. You could shop for a car, a house, etc. If I knew web design, I would try to create a website that does all the calculations--users would just plug in criteria and ranks and then judge how important the criteria are to them.

Again, all the best to everyone!

[fuzzylogician]

This is why I could never be a social scientist. Arbitrarily assigning values to things gives me the heebie-jeebies.

Well, ultimately that *is* how you decide what school to attend. There are different factors that enter into the decision, different people care about them to varying degrees, and even if you don't sit down and write an equation with weights and ranks, in the end considering all the options and coming up with the winner amounts to just that. (I'm also willing to bet that there are more people out there than will admit who actually had weighted criteria and came up with a full-fledged formula for ranking schools and offers..).

OP: this looks like a useful tool, good luck with ti!

[was1984]

Well, ultimately that *is* how you decide what school to attend. There are different factors that enter into the decision, different people care about them to varying degrees, and even if you don't sit down and write an equation with weights and ranks, in the end considering all the options and coming up with the winner amounts to just that. (I'm also willing to bet that there are more people out there than will admit who actually had weighted criteria and came up with a full-fledged formula for ranking schools and offers..).

OP: this looks like a useful tool, good luck with ti!

Oh I know that's how we do things, and I actually have little difficulty making decisions in general, but it's just the qualitative->quantitative conversion that I've always found difficult. More than anything I'm just intrigued by people who easily make that conversion, which was why I made the comment.

[BlueRose]

I remember doing something like that for undergrad.

Might I suggest using an absolute rank instead of relative? (You know...rate it from 1-5, or whatever). This will show the real magnitude of the differences between schools.

For example, suppose I have offers from A, B, and C. (Yeah, I wish. But never mind.) And I have location as one of my categories. Maybe A and B are in pretty good locations, not my absolute favorites, but I'd be happy to live there. I would give them both 4 out of 5. Maybe C is in a horrendous location, in the cold, snowy butt end of nowhere, and a five minute drive for my least favorite relative. I would give it a 1 out of 5. Simply rating them 1, 2, 3 wouldn't capture that.

But I suspect that my gut is going to make the decision, and then I will get busy on stuff like this to rationalize it.

[fuzzylogician]

But I suspect that my gut is going to make the decision, and then I will get busy on stuff like this to rationalize it.

I actually find that these kinds of tools are helpful precisely for that reason. You enter and rank some criteria, the machine spits out an automated answer, and your gut either goes 'YAY' or 'Oh..'; and right there you have your answer about that specific option. I usually end up playing with the rankings to get a specific option that makes me happy, and I know both that the decision is made and how 'rational' it is, given my initial stated preferences.

[sydney146]

I totally did this for undergrad. I went a little over the top though. I had 23 categories that I had ranked in order of importance, then ranked my three top schools 1, 2, 3 in each category. I multiplied the category weight by the rank and normalized by the total number of weighted points (Sum i from 1-23, 275 in my case) and then took the sum of the scores. I went to the school that won using this method.

Ex:

A B C

Cost 2 3 1

Campus 2 1 3

Research 1 2 3

It worked out pretty well in the end- I love my university.

[Vacuum]

this confirms yet again that I hate math. I'm gonna stick with my pro and con list hahaha

Edited February 18, 2011 by Vacuum

[firefly28]

I'm currently constructing my own spreadsheet to evaluate the schools that have accepted me.

I'm going to include:

Stipend

Prestige of the financial award

Number of faculty with common research interests

Methodological strength of the training

Rapport with faculty (this will be entered after I visit the schools)

Transportation around campus (I don't drive)

Church community

Browncoat community

Haven't quite figured out how I will weigh each variable.

Edited February 18, 2011 by firefly28

[Moxie42]

Browncoat community

I like that this went into your ranking system for your future!!!

I think two important things to include in a ranking such as this are happiness of current grad students and how hands on/off the PI is. The second one may be more directed toward the sciences, or any program where research is done.

Edited February 19, 2011 by Moxie42

[HyacinthMacaw]

I totally did this for undergrad. I went a little over the top though. I had 23 categories that I had ranked in order of importance, then ranked my three top schools 1, 2, 3 in each category. I multiplied the category weight by the rank and normalized by the total number of weighted points (Sum i from 1-23, 275 in my case) and then took the sum of the scores. I went to the school that won using this method.

Ex:

A B C

Cost 2 3 1

Campus 2 1 3

Research 1 2 3

It worked out pretty well in the end- I love my university.

Wow, that's awesome! Glad it worked out for you!

[kotov]

NERDS! Haha, kidding. I have my own spreadsheets for this kind of stuff (mostly so that I don't have to keep explaining everything to my mother due to her sub-par internet skills). But as far as actually evaluating the decisions for my sake, I guess I'm just kind of...more intuitive and less mathematical about it? Though cost of living and amount of funding I get is certainly an object for me.

[HyacinthMacaw]

If the intervals between the school ranks are not equal (e.g., School A has better funding that Schools B and C, but B is not much better than C), it's conceivable that you can run the same operations for school rank as well. That is, obtain a rank sum for n number of schools, distribute shares of the rank sum for each school, and then multiply the share of the rank sum by the weighted criterion score.

So if I were comparing 3 schools (rank sum of 1+2+3=6), and School A had the best funding but B and C were not far apart, then I might allocate shares of the rank sum like this: A=3.5, B=1.5, C=1.0. These are the adjusted raw criterion scores, i.e. weighted school ranks. Then I would multiply these by the share of the rank sum for that criterion. This is the germane score, the one to record based on weights assigned to that particular school for that particular criterion.

Not too calculation-intensive, I hope. This wrinkle does seem to capture a reality that was originally ignored--intervals between school ranks may not be equal.

I think. All these calculations are starting to get to my head!

Thanks, and all the best!

[ZeeMore21]

If the intervals between the school ranks are not equal (e.g., School A has better funding that Schools B and C, but B is not much better than C), it's conceivable that you can run the same operations for school rank as well. That is, obtain a rank sum for n number of schools, distribute shares of the rank sum for each school, and then multiply the share of the rank sum by the weighted criterion score.

So if I were comparing 3 schools (rank sum of 1+2+3=6), and School A had the best funding but B and C were not far apart, then I might allocate shares of the rank sum like this: A=3.5, B=1.5, C=1.0. These are the adjusted raw criterion scores, i.e. weighted school ranks. Then I would multiply these by the share of the rank sum for that criterion. This is the germane score, the one to record based on weights assigned to that particular school for that particular criterion.

Not too calculation-intensive, I hope. This wrinkle does seem to capture a reality that was originally ignored--intervals between school ranks may not be equal.

I think. All these calculations are starting to get to my head!

Thanks, and all the best!

This is too much math for me! Hah. I think I am just going to go with my gut feeling as far as my school choice is concerned.

Edited February 20, 2011 by ZeeMore21

[Phenom!]

Hey folks,

I've been trying to develop a way to rank offers of admission that incorporates weights for different criteria. Important criteria might be research fit and financial aid, while less important criteria might be the attractiveness of the campus, nightlife, etc. I've attached a method below that I've just hammered out, but I don't have a quantitative background and welcome comments and suggestions.

What first occurred to me is that we can't simply add the ranks of each school for each criterion; this assumes that each criterion is weighted equally. What also occurred to me is that the intervals between the criterion ranks may not be equal. For instance, research fit may be the most important criterion, followed by financial aid and then nightlife, but the interval between research fit and financial aid may be much smaller than the interval between financial aid and nightlife.

I think the method I outline here solves these problems, but I doubt I've explained it coherently. It involves summing the criterion ranks and distributing shares of the rank sum for each criterion. So if I were ranking three criteria, the rank sum would be 1+2+3=6. If my three criteria were research fit, financial aid, and nightlife, I would ask myself, "How much do these criteria account for my decision?" Let's say that research fit accounts for 50% of your decision, financial aid accounts for 40%, and nightlife accounts for 10%. So then the share of the rank sum for research fit would be 50% of 6 = 3; the share for financial aid would be 40% of 6 = 2.4; and the share for nightlife would be 10% of 6 = 0.6.

Not a big fan of this kind of thing. it's more after-the-fact rationalization than genuinely illuminating.

Also, "rank sum" seems entirely unnecessary. Choose an arbitrary number, say, 10, and then the weighted scores of each of the schools will be proportionately identical, since you're ultimately multiplying the "rank sum" by the arbitrary assessment of relative importance that you've made (i.e. your percentages). Think about it---the rank sum is gotten by summing 1...n, where n is the number of criteria; but the sum obviously doesn't carry over any information about the order in which you've ranked the criteria. That column serves only as a reminder that when you assess the relative importance of each criteria, your numbers should reflect those rankings; but actually calculating that sum is completely unnecessary (and the fact that you've made it a step of the process, and that it changes with the number of criteria, seems to indicate that it's relevant when it's not; though I imagine you might respond that the bigger number makes it easier to split more criteria, while still being able to cope with "rounder numbers," but this is something that an excel spreadsheet would best do in any case.)

[Kathiza]

Browncoat community

What does this mean? I googled it and found something about Nazis and hope that's NOT what you were talking about

[jergensultrahealing]

The spreadsheet looks good. I think the only thing I would add is that after all the math and analysis are done and you end up with what appears to be a clear "top" choice, if it doesn't jive with what your gut feeling says, I would be inclined to roll with my gut feeling nonetheless.

I guess that's pretty obvious. Sometimes a simple, intuitive gut feeling can be more meaningful and decisive than sophisticated and thoughtful models.

[firefly28]

What does this mean? I googled it and found something about Nazis and hope that's NOT what you were talking about

Haha no, that'd be Brownshirt community

Browncoats are fans of Firefly and the movie followup, Serenity. Check out the following:

www.fireflyfans.net

www.serenityfirefly.com

And, watch Firefly when it runs on Discovery Science starting March 6, at 8:00 EST. It's only the greatest show ever.

[Kathiza]

I found this series on our server, so I'll watch it when I have time. Thanks for explaining!

[firefly28]

Be sure to post if you like it--I've been looking to convert someone for some time now.

And then if you like it, 'like' this facebook group:

http://www.facebook.com/HelpNathanBuyFF#!/HelpNathanBuyFF

In news relevant to the original thread topic, I think that I will include 'niceness of university staff and faculty' as a variable. There's one university that really stands out in terms of how friendly it's been so far, and that's really going to weigh in its favor.