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For me to understand how it works, I need excel

Excellent....
Now if we use triangles, we are limiting the solution to the number 3
And the beauty of the algorithm is, it can be ANY NUMBER of parameters.
Following the rental example, the problem could be a building with n flats, and m candidates.
Each flat has plus and minus features and we need to collect say x per month. The x is the total rent of all flats.
That is why I think we need to come up with design approach first.

Do you agree with this logic....
 
Hi @deb,

I just read this post of yours so let me try! :)

Edit: If is just about changing the number of triangles in a triangle, that could be tried upon but what is really is that it more seems to me an optimization problem then plotting triangles.
 
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The increase of the number of triangle is not to cater for more than 3, it is to improve on the accuracy of the calculation. The article picked 3 to demo the algorithm. If you go to the calculator, you can see what I mean.

This is how I understand it so far. Correction is greatly appreciated.

If we can come up with an "excel" approach may be we can pin it down......

Remember; I posted it here so we can get to the guts of this very important algorithm. In my view!!
 
What i observed from an excel's view point is that it will be a triangle but each vertex of it will be cut larger number of time. So how many times would u like to have them??
 
Since we are attempting to develop the "general" excel model, this will be a parameter that the user will define.
and since we can use the site calculator to compare our results with the calculator; let us start work with the given example of 3 tenants and three rooms and total rent of 3000.
If you have the design worked in your mind, may be I can do some ground work to help build that model..

I am so excited about this project, and I am glad that I have your attension
 
Hi arishy,

Kindly give me some some, just few hrs to outline and then i will revert, mean while u can focus on how you will divide the amount of 3000. Thanks
 
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Hi ,

Just my two cents worth ; has anyone read the paper and understood what the model is , and what is the mathematical basis ?

Just because the NY Times has illustrated the subject using triangles does not mean it can be simulated using charts !

The calculation is an iterative and also interactive process which gradually narrows down the values till they converge to an acceptable solution ; this iteration is the heart of the calculator , and it has nothing to do with triangles or charts.

The modelling can be done using Excel provided someone takes the trouble to understand the maths behind it.

Narayan
 
Narayank991,

You hit the nail, I read the article and knew that the triangle was a way to demo the concept for the average reader.
(see my responses).

Let us move forward, and yes it is an interactive process and the final result is actually a SELECTED result BY THE USER. ( by that I mean, the user is offered a price and the user must select it, to go on)
That is why it will be acceptable ( somebody in NT commented by suggesting 'just do a bid'....)

Now, please refer to the post heading:

The million "Euro" question; is it "excelable"???? I just coined the word !!!!

The interactive process suggests a No response

I will stop here and wait eagerly for your response
 
Hi Arishy ,

My comment was more directed to the fact that after Deb's post triangles were being discussed , when the issue was something else altogether.

It can certainly be done in Excel , provided , and this is a big IF , someone takes the trouble to go through the mathematics behind it ; this cannot be done on the basis on the article in the NY Times ; it has to be done by going through Su's paper on the subject here :

http://www.math.hmc.edu/~su/papers.dir/rent.pdf

I'd like to correct you on one point , and I believe this is a very crucial point ; the point is not the interactivity , not that the user is being offered a selection ; the point is the values which are offered for selection are precisely calculated ; if you go through the online calculator , you will see that the process is iterative , and users will be asked to choose multiple number of times , and it is this iterative process which ensures that the final choices of every user is fair and envy-free.

Narayan
 
Narayan,

The Algorithm......The holy grail.......

You know, I sometimes use excel to help me out with understanding a concept I cannot visualize.

We have two alternatives:

1. A mathematician that read some abstract material and hand us the holy grail or
2. Use a common sense approach to build possible scenarios

I was hoping for the second ( unprofessional approach). And that will need some planning.....

I will end this comment with a famous quote:

<< Common sense is NOT that common >>
 
Dear @NARAYANK991 & @arishy

I think i already mentioned and commented that the mathematical background of how researcher has divided the Rs. 3000 is beyond the level of my intellect, at-least if some one does't explains it to me explicitly each single step. What i can do is to make a graph with excel where you have increasing or deceasing number of triangles to imitate the original online calculator.

Besides me too have also searched the for understanding Sperner's Lema but as i already said that the mathematics is just....

That worksheet, hopefully, i will upload very soon.
 
Reverse Engineering.....Wow ....what a good idea...
I will start this .....( collecting the row data for your chart).

P.S. It seems there are "few" calculators not one.....I will pick one and see how it goes.
 
@arishy

I just visited the page and speaking truly, this does not seems tobe related to these triangles, rather it appeared like a weighted average sought of thing a where a person who enjoys more pays more, what those triangles were saying was none will be in loss so that is the diff i found:)
 
Hi All,

Watching this thread from morning and going through the links and all of your comments I would like to add few of my observations which you all might have noticed.

1. It's a triangle because there are three rooms and three persons, if it would have been 4 than it should have been a quadrilateral and so on as the choices increases the shape of the polygon will change to pentagon, hexagon and so on...
2. Each vertices on the BIG triangle is a person taking a room and has to pay full $3000.
3. Each edge of main triangle is a room. So edge AB lets say is Room 1 and it can be taken by A or B but not C as per original theorem, but the rule is not followed here.
4. As the triangle increases the price of the room is equally divided. So if you divide the main triangle by adding one more triangle inside, each edge will be divided into two half so price will come down to $1500 and so on...
5. The distribution of price is purely based on some assumptions and no scientific methods, such as no. of doors, accessibility to bathrooms and other features shared by room.


That's my thought.

Correct me if my observations are wrong somewhere.

Regards,
 
I had the same feeling too....But I forward it for the following reason:
There must be some "practical" parameter(s) other than RANDOM or pure MATHEMATICAL treatment ( the holy grail ) approach that the model has to follow.

For me to choose a price to pay I need to know what I am getting for it. There must be some tangibles.
The site I mentioned did a good job on that. That was my reason.

Back to our issue, there could be an assumption that each person has his own tangibles and they are invisible to the model BUT they are the deciding factor for accepting a certain price.....Wow I hope you understand what I am trying to say !!!
 
See below image,

Capture.JPG

It clearly states that the prices are already given based on some features shared by room. Now that part is not shared here.

Regards,
 
already given based on some features shared by room
Click to expand...
The only given :
1- 3 Persons
2- One price
3- 3 different rooms (no quantitative figures) , this part is NOT figured in the model.

Did I miss something ???
 
Hi All ,

First , can we please stop using the word triangles !

This is the problem with newspapers ; in their bid to grab the reader's attention , they can dumb down a topic , where the article bears no relation to the topic.

The online calculator does not anywhere show triangles ; the triangles are just a way of visualization , but having the triangles is in no way necessary or even helpful to building the same calculator in Excel.

What the online calculator has is as follows :

1. An overall amount , which is to be 'fairly' shared between a specified number of people ; note the word 'fairly' ; this is not the same as equally.

2. The calculator starts off with an initial distribution of the overall amount ; how this is arrived at needs to be understood.

3. The user is asked to select which of the amounts they would like to choose for themselves.

4. Based on the user's selection , another distribution of the overall amount is arrived at , which again needs to be understood.

Steps 3 and 4 are repeated as many number of times as are required to arrive at a distribution where every user has had at least one chance at selecting an amount of their choice ; some users may get many chances.

The interactivity is easily possible using macros ; how do we get the distributions , since there is a mathematical basis to this ?

I have not seen any resource which explains the lemma with specific reference to the rent sharing problem ; if anyone can share such a resource , it will be nice.

Narayan
 
partition the rent so that each person will prefer a
di erent room?"
Click to expand...

From the article, I think the key to the problem is that the algorithm is used to reach a DIFFERENT choice for each person
 
Here is an example, if you agree you are on your way to succeed, (MY PROBLEM is that I disagree)
<<
Let’s see how this works for two players. Let’s say that I divided up the cake into two
parts that I believe to be equal. You disagree: you think one part has 60% (which you
take). Now, appealing to your better nature, I suggest that you might donate some of your
“excess” back to me. Let’s say I convince you to give me 5%, leaving you with 55% of the
cake.
Now you can’t just cut a sliver and give it to me - I might not have assigned any value to
it at all. But here’s a trick. You divide your piece into 12 equal parts. Since you believe the
piece is worth 60% of the cake, you believe that each piece is worth 5%, and you’re willing
to give one of them to me. Now I believe that the piece was worth 50% of the cake, so there
is at least one piece that I think is worth 50%/12.
I take that piece, giving me a net share of

1/2 + 1/24 <---- this is where I disagree

, and you retain 55% of the cake by your estimate. And lo and behold, we both have more than half the cake.


The moral of the story, and a recurring theme in cake cutting, is that disagreements over
value make the problem easier, not difficult.

The reference is attached
 

Attachments

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