Survey the people of Philadelphia

In order to tell if a zip code in Philadelphia is getting more dangerous maybe we should ask people who live there.

So I created a survey here to ask them here. If you are or know someone living in Philadelphia if you could fill that out it would be great.

The idea is to find areas people think are changing in safety and see this turns out to help predict homicides. If it does this could be used to focus police resource in future to help reduce homicides.





I will release any data that is input as I am not the best person to do analysis on them. People going to the effort to submit a survey deserve to get the most out they possible. I will anonymise any data that does contain personal info before releasing it. There shouldn't be any info like this but I will check through the data in case.

I think ideally such a survey would let user place pins in a map in areas they think are improving/disimproving. Any thoughts on the survey? Or the idea of asking people for their local predictions in general?

Analytics X Prize

There is a competition here to try and predict what proportion of murders in Philadelphia will occur in each of the cities 47 zip codes. Many people who are interested in these sorts of puzzles have started submitting predictions.

So how would you go about predicting the murder proportion in each zip code?
Well if nothing changes in Philadelphia you would expect each zip code to keep exactly the same proportion of murders, well with some random variation you could not predict. So my first guess is a repeat of exactly what happened last year.

But in the real world things do change. Say the population changes if every person had the same chance of being murdered then the proportion of murders in a zip code would change proportionate to the change in population. If this was the case the prediction problem would become to find out what changes in population will take place over the year.



The dataset I am using is here and some errors in it need to be removed. Each dot is a zip code. It looks like number of murders does roughly follow population but it is not nearly an exact match. So changes in population are important but they are far from the only thing we need to predict.

How expensive the house in an area are or the average income or the number of people per house might help indicate the murder rate. Here I am looking at number of (murders/population)*10000.





So it looks to me a bit like areas with crowded houses could be more likely to have murders.






House cost looks like it is not connected to murder rate. This could be because zip code is too rough grained for this to be a good judge. Maybe the average cost of a house in a block would be a better measure of risk. Philadelphia has even been broken down into 60ft squares here



Does household income look like it is related to murder rate?

So if the graph is a random scattering of dots then it looks like the independant variable on the x-axis has no relation to homicide rate the dependant variable on the y-axis. If the dots form a line (well not just a line but that is another story) then the homicide rate may be related to that independant variable. It really is not this simple but that's the basics.



As Siah pointed out here young black males seem to be murdered out of proportion. The graph above does seem to suggest that predicting changes in ethnicity of a zip code may improve predictions. Age is another important variable and I do not have data on that so that might be the next thing to get.

There are interesting posts already on this puzzle
"Evaluating Spatial Predictions" and "Second Pass at Analytics X Prize" and "Homicides as non homogeneous poisson processes" are very informative.

Dublin pubs and the El Farol Bar problem

I was in town last night and i noticed how empty the superpubs were. these are the giant warehouse like pubs that need to be packed all the time to pay for the giant rents they have.

They also need to be full to make it look like they are not just giant warehouses. This is a version of the El Farol Bar problem. The game theory is this

* If less than X% of the population go to the bar, It will be too empty and they'll all have a worse time than if they stayed at home.
* If more than X% of the population go to the bar, they'll all have a better time than if they stayed at home.

People realise the pubs will be empty so no one goes. It is a positive feedback problem. Which means these big pubs are in big trouble.

Human Nutrient Needs

What nutrients does a person need per day?
I am not a dietician or indeed sober so don't take this as actual advice. But what does ten minutes googling give as a list of the needed nutrients?
This is item 1 of the list of things to do for a modern version of Stigler's diet. Wikipedia the universal source of all truth (TM) italic has an article on this here.

It gives the RDA for an average 25-year old male (for ones that use IU which appears to be nonsense so I have taken some figures from here and here)
all figures are in µg

param RDA:=
Vitamin_A 900
Vitamin_C  90000
Vitamin_D  5
Vitamin_K   120
Vitamin_B6   1300
Vitamin_E  15000
Biotin    30
Calcium    1000000
Chloride    2300000
Chromium    35
Choline   550000
Copper  900
Cyanocobalamin  2.4
Fluoride    4000
Folate  400
Iodine  150
Iron   8000
Magsium  400000
Mangase    2300
Molybdenum  45
Niacin 16000
Nickel 1000
Pantothenic_acid    5000
Phosphorus  700000
Potassium    4700000
Riboflavin   1300
Selenium  55
Sodium   1500000
Thiamin 1200
Zinc 11000
;

And the upper limit as

param UL:=
Vitamin_A 3000
Vitamin_C  2000000
Vitamin_D  50
Vitamin_B6   100000
Vitamin_E  1000000
Boron 20000
Calcium  2500000
Chloride 3600000
Choline 3500000
Copper  10000
Fluoride  10000
Folate 1000
Iodine   1100
Iron 45000
Magsium 350000
Mangase 11000
Molybdenum 2000
Niacin 35000
Nickel 1000
Phosphorus  4000000
Selenium  400
Sodium   2300000
Zinc 40000
;

The figures we are interested in are RDA's which must be met and Tolerable upper intake levels which cannot be exceded.
Macro nutrients are in grams

param Macro:
Waterb  3700
Carbohydrates  130
Proteinc  56
Fiber  38
Linoleic 17
alpha-Linolenic 1.6 
end;

Also some nutrients must be minimised Cholesterol, Trans fatty acids, Saturated fatty acids. These will have to be aims of a optimiser for diets.
These are a bit more difficult to deal with so I will ignore them for the moment.
Cholesterol As low as possible
Trans fatty acids As low as possible
Saturated fatty acids As low as possible

Also two types of macro nutrients must be a % of calories.
Added sugar No more than 25% of calories
Fat 20–35% of calories

I am going to guess a 25 year old male needs 2500 calories until I am corrected.
So we have a first approximation of what nutrients people need.

So next up is getting a price and nutrient contents for loads of different foods.

The Diet Problem

What is the cheapest way to feed yourself? This is not a minor issue our diets and health could be much better if they were optimised to provide the most needed nutrients at the smallest cost and also to provide the most palatable diet that is as healthy as possible.

Stigler in 1939 worked out a near optimal miminum price needed to supply a person with the nutrients they need for a year. The diet consists of five not very pleasant foods so is not intended to be realistic dietry advice.

Still given current knowledge of nutrition a list of prices from various supermarkets could you optimise you shopping basket to provide your family with groceries? Here we want to give people the nutrients they need in a form they will actually eat that is healthy and cheap.

We need a list of
1. What nutrients are needed by a person
2. Foods preferences of people.
3. A price list of foods
4. A Linear program to optimize a shopping basket based on these variables.

All of these requirements need some explanation. I think its best if each gets it's own post. So tomorrow I will have a post on what quantities of nutrients people require. If you have any suggestions please comment.

215 is the first Wikipedia dull number

I have always wanted my own constant and now for a short period I have one. Imagine numbers were 'interesting' or 'dull'. The first dull number would be interesting because it was the first dull number so no dull number can exist. So all number are interesting.
Now you would think any interesting number would be notable enough to have its own wikipedia page. The first number without a wikipedia page is 215. This should be notable enough to deserve a wikipedia page. So as long as 215 has no wikipedia page it is dull and thus as the first non notable number it is notable. The paradoxes of wikipedia notability were brought up here.

Counting money across cultures

One great bit in the execrable Inglorious Basterds was where someone noticed that Germans and British people make the sign for three in different ways. I love these cultural comparisons that show how arbitrary much of what we do is. I looked at information from laces here

This is a video showing how money is counted in different countries.


How People Count Cash? - Click here for more free videos

I have heard Japanese people ring out clothes differently to the rest of the world but can find no evidence of this in spite of asking a few of them. Do you know of any other cultural differences?

Matchbox Maths Games

There is a great article here on Matches on India. No really read it.

In fact, 97% of rural households purchase matches on a monthly basis. Matches are a unique product because of their high, constant demand and low price point.Their ubiquitous presence provides fascinating insights into India's rural distribution networks, and offer potential ways to inform and interact with India's relatively untouched market.

The article then suggests using the matchboxes to spread public health messages

What if that space was used to relay information? Imagine the possibilities of spreading new health/educational information or advertising to 97% of rural families on a monthly basis. Simple pictorial designs would pique interest and accommodate India's vast differences in literacy rates and languages. Awareness of important topics such as the installation of chimneys to reduce smoke inhalation or cleaning and covering water containers to prevent stomach ailments could be spread to households across India, and potentially save lives

I would recommend selling the glamor of flushing toilets and chimneys and such rather than nagging in your images. But i do not know enough about rural Indians and their diseases to advise on what health images to provide them. There are some interesting studies on what does kill these people here.

However what if all you put on the boxes was games? Many people have a ludic philosophy of life. You see a love of games in maths nerds in particular. This love of games I believe adds a cognitive richness that aids intellectual development.

There is a great book called "everything bad is good for you". That claims the increase in IQ in recent decades is due to increased complexity in our culture. I have not studied the Flynn effect enough to be sure it is not caused by nutrition or even to be sure it is important. But I will assume it is and that intellectual challenges improve general cognitive abilities. I will go further out on a limb and claim that such improvements in cognitive abilities would aid rural Indians. Never having been a rural Indian this really is a big assumption.

So what intellectual challenges could fit on a matchbox and be read by an illiterate farmer? How about puzzles and games?

There are some face meltingly brilliant match puzzles here(pdf). Other then puzzles there are games like NIM, dots and boxes, chomp and loads of others you can play with matches. I would imagine if a brand of matches has a game on it that keeps the kids from bothering you this would be a popular feature.

So can you think of some way to explain a puzzle or the rules of a game on a matchbox without using text? Do you think it really could be useful to put mathematical games and puzzles on matchboxes?

A work sceduling problem

I saw this problem recently

A city authority is considering placing a toll booth on its new bridge. The beginning
times for the shifts are 8am, noon, 4pm, 8pm, midnight and 4am. A collector
beginning a shift at one of the above times works for the next 8 hours.
The following staffing levels during each of the 24-hour periods have been estimated

Hour.................... Minimum Collectors Needed
8am - Noon.............. . 5
Noon – 4pm ................6
4pm – 8pm .................10
8pm - Midnight........... .7
Midnight – 4am ...........4
4am – 8am .................6

Find the minimum number of collectors that need to be hired to begin the 8 hour shifts
at each of the six times.

A GLPK program to calculate this is

var x1 >= 0, integer;
var x2 >= 0, integer;
var x3 >= 0, integer;
var x4 >= 0, integer;
var x5 >= 0, integer;
var x6 >= 0, integer;
/* objective function */
minimize z: x1+x2+x3+x4+x5+x6;

/* Constraints */
s.t. ctr1:x1 + x6 >= 5;
s.t. ctr2:x1+x2>= 6;
s.t. ctr3:x2+x3>= 10;
s.t. ctr4:x3+x4>= 7;
s.t. ctr5:x4+x5>= 4;
s.t. ctr6:x5+x6>= 6;
data;
end;

The answer is 19 and no one starts working at 8am.
This is a simplified version of the program described here. Not a major revelation or anything but always find these puzzle solving programs cool.

Prediction with game theory

I am going to this talk on Thursday so I am reading the book Predictioneer by Bruce Bueno De Mesquita. He has a ted talk video on his prediction ideas.


The use of game theory in forecasting seems based on the axiom that people are rational. The problem is they are not, here is a list of the different ways they are not. If you know how they are going to be irrational you can alter your models to take this into account. However if you fail to do this you will end up with less accurate models.

In chapter 2 the book claims people are rational and particularly that we are transitive in our preferences. "to be rational.. their preferences must not go in circles. For instance if I like chocolate ice cream better then vanilla and vanilla better then strawberry i presumably like chocolate ice cream better than strawberry." So no rock paper scissors can exist in human preferences.

The problem is they do. There is loads of evidence that people can have intransitive preferences. For example May showed in 1952 that people can have intransitive preferences for wealth, looks and intelligence in a partner. So how can you have a mathematical system modeling the world where one of your axioms is false?

While on the subject of intransitive never play dice with Warren Buffet. There are loads of stories of how he tries to con people with a set of intransitive dice. Edward Thorpe for example. Or Bill Gates as described in Bill Gates Speaks: Insight from the World's Greatest Entrepreneur By Janet Lowe

Buffet once attempted to win a game of dice with Bill Gates using intransitive dice. "Buffet suggested each would choose one dice and discard the other two. They would bet on who would roll the highest number most often. Buffet offered to let Gates pick first. This suggestion instantly aroused Gates curiosity. He asked to examine the dice after which he demanded buffet choose first."

Boy in Balloon, did the balloon have enough lift?

I love this story, it reminds me of the time myself and my dad nearly burned down the house. We made a tinfoil hot air balloon with a gas camping cooker to power it. The cooker was tipped onto the lino and the melting began. It was my mums fault for leaving us alone in the house together. In general I love these homemade balloon stories, like Larry Walters across California.

Could we have told in advance it was a haox? "Few had raised the issue of whether such a balloon could even lift off with a 50-pound kid inside, and then float the way it did"

So how big was the balloon? "Authorities said the silver balloon, 20-feet long and 5-feet high, at times reached 7,000 feet above the ground while adrift. It was found more than 90 minutes later in a field near Colorado Springs."


Then it would have a diameter of 6 meters and a height of 1.5m high. Taking the balloon as a cylinder then according to here would give it a volume of 42.5 cubic meters.



Gross Lift (Helium) = Volume (cubic meters)*1.05kg
So 42.5 * 1.05=44.625 kg lift.

Now that seems just within the bounds of possibility as the kid weights about 20 kilos and the balloon itself should be light. But could the balloon have gotten to a height of 2000 meters? There are all sorts of tables for these I might work it out later

Another site gives "Helium provides about 9.8 newtons of lift per cubic meter, at sea level and room temperature. That's enough to lift 1kg". So 20 kilos would require 20 meters squared to lift it. Same result as before.

Thanks to the best program on Television we know how many balloons it takes to lift a small child.
"It would require such a large number of balloons (3,500) to lift an average four-year-old girl of 44 pounds (20 kg) just a few feet off the ground that there is no way the myth could have happened unintentionally."

Update: Wired have an article here about how people should have realised the balloon was empty. Their estimation of the carrying capacity of the balloon is similar to mine. they point out that the balloon does not move like it has a heavy weight hanging from the bottom of it.

NAMA, how much is 54 billion euro?

Nama, the Irish governemts agency to take on bad loans, is paying 54 billion euro to buy property. How much money is that? There is a great visualisation here about how much is a trillion.

So lets picture Croke Park. Its pitch is 144.5 m x 88m. That is much bigger then a soccer or rugby pitch. A 20 euro note is 133 × 72 milimiters. So to pave Croke Park pitch with 20 euro notes requires. So that is 1087 notes long 1223 wide or 1,329,401 notes are needed to pave croke park pitch in 20 euro notes. So that is roughly 2 layers of 20 euro notes being 54 million and paving it two notes deep. A billion is a thousand million so 54 billion is 1000 times this. So 54 billion is paving Croke Park in 20 euro notes 2000 deep.

So if your looking at the game on Sunday imagine there is a 20,000 euro pile of cash on the pitch that you now owe. That is 54 billion divided among the people who pay tax. So you and the person sitting next to you owe a 2000 deep 20 euro sized chunk of the Croke Park pitch.

A comment vaguely asked how much euro coin is this? "Did you know its also enough Euros placed end to end to reach the moon". According to here a 2 euro coin has
Thickness (mm): 2.20
Weight (g): 8.50

So 27 billion 2 euro coins are needed. So in weight that is 229.5 million kilos.
"The maximum gross mass for a 20 ft (6.1 m) dry cargo container is 30,480 kg" so that is 7540 containers full of 2 euro coins.

How long would the stack be? 2.2 * 27 billion millimeters = 59 400 kilometers. Or enough to go around the earth one and a half times. But less than a fifth the distance to the moon.

Ask the waiter

If you want to know what someone is like ask their waiter. Because as a waiter you are far down the social rung anyone who is just a poseur treats you like dirt. Keith Floyd who died yesterday used to come into an Indian restaurant I worked in. He was much quieter then his media image and a complete gent. As was Liam Neeson BTW. I am not claiming to have known him just that he always treated the waiters well, which I believe is a good sign about someone.

Belinda Carlisle owes me a set of cutlery, she may think I have forgotten but I haven't. She promised she would bring them back and didn't. Try saying "if you cannot trust the singer of the Go-Go's, who can you trust?" to a middle aged Bangladeshi and see if your wages don't get docked.

Apart from an unfortunately forgetful singer I have a long list of who is a complete wanker. I'll post that again.

Prediction Market In Adwords?

Can we predict how much an adword word will cost in the future? I find prediction markets fascinating but have not talked about them for a while. Here is an interesting game for predicting the popularity of words.

If this prediction market can accurately predict what words people will in the future find interesting and will discuss then you could buy up these adwords in advance and watch their market value (well cost in google) rise. So anyone want to buy a futures contract in the word "Cromulent"?

Fair division in googledocs using Ruby

I figured out how to access google docs spreadsheets using Ruby's roo library.

So for the spreadsheet
https://spreadsheets.google.co/ccc?key=0AifEYKk1FmScdDUwcTE1c2c4aFF6Wl93cENkWVF1Smc&hl=en
#you can create a object for this document by

        
oo=Google.new("0AoBJp9mMcWUrdDZUY1diRm5KOTd4ZWtKWUpib2V3ZHc"
,user="stuffsplitter",password="thepassword")  

where user and password are the username and its password for the account that has the document. 0AoBJp9mMcWUrdDZUY1diRm5KOTd4ZWtKWUpib2V3ZHc is the key
no http, no google.com, no key= and no &hl=en at the end. Good thing I am not an idiot who would take hours to figure this last one out...

Then this data is sent off to the GLPK program described ad nauseum previously.
Then using ruby's standard regular expression methods the solution file fair.sol can be easily parsed. This can be easily written to the googles doc using roo.

o2.default_sheet ='Sheet3'
#match fair.sol output file of glpk. 
  if line=~/^\s+\d+ y\[(\d+).(\d+)\]\s+\*\s+(\d+)/
#   2 x[1,1]       *              0             0             1
   if $3=='1'
   o2.set_value(row, col, $1)
   o2.set_value(row, col+1, $2)
   o2.set_value(row, col+2, $3) 

Next thing is to get a web interface for people to add their own fair division problems. There are some guides for doing that here and here. So automated processing is the next task.

By the way if you do have a fair division problem you can mail it to stuffsplitter[at]gmail.com and I will run the processing for you.

Fair division using a spreadsheet and Ruby

It has taken me a month to get over the idea that someone expected this blog not to be the ranting of an inane balding drunk but actually good. Still it is time to get back to the drunken inane rambling.

There is no point having all these cool algorithms unless people can actually use them. So what is a good way to actually get the data into the program? We'll spreadsheets are used for this sort of thing all the time. Unfortunately I cannot figure out how to get openoffice, excel or gnumeric's solver to carry out this minimax fair division program.

Ruby has a cool library called roo for interacting with spreadsheets. So heres a program to get the data out of a spreadsheet and send it off to GLPK

  require 'rubygems'
  require 'roo'
  
  #open office version
 # oo = Openoffice.new("spreadsheetOO.ods")
 #  o2 = Openoffice.new("spreadsheetOO.ods")
 
 #excell version
   oo = Excel.new("spreadsheetOO.xls")
   o2 = Excel.new("spreadsheetOO.xls")
  oo.default_sheet = oo.sheets.first

 o2.default_sheet ="Sheet2"
st="" #data being written toa file
div= o2.last_column


#start writing data to model file
st<< "data;\n"
st<< "param m := #{oo.last_row-1};\n"

   st<< "param n := #{div};\n"
 #the non divisible is whatever is left
    st<< "param o := #{oo.last_column};\n"
 
st<< "param c :"
 i=1
 (oo.last_column).times{st<< "#{i} " 
 i=i+1}
 st<< ":=\n"
 
# number of people
  i=1

 2.upto(oo.last_row) do |line|  
 st<< "#{i} "
 1.upto(oo.last_column) do |col|
    st<< "#{Integer oo.cell(line,col)} "#Integer
    
   end
   st<< "\n";
   i=i+1
 end
 st<< ";\n"
  st<< "param d :"
 i=1
 (o2.last_column).times{st<< "#{i} " 
 i=i+1}
  i=1
 st<< ":=\n"
  2.upto(o2.last_row) do |line|  
 st<< "#{i} "
 1.upto(o2.last_column) do |col|
    st<<"#{Integer o2.cell(line,col)} "
 end
   st<< "\n";
   i=i+1
 end
 
 
 st<< ";\nend;"

#write data to a file
File.open("data","w")do |file|
file.write(st)
end

#call glpk program on the data
system('./glpsol -m fair.mod -d data -o fair.sol');

The input spreadsheets are openoffice and excelin the first row is the list of items.
Every other row is each persons valuation for each item. The first sheet is the indivisible items and the second sheet are the divisible ones. Unfortunately roo does not allow you write to these spreadsheets so I cannot print out the answer to a spreadsheet.

The roo interface to the google docs spreadsheet does allow cells to be written to. So getting that version up and running is the next task.

Filling knapsacks with candies

This paper by Marco Dall’Aglio and Raffaele Mosca on using linear programming (and dynamic programming)
it gives two examples of dividing non divisible goods between two people. The paper uses hard candies as a metaphor for any indivisible item.

The valuations are not based out of 100% but just plain numerical values.

candy 1 2 3 4 5 6 7 8 
Alice 12 18 50 40 20 20 10 5 
Bob 5 10 35 30 15 22 30 28 

Which as data for glpk looks like this

data;
param m := 2;
param n := 0;
param o := 8;

param d : :=
1      
2      
;
param c : 1 2 3 4 5 6 7 8 :=
1 12 18 50 40 20 20 10 5
2 5 10 35 30 15 22 30 28
;end;

the worst person got 102 of what they wanted

Person alice gets item number 1 3 and 4
Person bob gets item number 2 5 6 7 8
This is the same allocation as the paper come up with.

The next example given is

candy 1 2 3 4 
Alice 32 28 22 18 
Bob 25 25 25 25

which is the data file

data;
param m := 2;
param n := 0;
param o := 4;

param d : :=
1      
2      
;

param c : 1 2 3 4 :=
1 32 28 22 18
2 25 25 25 25
;end;

Alice gets item 1 and 2
Bob gets item 3,4
The worst performing person gets 50.

To use these data files with the fair divider for two people (the code of which is here)
./glpsol -m fair2.mod -d data -o fair.sol

As pointed out in the comments this isn't earth shaking or anything it just shows another use of fair division which can be used when items cannot be divided.

Fair Division of an estate

This page describes a fair division of an estate between 5 people. The process is described in the "method of Sealed Bids" section. It that requires each participant has money they can use to pay off the others. I think this is a fairly serious drawback as not everyone has loads of money. Also in the case of an estate division it seems slightly galling that the person with more money gets more things, possibly of only sentimental value, then others.

The division works by
"# Step 1. Bidding. Each player produces a sealed bid in which he or she attaches a dollar value to each item in S. A player's fair share is 1/N of his total assessment.

# Step 2. Allocation. Each item in S goes to the highest bidder for that item. If her/his assessed value of the items received exceeds her/his fair share, she/he must pay the difference. If the assessed value of the items received falls short of a fair share, then she/he is paid out of money that others have had to pay.

# Step 3. Dividing the Surplus There is almost always a surplus of cash that is divided equally among the players. "
given results in people getting

Al  BMW, Saab, Miro 
Ben  House  
Cal  Cottage 
Don  Klee
Ed  Yacht

And the minimum receive is $62,500 + $52,100+$18,340=132 940 out of a possible $679,000 or 19% of their desire.

If instead of assuming each player has money to buy stuff off the others I assumed each layer had equal claim to happiness. So I give each persons 100% desire is worth $679000 and those who claimed less then that use the remainder of their allocation as cash.

So this gives a table of desire of this

data;
param m := 5;
param n := 1;
 param o := 7;
 
 /* n divisible items, o non divisible items*/

/*Divorce between Donald and Ivana Trump described in Win-Win solution.
Items to be divided are 
4 divisible items:cash
2 non divisible items: House cottage, bmw,saab,yacht,miro, klee
Item   Al   Ben   Cal   Don   Ed
House  29.46 31.66 28.71 25.77 30.19
Cottage  8.84 7.22 9.2 8.76 8.1
BMW  4.27 3.6 3.68 4.06 4.06
Saab  3.68 2.8 3.33 3.6 2.87
Yacht  17.67 18.4 17.53 19 19.51
Miro  13.99 13.13 7.36 11.05 9.57
Klee  22.09 19.88 14.58 26.36 21.94
cash 0 3.31 15.61 1.4 3.76
*/

param d :  1  2  3  4 5 6 7 :=
      1   29.46 8.84 4.27 3.68 17.67 13.99 22.09
      2   31.66 7.22 3.6 2.8 18.4 13.13 19.88
      3   28.71 9.2 3.68 3.33 17.53 7.36 14.58
      4  25.77 8.76 4.06 3.6 19 11.05 26.36
      5   30.19 8.1 4.06 2.87 19.51 9.57 21.94; 
      
param c :  1 :=
      1   0
      2   3.31
      3   15.61
      4   1.4
      5   3.76; 
      
end;

Running this on the linear programming fair division calculator program(you need to add s.t. wor5{i in I}: ((sum{j in J} c[5,j] * x[5,j])+(sum{k in K} d[5,k] * y[5,k])) >= worst;). gives a the person who gets least 20.5388%

Al BMW Saab Miro 
Ben House 
Cal  0.726381 of the cash  Cottage  
Don Klee
Ed Yacht 0.273619 of the cash

which is an slight improvement of over on the initial allocation. Everyone gets the same items as in the initial allocation but the money is divided amongst those who receive the least rather then everyone.

Fair Division in Treaty Negotiations

Raiffa in "the art and science of negotiation" describes the Panama Canal treaty negotiations in 1974. He got the value each country attached to each issue from the US negotiating team. In the fair division book chapter 5 describes this negotiation using their Adjusted winner algorithm. One weakness with this algorithm is that all items must be divisible.
There is no way to fix issues as non divisible as there is in my program (you will need to remove s.t. wor3 and s.t. wor4).
So if you take the data as

data;
param m := 2;
param n := 9;
param o := 1;
 
 /*m people,  n divisible items, o non divisible items*/
/*
1 non divisible items expansion routes
                  US Panama
US defense rights  22 9
use rights        22 15
Land and water   15 15
expansion rights  14 3
duration         11 15
expansion routes  6 5
compensation     4 11
jurisdiction      2 7
US military rights  2 7
defense role of Panama   2 13
*/

param c :  1  2  3  4 5 6 7 8 9 :=
      1  22 22 15 14 11 4 2 2 2
      2  9 15 15 3 15 11 7 7 13; 
      
param d :  1 :=
      1   6
      2   5; 
end;

where expansion routes is not divisible.

US gets item number us defense rights, use rights, expansion rights,expansion routes
Panama gets duration, expansion routes, compensation, jurisdiction and us military rights. For Land and water the US gets .1333 of this and Panama get 0.86667 which is ok as land and water are the sorts of things that can be divided up. Each country got 66% of what they wanted, In this case my program gets the same results as the Adjusted winner program.

A better fair division program

One problem with the wildly unpopular fair division programs discussed previously is that they assume either everything can be cut into pieces or nothing can.
In the real world as Solomon noticed some items cannot be divided up. But some items are easily splittable . So I have improved the fair division program to deal with combined divisible and indivisible items.

Another problem is that the code only dealt with the two person case. I have fixed this by adding a new constraint for each extra person.

The code for this Mathprog program fair.mod is here. I am providing the source code in case anyone can suggest improvements. Also the world is full of decisions that get made for us that we have no way to challenge or understand. So I would like people to be able to see why the reasoning in and results of an arbitration,

The program (glpk) is run by

Put this data in a data file. Call glpk on it.
./glpsol -m fair.mod -d data -o fair.sol
So the data file could be

data;
param m := 4;
param n := 4;
param o := 2;
/*m people, n divisible items, o non divisible items*/

/*
Items to be divided are
4 divisible items: cash, land, cake, gold
2 non divisible items: dog, table
*/

param c : 1 2 3 4 :=
1 20 30 0 20
2 30 20 0 20
3 20 30 0 20
4 0 10 40 40;

param d : 1 2 :=
1 10 20
2 20 10
3 20 10
4 10 0;
end;

Which means person 1 thinks 20% of the value to them in the estate is in the cash, 10% is in the dog etc.

So now you can divide up goods fairly between m people. I have never seen a program that does this before. Using this program the that parties in a will, divorce, international dispute, merger and all sorts of other areas can achieve optimal solutions. The solutions will be proportional, envy-free (in the two person case) and Pareto optimal.

Now to make the dispute resolution program more usable.