Marriage

1
Marriage Divorce Simulation

• The goal of this exercise to show the simulation
  of a society. In the larger context, its an
  example of how students might perform a
  simulation.
• Given a body of data, how do we arrange that data
  in order to represent how the society is
  behaving. This is essentially a model using
  the data.
• There are three ways we go about putting
  numerical values on this model.
• Given a series of equations, can we simply solve
  the equations?
• If the equations dont have a closed form
  solution, can we solve them recursively. There
  are no statistics involved here, but all we do is
  solve each equation over and over again and hope
  that it converges. This method gives us no
  details about the population since were simply
  solving equations.
• We can try for a real simulation. In this
  case, we use the probabilities and a random
  generator to try to simulate good years and bad
  years. This allows us to answer much more
  complex situations. We could now track
  characteristics for each individual in our
  society. We could, possibly, see how long a
  person in our society stays married for instance.

2
Marriage Divorce Statistics

• Theres lots of stuff on the web, confusing and
  maybe contradictory
• All data is for the US (unless otherwise noted)
• In 2007, there were 2,200,000 marriages. This
  represents a rate of 7.5 per 1000 total
  population. Note this is 2.2M / 296M 7.5.
  (Total US population is higher but some states
  dont report.)
• Another metric which may be saying the same thing
  is that there are 39.9 marriages per 1000 single
  women. Were going to use the first number here.
• In 2007, there were 856,000 divorces. This is
  3.6 per 1000 total population.
• Interesting numbers, but not used here
• 41 of 1st marriages end in divorce.
• 60 of 2nd marriages end in divorce.
• 74 of 3rd marriages end in divorce.
• The average remarriage occurs 3.3 years after a
  divorce.
• In 2007 there were 2.400,000 deaths representing
  a rate of 8.2 per 1000. Details of this on next
  page.
• 60 of all marriages last until 1 partner dies
• Birth rate is 13.8 per 1,000 population

3
Marriage Divorce Statistics

• In 2007 there were 2.400,000 deaths representing
  a rate of 8.2 per thousand.
• Details on this mortality data are for men and
  women 65
• Death rate for married man is defined as 1.00
• Death rate for a widowed man is 1.06 times that
  of a married man.
• Death rate for a divorced or separated man is
  1.14 times that of a married man.
• Death rate for a never-married man is 1.05 times
  that of a married man.
• Death rate for married woman is defined as 1.00
• Death rate for widowed woman is defined as 1.15
• Death rate for divorced or separated woman is
  defined as 1.26
• Death rate for a never-married woman is 1.18
  times that of a married woman.
• This information is from US Mortality by
  Economic, Demographic, and Social
  Characteristics The National Longitudinal
  Mortality Study, Sorlie, Backlund, and Keller,
  1995
• We use a rate thats above and below the 8.2 per
  1000 for the national average to take into
  account single and married rates.
• DeathMarriedRate 7.6 per 1000
• DeathSingleRate 8.7 per 1000

4
Zombie
Reincarnation 100
Birth Rate
Death while Single
Single
Divorce Rate
Widowed
Marriage Rate
Married
Death while Married
5
Marriage Divorce Equations

• Leaving Zombie
• DZ - Rbirth ( S M )
• Entering Zombie
• DZ Rdeath-single S Rdeath-married
  M
• Leaving Single
• DS -2 Rmarriage ( S M ) -
  Rdeath-single S
• Entering Single
• DS Rbirth ( S M ) 2 Rdivorce
  ( S M ) Rdeath-married M
• Leaving Married
• DM -2 Rdivorce ( S M ) -
  Rdeath-married M
• Entering Married
• DM 2 Rmarriage ( S M )
• In Steady State leaving equals entering
• Rdeath-single S Rdeath-married M -
  Rbirth ( S M ) 0
• Rbirth ( S M ) 2 Rdivorce ( S M
  ) Rdeath-married M -2 Rmarriage ( S M
  ) - Rdeath-single S 0
• 2 Rmarriage ( S M ) - 2 Rdivorce ( S
  M ) - Rdeath-married M 0

6
Marriage Divorce Equations

• In Steady State leaving equals entering
• Rdeath-single S Rdeath-married M -
  Rbirth ( S M ) 0
• Rbirth ( S M ) 2 Rdivorce ( S M
  ) Rdeath-married M -2 Rmarriage ( S M
  ) - Rdeath-single S 0
• 2 Rmarriage ( S M ) - 2 Rdivorce ( S
  M ) - Rdeath-married M 0
• Rearranging these equations gives
• - Rbirth ( S M )
  
  Rdeath-single S Rdeath-married M 0
• Rbirth ( S M ) - 2 Rmarriage ( S M )
  2 Rdivorce ( S M ) - Rdeath-single S
  Rdeath-married M 0
• 2 Rmarriage ( S
  M ) - 2 Rdivorce ( S M )
  - Rdeath-married M 0
• Maybe theres a solution, but they seem redundant
  to me.