The complex
systems model ‘Engagement vs Police Expenditure for Justice Reinvestment in
Bourke, NSW’ evaluates the effectiveness of allocating government funding to
either community engagement activities or law enforcement. In this model, it is
possible for the user to designate resources from a scale of 20-100 and to also
modify the crime rate for both adults and youth. Below, there are detailed
notes that describe the reasoning and assumptions that justify the logic
applied to this model. Similar notes can be found when stocks, flows and
variables is clicked under the field ‘notes’.
Portions
Government
statistics from the Australian Bureau of Statistics (ABS) show that Bourke
Shire Regional Council has approximately 3000 residents, made up of 65-63% adults
and 35-37% youths.
Crime
Rate
Police
variable is in the denominator to create a hyperbolic trend. The aim was to achieve a
lower crime rate if police expenditure was increased, thus also a higher crime
rate if police expenditure was decreased. The figure in the numerator can be changed with the ‘maximum crime rate’ variable
which represents the asymptotic crime rate percentage. Where police = 100 the selected crime rate is
maximised.
Avoiding Gaol
Originally
the formula incorporated the police as a variable, where the total amount of convicted crimes was subtracted from the total amount of crimes committed. However, the constant flow of crimes from repeat offender/a created an unrealistic fluctuation in the simulation. I
settled for a constant avoidance rate of 25%. This assumes that an adult or youth committing a crime for the first time is just as likely to
avoid conviction as a repeat offender.
Conviction
It
is difficult to predict in a mathematical model how many adults or youths are convicted of crimes they commit. I
determined a reasonable guess of maximum 75% conviction rate when Police = 100. In this formula, decreasing police spending equates into
decreased conviction rate, which is considered a realistic representation.
Released
It
is assumed that the average sentence for a youth is approximately 6 months
detention. For an adult, it will be assumed that the average sentence is 12
months gaol. The discrepancy is due to a few basic considerations that include
1. Adults are more often involved in serious crime which carries a longer
sentence 2. youths are convicted with shorter sentences for the same crime, in
the hopes that they will have a higher probability of full rehabilitation.
Engagement
Rate
of adult/youth engagement was estimated to be a linear relation. The maximum rate of engagement, assuming expenditure = 100,
is set to 80%. This rate of engagement is a reasonable guess with consideration that there will also exist adults who refused to engage in the community and end up in
crime, and adults or youth that refuse to engage in the community or crime.
Boredom
Engagement
Expenditure variable is in the denominator to create a hyperbolic trend. The aim was to achieve a
lower boredom rate with a higher engagement expenditure, and thus a higher
boredom rate with a lower engagement expenditure. The figure in the numerator of 25 represents the asymptotic boredom rate percentage,
where if engagement expenditure = 100 the adult/youth boredom rate is maximised at 25%.
