Priority Interdependencies 
Based on models of task progress, population and consumption, and priorities, the following relationships are assumed:
Relationship 
Definitions 
hself = F / ( u_{h} * F + Fmin ) = Env / Envtot 
 hself = personal happiness (fraction)
 F = percapita ecological footprint (consumption of ecological resources in Earths/year per person)
 Fmin = minimum ecological footprint
 u_{h} = constant
 Env = occupied environments
 Envtot = total environments

Fe = P * F 
 Fe = global footprint (consumption of ecological resources in Earths/year)
 P = population (people)

h = i_{4} * Fe^{4}  i_{3} * Fe^{3} + i_{2} * Fe^{2} + i_{1} * Fe 
 h = group (average) happiness
 i_{n} = constants

Lself = F / ( u_{L} * F + frate )

 Lself = personal longevity (years)
 frate = constant (footprint/year)
 u_{L} = constant

Ltot = [ FeTotal  ( Fe + FeMin ) ] / ( dFe/dt ) 
 Ltot = longevity of humanity (years)
 FeTotal = Fe where species population S = 0
 FeMin = P * Fmin
 dFe/dt = Fe rate of increase (global footprint/year)

S = b_{1} * Fe + b_{0} 
 S = typical population of other species (fraction)
 b_{n} = constants

Lspecies = ( FeTotal  Fe ) / ( dFe/dt ) 
 Lspecies = typical longevity of other species

Q = 1  (1  E )^{t/tmin} 
 Task quality achieved (fraction of total)
 E = efficiency (fraction)
 t = time
 tmin = minimum time to complete task (Q = 1, E = 1)

SUM(Priority_{goal})_{1 to g} = (1  Priority_{0})^{g} 
 SUM(Priority_{goal})_{1 to g} = sum of priorities
 Priority_{goal} = priority of goal
 g = current goal (integer), where g < G
 G = maximum goals (integer)
 Priorityraw_{g} = priority of goal if only a single goal (raw priority)
 Priority_{g} = Priorityraw_{g} * [ 1  SUM(Priority_{goal})_{1 to g 1} ]
 Priority_{G} = 1  SUM(Priority_{goal})_{1 to G 1}
 Priority_{0} = value of Priority_{1} if all Priorityraw are the same

Q_{goal} = 1  ( 1  E_{goal} )^{T} 
 Q_{goal} = fraction of goal achieved
 E_{goal} = efficiency in attaining goal
 T = Priority_{goal}* t / tmin_{goal}
 tmin_{goal} = minimum time to reach a goal (Q_{goal} = 1, E_{goal} = 1)

Effect = [ (P  N) * X_{P} + N * X_{N} ] / P 
 Effect = net result of new change and old trend
 X_{N} = Variable value for number of people N
 X_{P} = Variable value for number of people P  N


Key aspects can be summarized by the following rules of thumb:
INCREASE 
TO DO THIS 

 Increase personal happiness (hself)
 Increase personal longevity (Lself) to maximum, decrease afterward

 Footprint (F)
 Population (P)

 Increase others happiness (h) to maximum, decrease afterward
 Decrease others longevity (Ltot)
 Decrease species population (S)
 Decrease species longevity (Lspecies)
 Increase required ecological resources (FeMin)

 Total ecological resources (FeTotal)

 Increase supportable population (P)
 Increase others longevity (Ltot)
 Increase species population (S)
 Increase species longevity (Lspecies)


 Decrease time to accomplish goal


The following images show the results of simulations using several HalfWorld scenarios.
The total ecological resources are fixed at their current estimated value, and high priority is placed on others longevity, which is influenced by getting a number of people to adopt the same personal goals ("impact"). Graphs show the trajectories of progress for all goals (identified by index numbers) on a logarithmic scale, with each year marked at the middle of the year. 




The following graph shows lives saved (difference in casualties) as a function of impact for the combined case: 

The following graph shows impact as a function of time for full effect (7.26E+09/yr): 

While the graphs above assume that there is builtin impetus to follow the trajectories in the HalfWorld scenarios (which are modified by the changes due to priorities), the following graphs display how population and footprint are constrained if enough ecological resources are left to support the species we depend on for basic survival. That is, Fe + FeMin < FeTotal  FeMin, and therefore
 Varying F, then P < [ Pcritical = FeTotal / ( F + 2 * Fmin ) ]
 Varying P, then F < [ Fcritical = FeTotal / P  2 * Fmin ]
The next graph begins with values of population (Pstart) and footprint (Fstart) in mid2015, and plots
 P vs. F = P / Pstart on Xaxis, Fcritical / Fstart on Yaxis
 F vs. P = F / Fstart on Xaxis, Pcritical / Pstart on Yaxis


The following graph plots critical values of P and F as above, but over a broader range. Here, Pstart = 1 and Fstart = Fmin.
Note that, in 2015, P / Pstart = 7.26E+09 and F / Fstart = 3.29. Roll over the image for a closeup. 

Corresponding happiness values are shown below, where
 P vs. Critical h = P / Pstart on Xaxis, happiness at Fcritical on Yaxis
 F vs. h = F / Fstart on Xaxis, happiness at F on Yaxis
Current (2015) happiness is 0.66. 

Historical values of footprint and population from 19502015 are superimposed on the critical values (with Pstart = 1, Fstart = Fmin) in the graph below. Rollover the image to see P vs. F.
Also shown are results of a simulation that starts with F and P for 1950 and takes the following steps 2500 times:
 Calculate current F limit.
 Move F toward the limit as a fraction of the distance to it, with the fraction equal to a random number (between 0 and 1) times an efficiency of 0.002.
 Calculate the new P limit.
 Move P toward the limit as a fraction of the distance to it, with the fraction equal to a random number (between 0 and 1) times an efficiency of 0.01.


The following graph takes critical population values and calculates the corresponding critical footprints, then calculates happiness from the results to derive a plot like that used in the simulations of population and consumption used in version 4 of the PopulationConsumption model. 

For a discussion, see the following:


© Copyright 2015 Bradley Jarvis. All rights reserved. 