peter principle reworked in matlab
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Peter Principle
By Michael R. Munroe
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Problem description• How does an organizations structure, turnover rate, and employee
selectivity impact its maximum performance?• This is relevant because it provides avenue to maximize productivity, or
evaluate organizational performance.• This will be simulated in MatLab – accounting for each relevant degree of
freedom and variability to allow numeric handling of results.
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The Basic Model• Company
Six levels 160 employees
• Competence Uniform random Below 4 is culled Ranges from 0 to 1
• Promotion/Hiring Try first level below Try anywhere in the
organization Then hire from outside
• Ages Start is uniform random Lowest is 18, highest is 64
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Accounting Notes
Accounted for• There is no such thing as time. An
Epoch is a metaphor for hire/advance/fire as driven by Performance review.
• Performance is measured in “Degree of Competence” and so is also an abstraction. It is applicable to ROI, education, contribution, .. Or whatever.
NOT Accounted for• Change in competence over time
(Improvement with experience, trends in source)
• Increase/Decline/Change in Contribution vs. level in company.
• Increase in cost vs. level in company.
• Leaving by any means other than retirement
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The Basic Results
Observations:• From Epoch of zero to
48 system efficiency is increasing
• At about epoch 48 peak of 72.92 occurs.
• After 48 there is a trough that bottoms around Epoch 75
• After trough system stochastically orbits steady-state
0 50 100 1500.5
0.55
0.6
0.65
0.7
0.75
Epoch
Sys
tem
Eff
icie
ncy
Trend system efficiency (minCOP=40%, dwell=42)
0 20 40 60 80 100 120 140
0.72
0.722
0.724
0.726
0.728
0.73
X: 78Y: 0.7206
Epoch
Syste
m E
ffic
iency
Trend system efficiency (minCOP=40%, dwell=42)
X: 46Y: 0.7292
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Questions, Knobs and Stats
Statistics• Central tendency and
Variation Mean and stdev Median and iqr
• Ensemble Size Paper: 50 elements Exercise: 10,000
elements
• “Knobs” Number of evaluation samples or
“Epochs” Dwell time (age) Competence floor
• questions Is there an organizational equivalent of the
10,000 hour rule? How does organizational performance change
with number of samples? How does changing the minimum
competence impact peak and steady state values?
Is there a metric like WIP-turns that relates organization structure to organization efficiency?
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Varying Exit Age
As exit age increases:• Ramp to peak shallows• Peak height increases• Steady-State
competence increases• Post-peak decline
increases
Interesting points• Below age 34 there is
totally different phenomenology
• Differentiation based on “dwell time” starts to occur after epoch 4.
0 10 20 30 40 50 60 70 80 90 1000.68
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
Epoch number
Org
aniz
atio
nal c
ompe
tenc
e
Competence vs. Epoch for varying exit "age"
age 34age 39
age 44
age 49
age 54
age 59age 64
age 69
age 74
age 79age 84
2 4 6 8 10 12 14 16 18 20 22
0.7
0.72
0.74
0.76
0.78
0.8
0.82
Epoch number
Org
aniz
ational com
pete
nce
Competence vs. Epoch for varying exit "age"
age 34age 39
age 44
age 49
age 54
age 59age 64
age 69
age 74
age 79age 84
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Median Efficiency vs. Exit Age
0
50
100
150
1020
3040
50
6070
0.4
0.5
0.6
0.7
0.8
0.9
Epoch
Mean System Performance vs. Max Dwell time and Epoch
Dwell Time
Sys
tem
Eff
icie
ncy
Observations• There is an
immediate ramp as dwell time increases.
• There is a “ridge” of max system COP, after which SS is achieved.
Notes:• Dwell time is 18 plus
number of “FOCAL” or reviews experienced before mandatory termination.
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2040
6080
100120
140
20
30
40
50
60
0
0.2
0.4
0.6
0.8
1
Epoch
Variability (scaled IQR) of system efficiency
Retirement Age
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
IQR of Efficiency vs. “Retire” ageObservations• There is a peak near
the origin.• There is a line-shaped
ridge proportional to age and epoch.
• There is a ridge of maximum variablity given epoch near the fourth “review” or age ~22.
Note• This is dimensionless
variablity – the axis is scaled.
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0
50
100
150
0
0.2
0.4
0.6
0.8
10.5
0.55
0.6
0.65
0.7
0.75
Epoch
Mean of system efficiency
minCOP
Sys
Eff
Median Efficiency vs. Minimum COP
Observations• There is a peak of
variability around epoch 40, followed by a trough.
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IQR Efficiency vs. Minimum COP
Observations• There is a peak of
variability around epoch 40, followed by a trough.
2040
60 80100
120140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.03
0.035
0.04
0.045
Minimum Competence
Epoch
IQR of system efficiency
Sys
Eff
0.03
0.035
0.04
0.045
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Varying Minimum Competence
As competence increases• Steady-state increases• First ramp increases• Second ramp decreases• Peak Epoch occurs slightly
later
Interesting Points• Nature of the system
significantly transitions over 80%. General form and rate of increase changes.
0 50 100 1500.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
X: 136Y: 0.7374
Org
aniz
atio
nal c
ompe
tenc
e
X: 135Y: 0.7662
X: 135Y: 0.793
X: 135Y: 0.8198
X: 134Y: 0.8456
X: 133Y: 0.8695
X: 133Y: 0.8905
X: 132Y: 0.9054
X: 135Y: 0.9006
X: 47Y: 0.7456
X: 48Y: 0.7725
X: 48Y: 0.7979
X: 49Y: 0.8236
X: 49Y: 0.8482
X: 52Y: 0.8714
X: 55Y: 0.892
X: 58Y: 0.9066
X: 30Y: 0.9044
Epoch number
Competence vs. Epoch
min 10%
min 20%min 30%
min 40%
min 50%
min 60%
min 70%min 80%
min 90%
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Min Competence vs. Steady State
As “filter level” increases:• Initial variation is
linear• Diminishing
returns starts kicking in
Interesting points• Around 0.85 is max
theoretical system efficiency.
• A 90% filter results in lower max than 80% filter
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
X: 0.8425Y: 0.9088
Minimum Allowed Competence
Max
Sys
tem
Com
pete
nce
Max System Competence vs. Min Competence Threshold
myy vs. x
fit 1
y max
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Next Steps
• Company of youth Explore organization behavior between dwell time of
2 and 18 by computing ensemble median at 1 epoch intervals
• Variation, not just mean Explore time and parameter variation in IQR
• Structure vs. Peak• Pushed from beneath vs. Pulled from above
What does management actually contribute. Is the increase in pay a reasonable compensation for the return in value?
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Backup
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Source Material
Ignoble Prize• http://improbable.com/ig/winners/#ig2010Paper• http://arxiv.org/abs/0907.0455• http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0455v3.pdfPremise• Given - Performance in new position isn’t indicated well by prior performance.• Thus - People rise to highest level of incompetence• And – the best strategy for ignorance is random rewards.
Bottom line: There is a time and place for random rewards – its called ignorance.