Table Of ContentDilbert-Peter model of organization effectiveness: computer simulations
Pawel Sobkowicz∗
(Dated: January 24, 2010)
We provide a technical report on a computer simulation of general effectiveness of a hierarchical
organization depending on two main aspects: effects of promotion to managerial levels and efforts
to self-promote of individual employees, reducing their actual productivity. The combination of
judgment by appearance in the promotion to higher levels of hierarchy and the Peter Principle
(which states that people are promoted to their level of incompetence) results in fast declines in
effectivenessoftheorganization. Themodelusesafewsyntheticparametersaimedatreproduction
of realistic conditions in typicalmultilayer organizations.
0
1
0
2 I. INTRODUCTION at their level of incompetence. Peter originally for-
mulated this idea in a joke-like fashion, but once we
n
recognize its importance, it becomes pretty obvious
a
Computer simulations have become increasingly
J and common sense. There are several works provid-
popular in describing social phenomena, from traffic ing more exact description of the effects of the prin-
4
jams to opinion formation. The number of topics and
2 ciple, for example Kane [5], Fairburn and Malcomson
worksisverylargeandthereareevenpopularexposi-
[6], Lazear [7, 8]. It should be noted that companies
] tions of the discipline, such as Ball [1]. In some cases fight against the “incompetence stasis” resulting from
h the newtoolsprovidesignificantinsightintoobserved
the Peter Principle via constant pressure on employ-
p
phenomena. Unfortunately, sometimes the computer
ees: promoting the best is usually accompanied by
-
c simulations and statistical mechanics serve the same firing the worst performers at each level of hierarchy.
o purposes as described by Andreski [2], namely to for-
But while this leads to culling of non-performers, it
s tifyworkthatistrivialfromsociologicalpointofview.
. mightmeanlossofcapablelowerlevelemployeeswho
s There is also another pitfall resulting from the focus
have been promoted beyond their skill range. The
c
onthemathematicalandcomputertools,namelymin-
i process creates a bad manager from a good worker,
s imal referenceto the actualsocialobservations. With
y and then gets rid of the bad manager. This problem
these dangers in mind it seems quite adventurous to
h can in turn be solved by providing horizontal career
propose a mathematical model of purely social phe-
p paths, which ensure that the best specialists could be
[ nomena, especially well established in descriptive so- recognizedand awardedwithout changing the areaof
ciology. their tasks,sothattheir skillswouldnotbe lostupon
1
v An example of such work, where computer model promotion. Yet, despite the fact that Peter Principle
5 genuinely allowsto gobeyondtraditionaldescription, is known for forty years, examples of loss of produc-
3 is a recent publication by Pluchino et al. [3], who tivityduetopromotingpeoplebeyondtheircapacities
2 have provided a simple and interesting simulation of are present in almost all types of hierarchical organi-
4
the famous Peter Principle (Peter and Hull [4]). The zations,fromscientificresearchtocommercialcompa-
.
1 principle results from observation that in any hierar- nies.
0 chical organization global effectiveness is diminished In our model we attempt to go beyond the earlier
0
due to the fact often skills which make a person an approaches, which assume that the basis for promo-
1
excellent worker at a given level in the organization tions is the actual performance of the organization
:
v may be unsuited at a higher one. Thus, promotion members. Ourmotivationcomesfromexperiencethat
Xi of the best employees (which looks like a reasonable decisions to hire and promote are based on perceived
way of action) results in loss of skilled workers and, performance. Thus, employees or external candidates
r
a possibly, creation of less than optimal managers. Of who focus on presenting themselves and their own
course, such ineffective manager would no longer be results in good light (instead of just working) have
promoted,soeventuallyeveryonewouldbecomestuck better chances of advancement. Such individual pub-
lic relations activity or self-promotion is quite nat-
ural and present everywhere: in commercial compa-
nies, universities or political parties. The result is
∗Electronic address: pawelsobko@gmail.com that not only people reach their incompetency level,
2
but also that the whole promotion process often fo- by accumulating the real output of the contributors,
cuses on those who have little to contribute to the their advancement within the organization is related
organization but rather spend their effort and time to comparative perceived results. Observations show
on getting promoted. In honor of the Scott Adams’ that often it is not the best performer that gets pro-
Dilbert comic strip (Adams [9]), we propose to call moted (as postulated by the original Peter Principle)
the resulting process Dilbert-Peter Principle. Simi- but those who appear to be the best workers. There
lar combination of the two phenomena, which limit are thus two main strategies to achieve the promo-
the effectiveness of organizations, has been proposed tion. The first is via improvement of the real output,
by Faria [10]. It might seem to be presumptuous which corresponds directly to the Peter model back-
to use Pointy Haired Boss and other characters fea- ground. The second way, observed all too frequently,
tured in the Dilbert strip as “real world” basis for is throughthe use ofpoliticalgames,thanks to which
computer modelling. Would it not be better to use apersonappears tobemoreproductiveandworthyof
official company data, histories and performance fig- advancement. TheseindividualPRactivitiesaredone
uresasasourceforinspirationforasimulationmodel? at the expense of the actual work,thereby decreasing
In our opinion, just the contrary. The official docu- the contribution of the individual to the overallorga-
ments are usually written with the purpose of hiding nizational effectiveness.
the very mistakes and ineffectiveness we want to dis- Following Pluchino et al. [3] we propose to com-
cuss. Onthe other hand, due to the popularity ofthe pare two possible scenarios, differing in description
strip and its WEB site (http://www.dilbert.com/), of individual productivity after the promotion. The
the accumulated “database” of cases of stupidity and first one, called continuity scenario (‘common sense’
mismanagement is much better and true to life than in Pluchino et al. [3]), in which the productivity at
the officialcorporateprofilesandannualreports. The the newpostissimilartothe oneatthe previousone.
author’spersonalexperience,gatheredinseveralcom- Suchsituationisexpectedwhentherangeoftasksre-
panies, Polish, American, German and French, sug- lated to the new position remains similar to the pre-
gests that what looks like jokes is often an uncannily vious ones. The Peter scenario assumes that due to
accurate description modern business organizations. difference in tasks at different levels of the organiza-
ThousandsofletterssenttoScottAdamsfromallover tion the productivity at the new post is unrelated to
the world confirm this experience. In many areas we theoldone. Inbothcasesourcurrentmodelmeasures
find organizationswhich share similar activities, sizes the perceived productivity, including effects of inter-
and structures, yet which differ widely in their effec- nal politics. We investigate the effects of promotion
tiveness. This is true for both commercial companies process on key characteristics of the organization: its
and public organizations. Our goal is to find which general productivity, averages of effectiveness at var-
which aspects of the model are crucial in determina- ious levels of the hierarchy, dynamics of changes due
tionoftheoverallproductivity,andperhapstosuggest to the promotion preferences.
measures to improve the operations in real life.
The simulations presented here are designed to in-
clude several phenomena associated with modern en-
terprisesandorganizations,namely hierarchicalorga-
II. MODEL DESCRIPTION nization, management contribution, measurements of
effects dependentonbothindividualqualitiesandcu-
The purpose of the model is to providea simplified mulativeresultsofsubordinatesandinterplaybetween
description of effectiveness of a hierarchical organiza- in-company promotion and external hiring. The goal
tion in which people act to maximize their promo- of the model is to provide some predictions regard-
tion chances. The promotions are achieved through ingthedependenceofthemeasuredqualitiesonafew
comparisons of productivity of individuals within a simple controls: importance of the political games-
given hierarchy level. One of the key differentiators manshipforpromotion,heritabilityofskillsafterpro-
of the model is the division betweenrealproductivity motion(thecontinuitymodelversusPeterhypothesis)
(for example sales results, number of research pub- and tendency for internal or external advancement.
lications, lines of code accepted into a project) and The basic model applies to organizations in which
employee productivity perception by the authorities activities are uniform, i.e. where the nature of tasks
responsible for making promotion decisions. While is the samefor allpositions ata givenhierarchylevel.
theeffectivenessofthewholeorganizationismeasured Examples might be provided by some governmentin-
3
stitutions (such as tax offices), research institutions wouldcorrespond,touseourexamples,tooverallsales
or by specialized parts of larger bodies, for example figures for a branch office, code submitted by a soft-
sales divisions in large corporations. While the basic ware development group or the research standing of
tasksandmeasurementcriteriaperlevelarecompara- the institute. We have decided to combine the two
ble throughout the organization, advancing from one contributionsintooneparameter,tokeepthespiritof
level to another might change (sometimes very signif- Peter principle, defining one "competence".
icantly) the nature of the job: from tax collection or The second characteristics of an agent is the ef-
salestomanagement,moreandmoreremotefromthe fort he or she puts into internal political positioning
outside world as we move up in hierarchy (self-promotion) denoted by p . This parameter may
i
Presented results are based on a small number of include activities and skills that are quite common-
selected conditions and, we hope, can be a starting place in modern organizations, for example excessive
point for a more advanced study. focusonpresentationofresultscomparedtotheactual
value of one’s own results (“PowerPoint economy”),
presenting other’s achievements in bad light, forming
A. Hierarchical structure and nurturing of cliques and power circles. We con-
sider here that p is focused on personal interest of
i
We are interested here in department based hierar- the agent and does not contribute to actual results
chical organizations, such as a commercial company – neither those related to direct output, nor to man-
with many local sales offices, or large software house agement contributions. In this work we separate the
with multiple project teams. To a certain degree this “productive” part of political activities (such as or-
description applies to research and government insti- ganizing,motivating, ensuring cooperation...),being
tutions as well. The simplest way of modeling such an inherent part of management activities and con-
organization is via pyramid structure of units of the tributing to the realwork done, fromactivities aimed
samesize. OrganizationisdividedintoK levels,num- at personal gain.
bered from top (k =1). Each unit consists of a man- In our simulations we assume that the wi is drawn
ager at level k and N subordinates (workgroup) at from Gaussian distribution centered around w0 (a
level k+1. good value for w0 might be 1, for reasons explained
The size of the whole organizationis thus NTOT = in SectionIIB2) with distribution width ofσw, while
(NK − 1)/(N − 1). To achieve reasonable number for pi the distribution is linear from 0 to pmax. The
of levels and unit sizes we may restrict ourselves to two parameters are used to model the actual results
N ≤ 10 and K = 4 or K = 5, resulting in organiza- of the work done by the agent and the perception of
tionswithenoughstructurebutlimitedtoabout1000 the work done within the organization. The effective
people. contribution to the organization productivity by the
agent is given by
′
w =w −p (1)
B. Agent characteristics i i i
This is the simplest way of describing the fact that
1. Real work and self-promotion focusing on improving one’s own position by politi-
cal activities must deduct some time from the actual
Employees are represented by computer agents work. On the other hand, effort spent on political
numbered via subscript i. Each agent is character- maneuversimprovesthe perceivedresults. This is de-
ized by two parameters. The first, w , is its capacity scribed in a more complex way, depending on addi-
i
toperformeffectiveworkatitscurrentposition,called tionalparameter: organization’ssusceptibility toself-
also raw productivity. We consider here two types of promotion (Eq. 3). Similar trade-off between techni-
contributions: direct work (for example value of sales cal and social skills has been proposed by Faria [10].
achieved by a salesman, lines of code written by a It should be noted, however, that in our approach w
i
programmer or research papers published by a scien- containsboththetechnicalandsocialskillsasdefined
tist) and managerial contribution, related to organiz- by Faria. The change of responsibility upon promo-
ing, coaching and monitoring efforts of others. Man- tion might result in a different optimal ratio of the
agers,bytheiractions,maysignificantlyinfluencethe two types of skills, and therefore, in different value of
sum of individual results of their subordinates. This w before and after promotion. The treatment of p
i i
4
is different: it measuresaninternalcharacteristicofa Thus we propose that effective results are given by
person, its drive to improve own position, which does
notimprovetheactualresultsinanywayandhasnot ′
W =w × W , (2)
been considered in the past. We have used values of i i X j
w = 1, σw = 0.3, p = 0.6 in the simulations. j∈SUB(i)
0 max
This choice has been motivated by real life observa- where SUB(i) denotes the agents that are directly
tions: for example such distribution of w allows dif-
i managed by agent i. Due to recursive nature of the
ferences of work in the range of 200% or even more.
above expression, the effective results of a manager i
As for pi, the choice of flat distribution rather than include contributions of all its subordinates. For the
Gaussian reflects relatively frequent cases of extreme lowest level of hierarchy W = w′. In such model, if
i i
behavior: totallackoffocusonself-promotion,orjust
all agents have the same value of w = 1 and p = 0
i i
the opposite. Author experiences lead to assumption
(no effort is wasted on political positioning) the re-
of pmax = 0.6; there are people who do spend more sults at a given layer k are NK−k, assigning much
than half of time on political ploys aimed to advance
greater importance to the managers that in the addi-
their position. tive model. But if w′ <1 then the managerdecreases
i
thesummedcontributionsofhisorherssubordinates.
Such model does not describe well situations where
2. Management contribution a manager combines the managerial tasks with the
same type of production as his or her subordinates
(e.g. programming team leader writing code, univer-
To take into account the fact that in most organi-
sity department head doing his or her own research
zations managers are measured on the results of the
or sales manager being directly responsible for some
teams they manage, we introduce here accumulated
customers). However, above certain realistic size of
versions of the effective work and perceived results,
which combine the results of the manager and his the workgroup, the qualitative results of our model
remain unchanged by such assumption.
or her subordinates. We have chosen to use a multi-
In contrast with the actual results, the perceived
plicative way of describing the influence of the man-
outcome for a manager is given by a combination of
ager on the results of the department. This is by no
therealresultsofhisdepartment(comparedtotheex-
means the only choice, but it provides a simple way
of describing situation where a bad manager(w′ <1) pected average at the appropriate level) and the out-
i
come of his political ploys. We have used a simple
would actually decrease the overall output of his de-
partment, while the good manager (w′ > 1) would sum of these two factors
i
increase it. This multiplicative approach differs from
U =W /W(k)+C·p , (3)
i i i
additive view of Pluchino et al. [3], who propose that
contributions at higher levels of hierarchy should be where W(k) is the average result at the level of the
modelledbysimpleadditionofmanager’sresultsmul- agent i. C is a numerical factor used to model self-
tiplied by an artificial factor ranging from 0.2 at the promotion importance - one of the key parameters in
lowest level to 1.0 at the top management, to simu- the simulations. We use the name “susceptibility” for
late the increased importance of the higher levels of C, as it determines the relative importance of self-
hierarchy. Increase of productivity of given employee promotion in the selection of candidates for promo-
over time is a real phenomenon found in many or- tion, and thus the way the organization responds to
ganizations, related with accumulation of skills and selfinterestsofemployees. Suchformoftheperceived
experiences. It would describe a horizontal progress resultsallowsnormalizationofits twocomponentsin-
fromanapprenticetoatopspecialist–withinagiven dependently of the level, number of subordinates etc.
level of hierarchy. It is less suited to vertical promo- Agents with highest and lowest values of U would
i
tionandmanagerialtasks,wherethecontributionofa be the candidates for promotion and sacking, respec-
managercomesfromorganizingtheworkofthesubor- tively. Figure1showssampleorganizationalstructure
dinates. Moreover,additiveapproachcannotdescribe withK =4andN =4,comparingW andU atvari-
i i
the Dilbertian influence of idiot bosses who often de- ous levels ofthe organization. The positions are color
crease the results of the departments they manage. coded, with highest values denoted by green, lowest
The importance of the individual contribution must by red. As may be seen, actual performance and per-
be higher as we move up in the organization levels. ceived one may be quite different.
5
Using the assumptions about the distribution of allow the “simulation time” to reflect actual time for
rawoutputw andself-promotionp describedinSec- realorganizations. The choiceofthe agenttobe fired
i i
tion IIB1, it is possible to calculate the average ac- in each workgroup is deterministic: the worst per-
tual and perceived results at each organization level ceivedperformerisselectedasthecandidateforfiring.
in a situation where the capabilities of eachagent are We have also considered a variant in which a man-
drawn randomly agerthreatenedbya possibilityofbeing fired,if suffi-
cientlyskilledinpoliticalgames,mightpasstheblame
W(k)RANDOM =N(K−k)wR′(K−k+1), (4) to oneofhis orher directreports. Inthis variant,the
existence of scapegoats further improves the chances
where
of those agents who focus on politics instead of the
′ realwork. However,suchblame-shiftingrequireshigh
w =w −p /2. (5)
R 0 max political skills, so we have assumed that it would be
Theoveralloutcomeofthepoliticalactivitiesonthe possible only withprobabilityproportionalthe politi-
real andperceived results of an agentat a givenposi- calskillsofthethreatenedmanager,pi. Forlowvalues
tionaresimply: increaseofpi leadstodecreaseofreal of pi putting the blame to others would be virtually
contribution but increase of the perceived one. De- impossible, but for those who have high values pf pi
pending on the value of C playing politics may prove closer to 1, the security of the manager in question
wouldbe greatly improved,at the expense of his sub-
tobeadvantageous-ornot. Asitturnsouttheresult
depends on the level of the organization, making the ordinates. So,inblame-shiftingscenario,survivalrole
model more life-like. of pi is enhanced.
The vacant positions can be filled either by inter-
nal promotion or by external hiring. This can by
C. Promotion, firing and hiring described by assuming two mechanisms of filling a
given empty post, each with probability being a part
To model the processes of promotion in an organi- of the model. First, there is a probability that the
zationwe needto providesomeassumptionsastothe post will be filled by externally hired agent (proba-
personnel mobility within it. This requires balanc- bility xe). To keep the model close to the real hir-
ing between model simplicity and the need to cover ing process we assume that for each vacant position
realistic situations. The rules proposed apply to or- some applicants with randomly drawn values of wi
ganization levels k ≥ 2. For the top level, there is and piwould be compared (we used 4 candidates in
no competition and no hiring/firing. Real organiza- the simulations). But it is important to remember
tions certainly experience changes at the CEO level, that this process would compare the perceived quali-
and such changes can bring large differences in the ties of the candidates. The same political skills that
overall performance. Charismatic leaders, like Steve are used during employment may be a rough mea-
Jobs, by their vision and management skills can rad- sure of how the candidate presents his or her past
ically change the evolution of their companies. Such achievements and value for the future employer. So,
contributions are, however, impossible to simulate in the hired agent would be the one with the highest
astatisticalcomputermodel. Ourgoalistomodelin- value of wi′/(w0−pmax/2)+C·pi. Itseems a reason-
ternalcompetitionandpromotionmechanismswithin able assumptionthatthe samesusceptibility factorC
an organization, coming from lower levels. To allow thatisusedtodescribethe organization’ssusceptibil-
such focus in our simulations we have assumed that ity to political maneuvering of the employees would
the top manager has no influence on the overall pro- be used for appraisalof candidates. We have alsorun
ductivity, having w =1, and p =0. simulations where no selection of external candidates
1 1
Atlowerlevelsthefiringandpromotionschemeeas- has been performed and thus the new agent would
ier to simulate. At the end of every quarter there simply have a random set of wi, pi values. This al-
is some chance (given by parameter x ) that from lows to study the effects of pre-selection of external
f
eachworkgroupofN employeessubordinatetoagiven candidates.
manager one would be fired. Thus the typical churn Thesecondoptionoffillingavacancyisthroughdi-
rate is the same at every level, being given by x /N, rect promotion of the best performer (again, we mea-
f
and the reason for introducing x is to allow adjust- sure perceived performance!) of the organizational
f
ment of the rate of change in the model. This would leveldirectly below the vacancy. It is possible to con-
6
Figure1: Examplesoforganizationsfromsimulationprogram. Organizationhas4levelsandworkgroupsizeN isalso4.
IntheleftpanelcolorscorrespondtotrueperformanceWi,intherightpanelcolorscorrespondtoperceivedperformance
Ui; green for highest performers in given level, red for lowest values, normalized for each level.
sider two options: local promotion, where the pro- might be correlated.
motedagentisselectedfromdirectsubordinatesunder Depending on the organization the change of the
the vacated position, and global where anyone from scope of activity due to promotion, from direct pro-
the lower level can be picked to fill the vacated post. duction (writing the code, visiting customers, con-
In the preliminary results presented here the global ducting experiments) to managerial tasks of organiz-
model has been used. The promotion will, of course, ing, planning and supervision may be more or less
leaveanothervacancytobefilledatalowerlevel. The gradual. The first promotion, turning a worker into
hiringprocessshouldstartatthehighestvacancyand first line manager introduces the greatest change and
continue down. All the vacancies at the lowest level one could expect that Peter hypothesis to hold. On
are, by their nature, filled by external hiring. the other hand further promotions may involve the
To make the model comparable to previous ‘Peter use of more or less the same set of managerial skills
Principle’studiestwooptionsoftreatingtheagentca- applied to larger groups and responsibilities, which
pacities after apromotionarepossible. They are: the would be better described by the common sense ap-
continuity hypothesis,inwhichtheproductivityat proach. It might make sense then to introduce a
the higher level remains close to the previous one mixed model corresponding to such situation.
w+ =w +δw, (6)
i i
wherew+ denotesagentscapacityonthehigherlevel. D. Simulation considerations
i
Agent’sproductivitychangesbyasmallrandomvalue
of δw, with normaldistribution centered at zero with During simulation process we are looking both at
width of σ . This hypothesis wouldbe applicable to global changes of organization effectiveness depend-
δw
situationswherethetasksatthehigherhierarchylevel ing on the promotion model as well as individual ca-
are somewhat similar to those at a lower level (ad- reer paths and results of individual strategies (given
vancement from programmer to programming team by unchangingvalues ofthe political factor p of each
i
leader,forexample). Ontheotherhand,insituations agent). The simulation steps should correspond to
where the new post calls for totally different set of realistic conditions, e.g. quarters or semesters – pe-
skills(salesmanpromotedtosalesmanagerortomar- riods where typically performance of employees is re-
keting manager position) it is sensible to assume the viewed. Thus we would be interested in, say, up to
Peter hypothesis in which w+ is randomly drawn, 64steps (16 years)– but manyof the interestingphe-
i
without any relation to previous w . For this reason nomena could happen on the shorter timescales. By
i
thepromotionmodes(localorglobal)andthepromo- experience, modern commercial organizations stay in
tion hypotheses (common sense or Peter hypothesis) the same shape (without major reorganizations) for
7
periods of 3-5 years. And, of course, major reorga- Thesecondgroupcontainedcontrolsthatwerevar-
nizations are not covered by the simplistic model de- ied between simulated organizations, describing their
scribed above. The individual results of the simula- maincharacteristics: number of levelsandworkgroup
tionrunsdifferedsignificantly(asdiscussedinSection size, presence or absence of blame-shifting, pere-
IIIA) and we for each combination of parameters we selection sample size for external candidates and, of
have accumulated results of 8000 runs, to obtain av- course,typeofpost-promotionefficiencymodel(Peter
erages and distribution of key characteristics. hypothesis, continuity model) and organization sus-
The key parameters and characteristics of the sim- ceptibility to self-promotion.
ulated organizationwere:
Wepresenthereresultsfortwohierarchies,thefirst
comprised of 5 levels of 5 people in a workgroup, the
• Overall performance of the organization, given
second of only 4 levels but 9 people in a workgroup.
by the averages of effective total result of the
This choice was motivated by a desire to keep the
topmost boss W =W and its changes dur-
TOT 1 overall sizes of the two configurations similar (781 in
ing simulation steps, as well as effective perfor-
the first case, 820 in the second). Also, the number
mances of organization units at different levels,
ofworkersinthe lowest(non-managerial)levelwasof
as given by their bosses’ W . We also recorded
i
the same order (625 vs. 729). Based on the distribu-
the number of new hires compared to internal
tion of w and p defined in Section 2, we can derive
promotions, to check the initial assumptions It i i
two“yardstick”measuresofthetotalorganizationpro-
is worth noting that these parameters are com-
ductivity. Thefirst,whichwewouldcall“neutral pro-
parableto realworlddata,anssuchcomparison
ductivity”, assumes that no self-promotion take place
couldleadtoimprovementsofthemodel(forex-
(p = 0) and that all workers and managers have the
ampleprobabilitiesofexternalhiringdepending i
same effective w′ = w = 1. Then the organization’s
on the level of the vacancy). i i
output is simply given by the number of lowest level
• Monitoring true productivity and self- workers (as managers neither improve nor diminish
promotion factor at various levels of the the results). The other standard is the average pro-
organization. Average hp i for each level k ductivity in a wholly random organization, this time
i k
as well as the average value of raw individual including the negative effects of time and effort lost
productiveness hw i were calculated at each on political games. The values of such static, random
i k
step of the simulations; to check if it is the distributionare,withourchoiceofparameters,rather
political manipulators or the real workers who low, (105 for the 5-by-5 case and 175 for the 4-by-9
move to the upper echelons, as suggested by one). This is, of course, due to the largely negative
common sense. impactofthemanagerialstructure,whereeveryman-
ager decreases the production of his/her department
by a factor of w′ = w −p /2 (0.7 in our case).
R 0 max
III. RESULTS AND DISCUSSION These values are also starting points of the results of
the dynamical simulations, as the starting conditions
used random distribution of agent characteristics. It
The model presented in this work is rather com-
should be noted that the random configuration and
plex, involving several parameters designed to mimic
associated productivity seems highly unrealistic, as
at least some of the crucial aspects of modern orga-
it means that all managers negatively influence the
nizational life. This complexity, however, makes de-
outcome. For this reason, we have used the neutral
rivingcleardependenciesratherdifficult. Forthepur-
productivity as the criterion of the improvement vs.
poseofthispreliminarypaperwedecidedtodividethe
decline of the organization effectiveness in the simu-
system controls into two groups. The first contains
lations. Interestingly enough, some combinations of
those that are static between various simulations, for
parametersresultedinconfigurationsthatwereworse
example the distributions of w and p . For most of
i i
than the random one – negative selection is real, es-
the simulations we have also kept the firing rate x
f
pecially if the organizationitself is under no threatof
and the external hiring rate x fixed. The values of
e
existence nor competition, as is often true for govern-
theseparameterswereselectedtokeepthe“simulation
ment structures.
time” ascloseaspossibletotherealworld,andobtain
reasonable values of the churn ratio and averagetime Despite the fact that in all simulations the pool of
spent as given position. agents’individualcapabilitiesremainedthe same,the
8
finallongtermresultsofthe modelorganizationsvar- leads to strong dependence of the average character-
ied by almost an order of magnitude! At the end of istics of agents on that level on the external hiring
this report we include detailed average results of the process – especially on the results of selection of the
simulations for severalcombinations of model param- external candidates.
eters (Figures 13 to 23). Due to the interplay of the
The most straightforward effects are due to the
processes introduced in our model, separation of the
presence or absence of selection of external candi-
individual contributions is not easy and the impact
dates. We have compared results when only one ex-
of various model parameters requires some detailed
ternal candidate is randomly drawn (denoted 1NH)
analysis.
and when the candidate with best perceived value of
w′/(w − p /2)+ C · p expected productivity is
i 0 max i
chosen from four candidates (denoted 4NH). With-
A. Simulation statistics out selection the expected values of w and p for the
i i
newly hired employees would be w and p /2, re-
0 max
Due to the multiplicative way the managerial con- spectively. AsFig. 5shows,allowingtheorganization
tribution is modelled here, the influence of individual to choose from only 4 candidates significantly influ-
characteristics of managers, especially at high posi- ences the resulting values of w and p and the re-
i i
tions,cansignificantlychangetheoverallproductivity sulting productivity. Such increase in the real pro-
oftheorganization. Asaresultweobserveratherwide ductivity w′ of newhires is especially important for
i
distribution of results between simulation runs. As the lowest level of organization. For the Peter model,
an example, Figure 2 presents distribution functions where only p are kept by an agent upon promotion,
i
of overall productivity W for the Peter model for the increases of w are largely lost at higher levels.
TOT i
various values of the susceptibility factor C, at differ- Forthe continuitymodelbothp andw areinherited
i i
ent stagesof the evolutionstarting fromrandomcon- and, as the new hires participate in later promotion
figuration: after3, 5 and 16 years. Figure 3 presents possibilities the values obtained with pre-selection on
similar data for a set of simulations in the continuity higherlevelsalsoshowanincreasecomparedwithsim-
model. ple random values for external hiring. As a result,
Thewidthsofthedistributionsareratherhigh,with the overall performance of the organization W is
TOT
half-width at half-maximum strongly correlated with higherin the 4NHcasethanin the 1NHcasefor both
the position of the peak center (Fig. 4). In the conti- Peter model and continuity model, but the difference
nuity model we observestrong reductionof the width ismuchhigherforthecontinuitymodel(50-70%com-
of the distributionofW withthe passageoftime, pared to 10-40%, see Fig.6).
TOT
but even after 16 years of continuous evolution, there
Theblame-shiftprocessduringwhichmanagerscan
are still significant differences of results between in-
place the responsibility for the department weak per-
dividual simulation runs. Thus, part of the trends
formance on one of their subordinates acts in a more
observed for average values as functions of model pa-
subtle way. First,it extends the lifetime ofmanagers,
rameters, discussed in the later part of this article,
especially the ones with weak real performance but
maybemaskedbyindividualdifferencesbetweensim-
highvaluesofp . Becausewehaveassumedtheproba-
i
ulation runs. We note here that the averagevalues of
bilityofusingascapegoattobegivenbymanager’sp
i
hp i and hw i for organization level k have similar
i k i k (and independent on C) the effect is the strongestfor
Gaussian distributions.
lowvaluesofC,whereitleadstomuchlargeraverage
valuesofp atmid-manageriallevelsforsmallC. This
i
isespeciallyvisibleearlyinthesimulations,withinthe
B. Evolution of individual agent characteristics first3yearsoforganizationevolutionfromtherandom
initial state. The overall effects of the possibility to
We note first that the behavior of the lowest and shift the blame for weak performancearedifferent for
themid-rangehierarchylevelsisdifferent. Thisisdue the continuity and Peter models (see Fig. 7). For the
to radically different mechanisms of changes in the Peter model there is a general but small decrease in
agents occupying these levels. The ratio of vacated organizationproductivity when blame-shifting is pos-
positions to level size was set as constant for levels sible. For the continuity model there is a large de-
below the topmost. It should be noted, however,that crease of productivity in initial stages that gets grad-
the lowest level is filled entirely from outside, which ually compensated at later times, so that for large C
9
Year3,4NH,noblameshift
0 200 400 600 800 1000 1200
W
TOT
Year5,4NH,noblameshift
0 200 400 600 800 1000 1200
W
TOT
Year16,4NH,noblameshift
0 200 400 600 800 1000 1200
W
TOT
Figure 2: Distribution of WTOT values for Peter model (organization with 5 levels with 5 positions in a workgroup)
dependingon C value after 3, 5 and 16 years. Probabilities of WTOT are verywell described by Gaussian distributions.
Increased values of C shift the center of the distribution to smaller values and decrease the width of the distribution –
top left curvesineachpanelcorrespondtoC =5, bottomrighttoC =0.01. Thedistributionsweredisplaced vertically
for clarity for increasing C values.
10
Year3,4NH,noblameshift
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
W
TOT
Year5,4NH,noblameshift
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
W
TOT
Year16,4NH,noblameshift
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
W
TOT
Figure3: DistributionofWTOT valuesforcontinuitymodel(organization with5levelswith5positionsinaworkgroup)
depending on C value after 3, 5 and 16 years. Probabilities of WTOT are verywell described by Gaussian distributions.
The distributions were displaced vertically for clarity for increasing C values.
