Exit, Voice, and Loyalty Model - Wikipedia
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The Exit, Voice, Loyalty (EVL) model or Exit, Voice, Loyalty, Neglect (EVLN) is used in the fields of comparative politics and organizational behavior.
Exit,Voice,andLoyaltyModel
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Frameworkformodellingpoliticalandeconomicbehavior
TheEVLModelwiththeCitizenasplayer1andtheGovernmentasplayer2.Eisthevaluethecitizengetsfromexiting,ListhevaluetheGovernmentgetsfromtheCitizen'sloyalty,andcisthecosttheCitizenusingtheirvoice.Inthismodel,thebenefitupforgrabsbetweentheCitizenandtheGovernmentisworth1.
TheExit,Voice,Loyalty(EVL)model[1]orExit,Voice,Loyalty,Neglect(EVLN)isusedinthefieldsofcomparativepoliticsandorganizationalbehavior.Itisanextensiveformgameusedtomodelinteractionstypicallyinvolvingnegativechangestooneplayer'senvironmentbyanotherplayer.[1]TheseconceptsfirstappearedinAlbertHirschman'smorebroadlyfocused1970book,Exit,Voice,andLoyalty:ResponsestoDeclineinFirms,Organizations,andStates.[2]Acommonuseinpoliticalscienceisbetweencitizensandtheirgovernment.UsuallyinthisusetheCitizenplayerisanygroupwithinasocietyrangingfromasingleindividualtothecitizenryasawhole.[3]
Contents
1Model
1.1FormalDefinition
1.2TheoreticalDefinition
1.3Dependent/AutonomousGovernmentsandCredibleExitThreats
2DifferentOutcomes
3Applications
3.1DependentGovernment
3.2Protests
4Exit,Voice,Loyalty,NeglectModel
4.1Exit
4.2Voice
4.3Loyalty
4.4Neglect
5References
Model[edit]
TheEVLModelinvolvestwoagentsandtheirresponsestoachangeinitiatedbeforethegamebegan.ThefirstagentiscommonlyreferredtoastheCitizenandthesecondiscommonlyreferredtoastheGovernment.EVLassumesthatthechangeimplementedbeforethegamebeganwasperformedbytheGovernmentandnegativelyharmstheCitizen.
FormalDefinition[edit]
TheformaldefinitionofEVListhefollowing:[3]
Therearetwoplayers:
N
=
{
Citizen
,
Government
}
{\displaystyleN=\{{\text{Citizen}},{\text{Government}}\}}
.The
Citizen
{\displaystyle{\text{Citizen}}}
movesfirst,andchoosesamongthreeactions
{
exit
,
voice
,
loyalty
}
{\displaystyle\{{\text{exit}},{\text{voice}},{\text{loyalty}}\}}
.Ifthe
Citizen
{\displaystyle{\text{Citizen}}}
chooses
voice
{\displaystyle{\text{voice}}}
,then
Government
{\displaystyle{\text{Government}}}
caneither
respond
{\displaystyle{\text{respond}}}
or
ignore
{\displaystyle{\text{ignore}}}
.Ifthe
Government
{\displaystyle{\text{Government}}}
choosesto
ignore
{\displaystyle{\text{ignore}}}
,the
Citizen
{\displaystyle{\text{Citizen}}}
thenchoosesbetween
exit
{\displaystyle{\text{exit}}}
or
ignore
{\displaystyle{\text{ignore}}}
.Subsequenttothis(andanyotheractionchoices),thegameterminates.
Formally,thisisrepresentedbythesetofhistories
H
=
{
∅
,
(
exit
)
,
(
voice
)
,
(
loyalty
)
,
(
voice
,
respond
)
,
(
voice
,
ignore
)
,
(
voice
,
ignore
,
exit
)
,
(
voice
,
ignore
,
loyalty
)
}
.
{\displaystyleH=\{\emptyset,({\text{exit}}),({\text{voice}}),({\text{loyalty}}),({\text{voice}},{\text{respond}}),({\text{voice}},{\text{ignore}}),({\text{voice}},{\text{ignore}},{\text{exit}}),({\text{voice}},{\text{ignore}},{\text{loyalty}})\}.}
Theterminalhistories,uponreachingwhichthegameterminates,isgivenby
Z
=
{
(
exit
)
,
(
loyalty
)
,
(
voice
,
respond
)
,
(
voice
,
ignore
,
exit
)
,
(
voice
,
ignore
,
loyalty
)
}
.
{\displaystyleZ=\{({\text{exit}}),({\text{loyalty}}),({\text{voice}},{\text{respond}}),({\text{voice}},{\text{ignore}},{\text{exit}}),({\text{voice}},{\text{ignore}},{\text{loyalty}})\}.}
Forallotherhistories,oneofthetwoplayersmakesamove,andthisisgivenbytheplayerfunction
P
(
∅
)
=
Citizen
,
P
(
voice
)
=
Government
,
P
(
voice
,
ignore
)
=
Citizen
.
{\displaystyleP(\emptyset)={\text{Citizen}},\P({\text{voice}})={\text{Government}},\P({\text{voice}},{\text{ignore}})={\text{Citizen}}.}
Theutilityfunctionofthe
Citizen
{\displaystyle{\text{Citizen}}}
isdefinedas
u
C
(
exit
)
=
E
,
u
C
(
loyalty
)
=
0
,
u
C
(
voice
,
respond
)
=
1
−
c
,
{\displaystyle\u_{C}({\text{exit}})=E,\u_{C}({\text{loyalty}})=0,\u_{C}({\text{voice}},{\text{respond}})=1-c,}
u
C
(
voice
,
ignore
,
exit
)
=
E
−
c
,
u
C
(
voice
,
ignore
,
loyalty
)
=
0
−
c
.
{\displaystyle\u_{C}({\text{voice}},{\text{ignore}},{\text{exit}})=E-c,\u_{C}({\text{voice}},{\text{ignore}},{\text{loyalty}})=0-c.}
Inwords,the
Citizen
{\displaystyle{\text{Citizen}}}
incursacostof
c
{\displaystylec}
whenevertheychoosetoraisetheir
voice
{\displaystyle{\text{voice}}}
,andifthe
Government
responds
{\displaystyle{\text{Government}}\{\text{responds}}}
,theygetapayoffof
1
{\displaystyle1}
.Irrespectiveofthischoice,theycanchooseto
exit
{\displaystyle{\text{exit}}}
forapayoffof
E
{\displaystyleE}
orremain
loyal
{\displaystyle{\text{loyal}}}
forpayoffofzero.
Similarly,thepayofffunctionofthe
Government
{\displaystyle{\text{Government}}}
isdefinedas
u
G
(
exit
)
=
1
,
u
G
(
loyalty
)
=
1
+
L
,
u
G
(
voice
,
respond
)
=
L
,
u
G
(
voice
,
ignore
,
exit
)
=
1
,
u
G
(
voice
,
ignore
,
loyalty
)
=
1
+
L
.
{\displaystyle\u_{G}({\text{exit}})=1,\u_{G}({\text{loyalty}})=1+L,\u_{G}({\text{voice}},{\text{respond}})=L,\u_{G}({\text{voice}},{\text{ignore}},{\text{exit}})=1,\u_{G}({\text{voice}},{\text{ignore}},{\text{loyalty}})=1+L.}
Inwords,the
Government
{\displaystyle{\text{Government}}}
incursacostofonefor
responding
{\displaystyle{\text{responding}}}
tothe
Citizen'svoiced
{\displaystyle{\text{Citizen'svoiced}}}
concerns,andgainsapayoffof
L
{\displaystyleL}
ifthe
Citizen
{\displaystyle{\text{Citizen}}}
doesnot
exit
{\displaystyle{\text{exit}}}
.
TheoreticalDefinition[edit]
TheprecursorypolicythattheGovernmenthasimplementedhastheeffectofremovingabenefitwiththevalueof1fromtheCitizenandgivingittotheGovernment.Thevaluewaschosentobe1sothatallcomparisonswithinthegamecaneasilybeconvertedtoratiosandthenadaptedtoothersituationswherethetruevalueofthebenefitisknown.
InEVL,allpossibleactionsthatcanbetakenbytheCitizenaregroupedintooneofthreeoptions.ExitoptionsarethoseinwhichtheCitizenacceptsthelossofthebenefitandinsteadalterstheirbehaviortogetthebestpossiblealternative.Examplescouldincluderelocatingassetstoavoidanewtax,reincorporatingabusinesstoavoidnewregulations,buyinggoodsfromadifferentstorewhenthequalityoftheoriginaldiminishes,votingouttheincumbent,etc.[1]ThepayoffofanExitoptionfortheCitizenisthevariableEandtheGovernmentgetstokeepthe1ittookinitially.[1][3]
LoyaltyoptionsareoneswheretheCitizenchoosestoputupwiththenewpolicyandnotaltertheirbehavior.ThepayofffortheCitizenis0astheydecidetotakethelossandtheGovernmentreceivesthe1ittookplusthevalueoftheCitizen'sLoyalty.ThevalueoftheCitizen'sLoyaltyisthevariableL.[1][3]
VoiceoptionsarewheretheCitizenmakesanactiveefforttoshowtheirdissatisfactionwiththenewpolicyandtriestogettheGovernmenttochangeitsmind.Examplescouldbelobbying,protesting,petitioning,etc.[1]VoiceoptionsdonothaveimmediatepayoffsbutareintendedtogivetheGovernmentachancetoRespondtotheCitizenandrevertthepolicy.IntheeventtheGovernmentdoesRespond,thepayofffortheCitizenisthe1theGovernmentinitiallytookminusthecostofusingVoice.Thiscostisthevariablec.IftheGovernmentchoosestoIgnorethentheCitizencanstillExitorremainLoyal.NomatterwhattheCitizenchooses,theystillhavetobearthecostofusingtheirVoiceandsothepayoffforExitwouldbeE-cand0-cforremainingLoyal.TheGovernmentwouldreceivethepayoffofL(thevalueoftheCitizen'sLoyalty)iftheychosetoRespondandrevertthepolicy,1iftheychosetoIgnoreandtheCitizenExits,and1+LiftheyIgnoreandtheCitizenchoosestoremainLoyal.[1][3]
Dependent/AutonomousGovernmentsandCredibleExitThreats[edit]
NashEquilibriaforaDependentGovernment(L>1)andaCitizenwithaCredibleExitThreat(0
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