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Centralbanks’votingcontest
21
2.
TheBankofEngland(BoE)votingscheme(
n
=9).Thedecisionisequal
tothemedianvotewhenthenumberofvotesisodd,andto0ifitiseven,
thatis:
Ψt={k:Σ
I
t
(κ)
+Σ
I
t
(κ)
=n−Σ
I
t
(κ)
}×(−1)n.
κ<k
κ>k
κ1k
3.
TheBankofSweden(BoS)votingscheme(
n
=6).Thisisathree-way
majorityvotingsystem,wherethedecisionistakenbythemajorityof
votesas
−
1,0and1,withtheChairhavingacastingvoteifthereisatie.
Thedecisionisdefinedas:Ψ
aone-elementset,meaningthereisnotie,or:Ψ
l
t
=
{k
:
max
(
I
t
(k)
)
t
}
=
andΨ
{κ
:
Iκ
t
c,t
=Ψ
=1;
l
t
κ∈
ifΨ
Ψ
l
t
l
t}
is
if|κ|=1,andΨt=0otherwise.
4.
TheBankofCanada(BoC)votingscheme(
n
=6).Thisisathree-way
majorityvotingscheme,butwithoutacastingvote.Ifthereisatie,Ψ
t
=0.
5.
TheBankofAustralia(BoA)votingscheme.Thevotingschemeisasin
BoC,butn=9.
6.
TheBankofPoland(BoP)votingscheme(
n
=10).Thisisanabsolute
majorityvotingschemesuchthatthevotersfirstvotefortheΨ
t
=1motion.
Ifthereisnoabsolutemajority,orifthereisatieandthemotionisnot
supportedbytheGovernor,thereisanothervotefortheΨ
t
=
−
1motion.
Ifthevotingisnotdecisive,Ψ
t
=0.Hence:Ψ
l
t
=
{k
:
max
[(
I
t
(k)
/n
)
−
0
.
5]
}
if(
notie,thenΨ
I
t
(k)
/n
)
>
0
.
t
5andΨ
=Ψ
l
t
;otherwiseΨ
l
t
=0otherwise.IfΨ
t
=
{κ
:
Iκ
l
t
c,t
isaone-elementset,meaning
=1;
κ∈
Ψ
l
t}
if
|κ|
=1and
Ψt=0ifκ=0.
Thesevotingalgorithmsaresomewhatstylisedandmightnotfullyreflect
therealityofvoting.Firstly,itisdifficulttofindclearinformationonthe
schemeofhowvotesinindividualcentralbanksareaggregated.Thesettings
givenabovearebasedonfragmentaryinformationfromtheminutesandother
documentsofvariouscentralbanks,andinsomecasesonprivateinformation.
Secondly,somebanksarequiteliberalinapplyingthevotingrules.Thereis
someanecdotalevidenceofvotingonmorethanonemotionsimultaneously
andofexceptionalvotingrulesbeingapplied.Consequently,thealgorithms
aboveshouldbetreatedasasomewhatarbitrarystylisationoftherealvoting
processes.
Itmightbethatallthesixschemesdescribedaboveresultindifferent
decisionsbeingtakenforthesamesetofextraneousinformationdeliveredto
thevoters.Itispossibletoevaluatehowfareachschemetendstotakeactive
decisions,thatissuchthat
|
Ψ
t|
=1,bycomputingthevotingactivityindex
(
VAI
)bydividingthenumberofallpossibleactivedecisionsbythetotal
numberofdifferentcombinationsofdecisionsavailabletoagivencomposition
