Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang
Univrsity of California BrklyThias issu is xplaind in thisgndrClark was ausd of having killd hrSallyhild at 11 wks of ag and hr sondfirstat 8 wks of ag. Sir Roy Madow, ahildand onsultant padiatriian, tstifidprofssoran xprt witnss that th proaility of twoasin th sam family dying from suddnhildrndath syndrom (SIDS, also alld otinfantwas approximatly 1 in 73 million. Thisdath)a gross undrstimat, arrivd at y takingwasproaility of a singl SIDS dath (1 inthand squaring it, with th assumption that8,543)proaility of suh daths is unorrlatdthinfants. Howvr, that assumptiontwnunjustifid, and in fat th opposit wouldwastru if a gnti prdisposition to SIDSRporting on th inidnt, Ray Hillxists.onludd that “aftr a first ot dath th(2004)of a sond om gratly inrasd”,hansa ot dath mothr is ausd“Whnmurdr, th prosution somtimsofa tati suh as th following.mploysth parnts ar afflunt, in a stalIfand non-smoking, thrlationshipwill laim that th hansprosutionth dath ing natural ar gratlyofand y impliation that thrdud,trms: Ar univrsitySarhiasd? Simpson’sadmissionsinrasd. But this impliation isgratlyfals, aus th vry sam fatorstotallymak a family low risk for ot dathwhihmak it low risk for murdr.”alsofaulty mathmatis did not stop thr.Thif th 1-in-73 million assssmnt wasEvnthis was not th proaility ofaurat,innon, ut rathr an a prioriClark’sthat ndd to wighdproailityth a priori proailitis of thagainstof thm vry unlikly—altrnativs—allwr:whih1. two sussiv SIDS daths in th2. doul homiid3. othr possiilitis (suh as on homiidwas an instan of th “prosutor’sItCruially, proaility stimatsfallay”.outoms 1 and 2 should hav nofin th statistial analysis of thompardClark was onvitd in 1999.prosution.Royal Statistial Soity raisd onrnsThth dision, issuing a prss rlasaoutstatd th following.thatth rnt highly-puliisd as of R v. Sally Clark, a mdial xprt witnss drw on pulishd“Into otain a figur for th frquny of suddn infant dath syndrom in familis having som ofstudisharatristis of th dfndant’s family. H wnt on to squar this figur to otain a valu of 1 in 73thfor th frquny of two ass of SIDS in suh a family.millionapproah is, in gnral, statistially invalid. It would only valid if SIDS ass arosThiswithin familis, an assumption that would nd to justifid mpirially. Not onlyindpndntlyno suh mpirial justifiation providd in th as, ut thr ar vry strong a priori rasons forwasthat th assumption will fals. Thr may wll unknown gnti or nvironmntalsupposingthat prdispos familis to SIDS, so that a sond as within th family oms muh morfatorslikly.IV. EthicsIV. Ethicsparadox part 2 YouTulinkd vido.Box 11.5: Faulty statistics and the “prosecutor’s fallacy”(Hill 2004)familyand also statd th following.and on SIDS).351
IV. Ethicswll-puliisd figur of 1 in 73 million thus has no statistial asis … . Th tru frquny of familisThtwo ass of SIDS may vry muh lss inriminating than th figur prsntd to th jury at trial.withfrom its invalidity, figurs suh as th 1 in 73 million ar vry asily misintrprtd. Som prssAsidat th tim statd that this was th han that th daths of Sally Clark’s two hildrn wrrportsThis (mis-)intrprtation is a srious rror of logi known as th Prosutor’s Fallay. Th juryaidntal.to wigh up two ompting xplanations for th ais’ daths: SIDS or murdr. Two daths yndsor two murdrs ar ah quit unlikly, ut on has apparntly happnd in this as. What mattrsSIDSth rlativ liklihood of th daths undr ah xplanation, not just how unlikly thy ar undr onisas of R v. Sally Clark is on xampl of a mdial xprt witnss making a srious statistial rror,Thwhih may hav had a profound fft on th outom of th as.onmany sintists hav som familiarity with statistial mthods, statistis rmains a spialisdAlthoughTh Soity urgs th Courts to nsur that statistial vidn is prsntd only y appropriatlyara.statistial xprts, as would th as for any othr form of xprt vidn.” (Royal Statistialqualifid2001)Soityonvition was ovrturnd in 2003Clark’svidn mrgd that th pathologistaftrxamind oth ais had withhldwhothat on of thm may hav didvidna rviw of hundrds of similar ass,Aftrtwo womn onvitd of murdringanothrhildrn had thir onvitionsthirA third woman who hadovrturnd.n ausd of murdring hr thralsowas aquittd in Jun 2003. Royhildrnhad tstifid as an xprt witnss inMadowas, dsriing th unliklihood ofahop with th thial hallngs arising fromToprodution or appliation of mathmatialtha numr of initiativs havknowldg,rlativly rntly. In th aftrmathformdth Camridg Analytia sandal, whihofdisuss at lngth in Chaptrs 2 and 3,wCamridg Univrsity sholars, Mauritwoand Pirs Bursill-Hall, st up thChiodoin Mathmatis (EiM) Projt, whihEthisits first onfrn in 2018. “Soorganizdas w know, thr is no univrsity in thfarthat urrntly offrs a wid-rangingworldot daths in a singl family. H wasmultiplfrom th mdial rgistr y thrmovdMdial Counil in 2005 for sriousGnralmisondut, ut latr rinstatd.profssionalor, mor spifially, statistisMathmatisusd rgularly in riminal lgal ass.isvidn, and its rlatd statistialDNAis rgularly usd oth inintrprtations,invstigations and on tlvision,riminalit is portrayd as fool-proofwhrHow should ourts nsurvidn.jurors ar apal of undrstandingthatmathmatis, or that lawyrs do notthmathmatial argumnts?misusmathmatial thial training forspifiallythy writ (Chiodo, Bursill-mathmatiians”,2018). To fill this gap, thy hav dsigndHallpilotd a ours alld “Ethis for thandmathmatiian”, a sris of ight hourlongworkinglturs. Follow th link to larn mortrms: Ltur ours:Sarhfor th workingEthis11xplanation. …from an inftion.IV.3 Professional standardsaout th issus it xplors.mathmatiian Chiodo352
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Univrsity of California Brkly
Th
ias issu is xplaind in this
gndr
Clark was ausd of having killd hr
Sally
hild at 11 wks of ag and hr sond
first
at 8 wks of ag. Sir Roy Madow, a
hild
and onsultant padiatriian, tstifid
profssor
an xprt witnss that th proaility of two
as
in th sam family dying from suddn
hildrn
dath syndrom (SIDS, also alld ot
infant
was approximatly 1 in 73 million. This
dath)
a gross undrstimat, arrivd at y taking
was
proaility of a singl SIDS dath (1 in
th
and squaring it, with th assumption that
8,543)
proaility of suh daths is unorrlatd
th
infants. Howvr, that assumption
twn
unjustifid, and in fat th opposit would
was
tru if a gnti prdisposition to SIDS
Rporting on th inidnt, Ray Hill
xists.
onludd that “aftr a first ot dath th
(2004)
of a sond om gratly inrasd”,
hans
a ot dath mothr is ausd
“Whn
murdr, th prosution somtims
of
a tati suh as th following.
mploys
th parnts ar afflunt, in a stal
If
and non-smoking, th
rlationship
will laim that th hans
prosution
th dath ing natural ar gratly
of
and y impliation that th
rdud,
trms: Ar univrsity
Sarh
iasd? Simpson’s
admissions
inrasd. But this impliation is
gratly
fals, aus th vry sam fators
totally
mak a family low risk for ot dath
whih
mak it low risk for murdr.”
also
faulty mathmatis did not stop thr.
Th
if th 1-in-73 million assssmnt was
Evn
this was not th proaility of
aurat,
innon, ut rathr an a priori
Clark’s
that ndd to wighd
proaility
th a priori proailitis of th
against
of thm vry unlikly—
altrnativs—all
wr:
whih
1. two sussiv SIDS daths in th
2. doul homiid
3. othr possiilitis (suh as on homiid
was an instan of th “prosutor’s
It
Cruially, proaility stimats
fallay”.
outoms 1 and 2 should hav n
of
in th statistial analysis of th
ompard
Clark was onvitd in 1999.
prosution.
Royal Statistial Soity raisd onrns
Th
th dision, issuing a prss rlas
aout
statd th following.
that
th rnt highly-puliisd as of R v. Sally Clark, a mdial xprt witnss drw on pulishd
“In
to otain a figur for th frquny of suddn infant dath syndrom in familis having som of
studis
haratristis of th dfndant’s family. H wnt on to squar this figur to otain a valu of 1 in 73
th
for th frquny of two ass of SIDS in suh a family.
million
approah is, in gnral, statistially invalid. It would only valid if SIDS ass aros
This
within familis, an assumption that would nd to justifid mpirially. Not only
indpndntly
no suh mpirial justifiation providd in th as, ut thr ar vry strong a priori rasons for
was
that th assumption will fals. Thr may wll unknown gnti or nvironmntal
supposing
that prdispos familis to SIDS, so that a sond as within th family oms muh mor
fators
likly.
IV. Ethics
IV. Ethics
paradox part 2 YouTu
linkd vido.
Box 11.5: Faulty statistics and the “prosecutor’s fallacy”
(Hill 2004)
family
and also statd th following.
and on SIDS).
351