Sch amm, Joshua Benjamin; Lich e s, Ma cel
A icle — Published Ve sion
Incen i e alignmen in ancho ed MaxDi yields supe io
p edic i e alidi y
Ma ke ing Le e s
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Sch amm, Joshua Benjamin; Lich e s, Ma cel (2024) : Incen i e alignmen in
ancho ed MaxDi yields supe io p edic i e alidi y, Ma ke ing Le e s, ISSN 1573-059X, Sp inge
US, New Yo k, NY, Vol. 36, Iss. 1, pp. 1-16,
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h ps://doi.o g/10.1007/s11002-023-09714-2
1 3
Incen i e alignmen inancho ed MaxDi yields supe io
p edic i e alidi y
JoshuaBenjaminSch amm1,2 · Ma celLich e s2
Accep ed: 26 Decembe 2023 / Published online: 11 Janua y 2024
© The Au ho (s) 2024
Abs ac
Maximum Di e ence Scaling (MaxDi ) is an essen ial me hod in ma ke ing con-
ce ning o ecas ing consume pu chase decisions and gene al p oduc demand.
Howe e , he use ulness o adi ional MaxDi s udies su e s om wo limi a ions.
Fi s , i measu es ela i e p e e ences, which p e en s p edic ing how many consum-
e s would ac ually buy a p oduc and impedes compa ing esul s ac oss espond-
en s. Second, ma ke esea che s apply MaxDi in hypo he ical se ings ha migh
no e eal alid p e e ences due o hypo he ical bias. The i s limi a ion has been
add essed by implemen ing ancho ed MaxDi a ian s. In con as , he la e limi-
a ion has only been a ge ed in o he p e e ence measu emen p ocedu es such as
conjoin analysis by applying incen i e alignmen . By in eg a ing ancho ed MaxDi
(i.e., di ec s. indi ec ancho ing) wi h incen i e alignmen (p esen s. absen ) in a
2 × 2 be ween-subjec s p e egis e ed online expe imen (n = 448), he cu en s udy
is he i s o add ess bo h h ea s. The esul s show ha incen i e-aligning MaxDi
inc eases he p edic i e alidi y ega ding consequen ial p oduc choices—impo -
an ly—independen ly o he ancho ing me hod. In con as , hypo he ical MaxDi
a ian s o e es ima e gene al p oduc demand. The a icle concludes by showcasing
how he manage ial implica ions d awn om ancho ed MaxDi di e depending on
he ou es ed a ian s. In addi ion, we p o ide he i s incen i e-aligned MaxDi
benchma k da ase in he ield.
Keywo ds Bes -wo s scaling (BWS)· Incen i e alignmen · Ma ke esea ch
me hods· Ancho ed maximum di e ence scaling (MaxDi )· P edic i e alidi y·
P e e ence measu emen
* Ma cel Lich e s
ma cel.lich e s@o gu.de
Joshua Benjamin Sch amm
[email p o ec ed]hemni z.de
1 Facul y o Economics, Chemni z Uni e si y o Technology, Chemni z, Saxony, Ge many
2 Chai o Ma ke ing, Facul y o Economics andManagemen , O o on Gue icke Uni e si y
Magdebu g, Magdebu g, Saxony-Anhal , Ge many
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Ma ke ing Le e s (2025) 36:1–16
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1 In oduc ion
Companies con inuously y o in oduce success ul p oduc s ha i consume s’
needs. Maximum Di e ence Scaling (he ea e MaxDi , see Lou ie e e al., 2013)
is a p e e ence elici a ion echnique o en applied in ma ke esea ch o assess con-
sume s’ needs and design u u e p oduc s acco dingly. S udy pa icipan s he eby
answe mul iple MaxDi asks ( ypically comp ising h ee o ou al e na i es) and
indica e he bes and he wo s al e na i es (Lou ie e e al., 2013). Typical MaxDi
use cases a e es ing di e en p oduc la o s (e.g., Ch zan & O me, 2019, p.4), p i-
o i izing p oduc a ibu es (e.g., Rausch e al., 2021), o es ing ad e ising claims
(e.g., Chapman & Rodden, 2023, p.195).
MaxDi was ini ially in oduced as an al e na i e o anking and a ing scales
(Finn & Lou ie e, 1992) o o e come issues such as ha pa icipan s a e no ading
o be ween i ems when answe ing a ing ba e ies o he cogni i e bu dens o ank-
ing a high numbe o i ems (Lou ie e e al., 2013). Nowadays, howe e , MaxDi
is also men ioned in he same b ea h as conjoin analysis, which is o en applied
in business o ecas ing. In con as o conjoin me hods such as choice-based con-
join (he ea e CBC), MaxDi is no used o p edic he success o holis ic p oduc
concep s, including p oduc p ices in ma ke simula ions. Ins ead, p oduc a ibu e
le els o consume needs (e.g., oppings on a pizza, see Chapman & Rodden, 2023)
cons i u e he al e na i es.
In he li e a u e, MaxDi is also known as bes -wo s scaling (he ea e BWS)
case 1. Besides BWS case 1 (MaxDi ), he e a e wo mo e BWS cases, namely case
2 (p o ile case) and case 3 (mul i-p o ile case). In case 2, pa icipan s choose he
bes and wo s a ibu e le el om a p o ile ha consis s o mul iple a ibu es (e.g.,
Flynn & Ma ley, 2014, p.183). Case 3 esembles he adi ional CBC; howe e , pa -
icipan s mus also choose he wo s al e na i e besides he bes al e na i e (e.g.,
Mühlbache e al., 2016). The p esen esea ch ocuses exclusi ely on case 1 (i.e.,
MaxDi ), which has gained impo ance in ma ke esea ch p ac ice in ecen yea s
(Saw oo h So wa e Inc. 2022b). Howe e , his end is no ye e lec ed in academic
ma ke ing esea ch.1
One o he p esen a icle’s wo goals is o ini ia e e hinking he common
MaxDi p ac ices owa d using holis ic p oduc concep s wi h co esponding
p ices as al e na i es in MaxDi (see Fig.1A, which illus a es he MaxDi asks
o he epo ed s udy). The s imuli in a MaxDi a e lis i ems (Flynn & Ma ley,
2014, p.181) consis ing o only one holis ic p oduc /cha ac e is ic (e.g., di e en
so d ink la o s). In each ask, pa icipan s see di e en i ems and choose bo h he
bes and he wo s -liked al e na i e (Lou ie e e al., 2013), he e o e p o iding mo e
in o ma ion pe ask han in, o example, CBC. Impo an ly, MaxDi does no pe -
mu e combina ions o le els o di e en a ibu es ac oss hese i ems, as is usually
1 A li e a u e e iew (Web o Science, a icles published be ween 2000 and 2023, sea ch e ms (Müh-
lbache e al., 2016): “Bes -Wo s -Scaling” OR “MaxDi ” OR “Maximum Di e ence Scaling”) o he
op ma ke ing jou nals and Saw oo h So wa e Con e ence pape s is p esen ed in TableA1 in he Web
Appendix.
3
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Ma ke ing Le e s (2025) 36:1–16
seen in conjoin s udies (Flynn & Ma ley, 2014, p.181). This has wo ad an ages
compa ed o CBC: Fi s , i allows pa icipan s o e alua e all p oduc s o in e es
in a MaxDi since a comple e design ( s. ac ional design) can be implemen ed.
Fig. 1 T ansla ed sc eensho s o MaxDi a ian s in he p esen s udy
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Ma ke ing Le e s (2025) 36:1–16
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Second, he pa icipan s do no ha e o assess un ealis ic p oduc combina ions (e.g.,
cheap p oduc s a p emium p ices).
MaxDi ’s ul ima e pu pose is o ecas ing u u e pu chases, making p edic i e
alidi y a cen al ene . The e o e, esea che s cons an ly seek ways o imp o e he
p edic ions d awn om MaxDi s udies (e.g., Ch zan & Pei z, 2019; Lage k is
e al., 2012) since educing p edic ion e o s lowe s he company’s cos (Hause
e al., 2014).
Two d awbacks limi he use ulness o he adi ional MaxDi s udies, and he
second goal o he p esen a icle is o e alua e solu ions o hese issues. Fi s , a-
di ional MaxDi s udies measu e ela i e ins ead o absolu e p e e ences because
pa icipan s canno indica e ha none o he i ems p esen ed is an ac ual pu chase
op ion (Lou ie e e al., 2013). This is accep able i manage s a e only in e es ed in
anking he i em lis . Howe e , i hey wan o know whe he , o example, p oduc s
a e ac ually conside edas pu chase op ion, adi ional MaxDi is no applicable o
his ype o ques ion (Ch zan & O me, 2019, p.86). Mo eo e , i he goal is o es i-
ma e pu chase likelihood o o simula e a ealis ic ma ke si ua ion, no including a
no-buy al e na i e lacks ealism (Lich e s e al., 2015) and ul ima ely hu s p edic-
i e alidi y. Second, esea che s and p ac i ione s ha e conduc ed MaxDi s udies
exclusi ely in hypo he ical se ings whe e pa icipan s migh be less mo i a ed o
e eal hei ue p e e ences since hei choices do no bea economic consequences
(Ding e al., 2005).
To add ess he i s issue, esea che s de eloped, among o he s, he
di ec ancho ed (La e y, 2010; O me, 2009b) and he indi ec ancho ed (O me,
2009a; de eloped by Jo dan Lou ie e) MaxDi . Bo h ancho ing app oaches enable
es ima ing an ancho in he u ili y space o lis i ems, which b ings he esul s o
a MaxDi o an absolu e scale. This ancho can se e as a consume ’s no-buy
h eshold when he MaxDi and ancho ques ions a e adequa ely amed (see
Fig.1B and C). To o e come he second issue, esea che s in oduced incen i e
alignmen o p e e ence elici a ion me hods o he han MaxDi . Ex an s udies
in his ield ha e mainly ocused on CBC s udies and ha e p o ed incen i e
alignmen ’s e ec i eness in inc easing p edic i e alidi y o consequen ial
p oduc -choice asks (e.g., Ding e al., 2005). Al hough he implemen a ion o
ancho ed MaxDi enables he es ima ion o he no-buy u ili y (i.e., he ou side
good’s u ili y) and, he e o e, also makes consequen ial p oduc choices a alid
al e na i e in MaxDi s udies, an equi alen p oposal o an incen i e-aligned
(ancho ed) MaxDi s udy is s ill lacking (see Table A1 in he Web Appendix,
he ea e WA).
The p esen esea ch add esses his gap and guides ma ke esea che s in
deciding whe he applying incen i e alignmen when conduc ing MaxDi is
wo h conside ing and whe he hey should p e e a speci ic ancho ing app oach.
Such an endea o is necessa y o mul iple easons. On he one hand, one can
a gue ha in MaxDi , any measu es ha seek o enhance pa icipan mo i a-
ion (i.e., incen i e alignmen ) migh ha e only a limi ed e ec since MaxDi
asks (compa ed o CBC asks) a e ela i ely simple pe se (e.g., Lage k is e al.,
2012), which could po en ially weaken he incen i e alignmen ’s o e all e ec .
On he o he hand, al hough ancho ed MaxDi is al eady applied in comme cial
5
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Ma ke ing Le e s (2025) 36:1–16
so wa e (i.e., Saw oo h So wa e; La e y, 2010; O me, 2009a), esea ch on his
opic is lacking in he op ma ke ing jou nals. In he academic li e a u e, adi-
ional (unancho ed) MaxDi s ill domina es, which, as discussed abo e, does no
enable he ex ac ion o much in o ma ion ele an o ma ke ing ques ions and
ealis ic ma ke simula ions. This pape , he e o e, aims o inc ease awa eness
o he me hod’s ad ancemen s. Finally, his pape is he i s o p o ide MaxDi
da ase s wi h consequen ial p oduc choices o e alua e p edic i e alidi y ( he
Open Science F amewo k, he ea e OSF, p o ides he comple e da a and R anal-
ysis sc ip s: h ps:// os . io/ 5h4 k/). This unique da a can be he basis o esea ch-
e s o e alua e u he ques ions, o example, he abili y o di e en modeling
app oaches o os e p edic i e alidi y.
Ou esul s highligh ha incen i e-aligned MaxDi bea s supe io p edic-
i e alidi y, while hypo he ical MaxDi s udies o e es ima e he gene al p od-
uc demand, which may ha e de as a ing downs eam consequences o compa-
nies. Wi h ou esea ch, we aim o ini ia e a e hink in ma ke esea ch owa d
a s onge emphasis on incen i e-aligned p e e ence measu emen echniques. In
pa icula , incen i e-aligned ancho ed MaxDi a ian s (when amed as p oduc
decisions) migh cons i u e a ui ul al e na i e o mo e complex CBC s udies.
2 Concep ual backg ound
2.1 Ancho ed MaxDi
In MaxDi s udies, pa icipan s indica e he bes and wo s al e na i es in mul-
iple MaxDi asks (Fig. 1A p esen s a MaxDi ask om ou s udy; Finn &
Lou ie e, 1992). This helps es ablish a anking among all i ems unde esea ch in
pa icipan s’ u ili y space, a ela i e p e e ence measu e (Lage k is e al., 2012).
Thus, he esul ing indi idual-le el u ili ies can nei he be compa ed ac oss pa -
icipan s (Lage k is e al., 2012) no be used o p edic choice sha es in ma -
ke s ha include a no-buy al e na i e. To measu e absolu e p e e ences ins ead,
esea che s de eloped ancho ed MaxDi . Two app oaches a e commonly e e ed
o in he li e a u e: he di ec ancho ed (La e y, 2010; O me, 2009b) and he
indi ec ancho ed (O me, 2009a)MaxDi . Wha is lacking hus a is a igo ous
assessmen o he p edic i e alidi y o he wo app oaches, which would help
esea che s choose be ween hem. We posi ha he wo app oaches bene i ma -
ke esea che s mos when he MaxDi asks a e amed as pu chase likelihood
ques ions and when holis ic p oduc s, including p ices, a e o be e alua ed (see
abo e). In his case, adhe ing o he di ec app oach, pa icipan s i s answe all
MaxDi asks, ollowed by an addi ional ask indica ing whe he each p oduc
(o a subse ) ep esen s a pu chase op ion (Fig.1B). In con as , in he indi ec
ancho ed MaxDi (Fig.1C), also known as he dual- esponse app oach, pa ici-
pan s answe whe he all, none, o some o he i ems shown in each MaxDi ask
ep esen a pu chase op ion (Lage k is e al., 2012).
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Ma ke ing Le e s (2025) 36:1–16
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2.2 Incen i e alignmen
P e e ence measu emen echniques usually in ol e hypo he ical decisions and do
no conside ha pa icipan s in such se ings end o o e es ima e hei pu chase
likelihood and show less p ice sensi i i y (e.g., Mille e al., 2011). To add ess
his adequa ely, esea che s in he domain o conjoin analysis ha e u ilized incen-
i e alignmen (e.g., Ding e al., 2005;Sablo ny-Wacke shause e al., 2024). By
making each p oduc choice in he su ey po en ially payo - ele an , pa icipan s
a e su icien ly mo i a ed o e eal hei ue p e e ences (Dong e al., 2010).
In he CBC domain, esea che s ha e in oduced se e al mechanisms o incen-
i e-align s udies ( o an o e iew, see Dong e al., 2010). Mos equen ly, pa ic-
ipan s ecei e one o hei andomly d awn choice ask decisions as a ewa d and
pay he co esponding p oduc p ice (Ding e al., 2005). This is possible because,
in CBC, pa icipan s selec he p oduc wi h he highes pu chase likelihood in
each choice ask, whe eas, al e na i ely, hey always ha e he op ion o indica e
ha none o he shown p oduc s is wo h buying (i.e., he no-buy al e na i e).
An equi alen mechanism o adi ional MaxDi would no ha e been easi-
ble since pa icipan s canno indica e ha hey do no wan o ecei e a p oduc
hey ha e ma ked as he bes al e na i e o s udy disbu semen . He e, i becomes
clea ha in oducing ancho ed MaxDi and e aming MaxDi asks as pu -
chase likelihood ques ions abou holis ic p oduc s ha e pa ed he way o imple-
men ing incen i e-aligned MaxDi a ian s o inc ease p edic i e alidi y. This
ad ancemen ul ima ely enables a igo ous assessmen o bo h desc ibed ancho -
ing app oaches wi h ega d o incen i e-aligned e sions o ancho ed MaxDi
and consequen ial p oduc choices as alida ion p ocedu e.
2.3 Resea ch goals
P io esea ch sugges s ha he di e ence be ween hypo he ical and incen i e-aligned
p e e ence measu emen me hods and he di e ence be ween di ec and indi ec
ancho ed MaxDi lead o di e ging o ecas s o p oduc choice as well as demand in
ma ke simula ions. The ques ion o ma ke esea che s emains: Which combina ion
o he wo p inciples p o ides he mos ealis ic p edic ions? This s udy se s ou o gi e
an answe ; i s , by in oducing incen i e alignmen o ancho ed MaxDi and, second,
by using a consequen ial alida ion p ocedu e ha allows assessing he ela i e me i s
o incen i e alignmen and ancho ing in MaxDi s udies on p oduc choices.
3 Empi ical s udy
3.1 Me hod andma e ial
In a p e egis e ed online expe imen , 16 Sony PlayS a ion 5 (he ea e PS5) ideo
games se ed as he ocal p oduc s (see WAB o s imuli), as ideo games ul ill
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Ma ke ing Le e s (2025) 36:1–16
he p econdi ion o being holis ic p oduc s (wi h ixed p ices).2 Mo eo e , Sony
also o e s PS5 bundles. De e mining he bes games o bundles is essen ial and
makes MaxDi a alid and in e es ing me hod o hese esea ch ques ions.
We chose he 16 PS5 games based on sales in Ge many (e.g., GamesWi scha )
and download numbe s in he PS5 s o e o 2021. Fu he mo e, we included games
eleased in 2022 (e.g., G an Tu ismo) and gen es ha we e unde ep esen ed in ou
sample (e.g., simula ion games such as O e cooked!). We de e mined p ices based
on ma ke p ices minus 5% o o e a ac i e p oduc s wi hin he s udy.
We andomly alloca ed pa icipan s o one o ou MaxDi condi ions in a 2
(incen i e-aligned: yes s. no) × 2 ( ype o ancho ing: di ec s. indi ec ) be ween-
subjec s design. Each MaxDi a ian comp ised 16 asks wi h ou al e na i es,
and each pa icipan saw each ideo game ou imes. In each MaxDi ask, pa -
icipan s indica ed which ideo game hey we e mos likely o pu chase and which
hey we e leas likely o pu chase (see Fig.1A). We implemen ed bo h ancho ing
app oaches in he same way as desc ibed in Sec ion2.1.
To assess p edic i e alidi y, each pa icipan esponded o he same ou conse-
quen ial alida ion asks (see WAB; excluded om u ili ies’ es ima ion). The i s
wo asks o e ed 7 and 11 games, espec i ely, plus a no-buy al e na i e. The hi d
alida ion ask was a dual- esponse choice (a o ced decision wi h subsequen no-
buy ques ion) o e ing eigh games. Finally, he ou h ask was an incen i e-aligned
anking ask comp ising six games (Lusk e al., 2008), ollowed by asking up o
which ank pa icipan s would op o a buy o i hey would buy none o he games.
We inco po a ed a payou mechanism as ollows: Besides ecei ing a ixed pay-
men o €3.50, each pa icipan had a 1-in-40 chance o winning a PS5 game and
cash ( he di e ence be ween he ideo game’s p ice and €55). Mo e p ecisely, pa -
icipan s in he incen i e-aligned g oups we e ins uc ed ha a andomly d awn
MaxDi o alida ion ask could become payo - ele an i a pa icipan was d awn
as a winne . In he hypo he ical condi ions, a andomly d awn alida ion ask se ed
as s udy disbu semen . To ensu e an unde s anding o he payo mechanism, pa ic-
ipan s needed o answe one o a maximum o h ee consecu i e p obing ques ions
co ec ly.
Pa icipan s ecei ed hei chosen game plus an amoun o cash (see abo e) i
alida ion ask one, wo, o h ee was andomly d awn. In he anking ask, he p ob-
abili y depended on he assigned ank. I was calcula ed ollowing he o mula
J+1− j
∑
J
j=
1j
×
100
, whe e J ep esen s he numbe o al e na i es and j ep esen s he
assigned ank o he al e na i ej (Lusk e al., 2008, p.488).
3.2 Pa icipan s
An independen Ge man ma ke esea ch ins i u e helped wi h ec ui ing pa -
icipan s o he online expe imen . All pa icipan s needed o ul ill he ollowing
2 h ps:// asp e dic ed. o g/ SLH_ 95Q; he p e egis a ion also p o ides in o ma ion on sample size plan-
ning and sc eening.
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Ma ke ing Le e s (2025) 36:1–16
1 3
c i e ia: (I) in e es in bo h ideo games and he PS5, (II) a leas 18yea s old, and
(III) playing ideo games a leas occasionally. We also included pa icipan s who
al eady own some o he games ( ega dless o he ideo console pla o m). We
sc eened ou 41 pa icipan s due o hei esponse beha io (e.g., a en ion checks,
see p e egis a ion). In he ne sample o n = 448 pa icipan s, (I) 118 eplied o he
di ec ancho ed hypo he ical, (II) 112 o di ec ancho ed incen i e-aligned, and 109
o he indi ec ancho ed hypo he ical o indi ec ancho ed incen i e-aligned MaxDi
(III and IV) espec i ely. The sample’s cha ac e is ics a e 42% emales, 57% males,
and one di e se pa icipan ; Mage = 39.25, SDage = 14.25, and 67% wi h a mon hly
income abo e €1,000. No signi ican di e ences eme ged be ween he g oups.3
3.3 Resul s
3.3.1 P edic i e alidi y
We applied hie a chical Bayes mul inomial logi analysis, making use o a single
mul i a ia e no mal dis ibu ion (Allenby & Gin e , 1995) o es ima e indi idual
pa -wo h u ili ies (see TableC2 in WA) in Saw oo h So wa e Ligh house S udio
(Saw oo h So wa e Inc. 2022a).4
In Saw oo h So wa e, he bes and wo s choices a e s acked oge he o an es i-
ma ion in a single un (Ch zan & O me, 2019, p.22). The e o e, he wo s choice’s
design ma ix is nega ed (Ch zan & O me, 2019, p.22).
We applied he mul inomial logi ule o p edic p oduc choice p obabili ies o
he alida ion asks. Based on hese esul s, we calcula ed he hi a e (i.e., co ec ly
p edic ed choices) and he mean hi p obabili y (MHP, i.e., he p edic ed p obabil-
i y o heac ual choice). We also applied a ou old ou -o -sample c oss- alida ion
wi hin each MaxDi condi ion o he i s h ee alida ion asks. In his c oss- ali-
da ion p ocedu e, we calcula ed he di e ence be ween he ac ual and he p edic ed
choice sha e (i.e., mean absolu e e o ). Las ly, o he p oduc anking ask ( alida-
ion ask 4), we calcula ed he mean ank o he p edic ed choice and he Spea man
co ela ion be ween he assigned and p edic ed anks.
Table1 p esen s he main esul s ( he OSF p esen s esul s o each alida ion
ask sepa a ely, as well as a compa ison be ween unancho ed and ancho ed MaxDi
o alida ion asks 3 and 4). Each condi ion p edic s be e han chance o all ali-
da ion asks (binomial es p’s < 0.001). Incen i e-aligned ( s. hypo he ical) MaxDi
p edic s pa icipan s’ p oduc choices be e , which is also ue when examining ou -
o -sample p edic ion.
We an a gene alized logis ic mixed-e ec s model o es o signi ican di e -
ences in he p oduc choice asks ( alida ion asks 1–3; Sablo ny-Wacke shause
4 We used 80,000 wa m-up i e a ions and 40,000 d aws o es ima ion, se p io deg ees o eedom o 2,
and p io a iance o 1.3 (O me and Williams 2016). We p o ide u he in o ma ion on he model and
he co esponding es ima ion on OSF in a ma hema ical appendix.
3 We es ed o di e ences in gende , age, income, gaming beha io , ideo console owne ship, o owne -
ship o one o he games (smalles p = .065; TableC1 in WA p o ides demog aphics spli by condi ions).
15
1 3
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