Choice his o y biases in dyadic
decision making
Ann Huang 1, Ma his Pink1, Vik o ia Zemliak1, A u Czeszumski1,2 & Pe e König1,3
How do we in e ac wi h ou en i onmen and make decisions abou he wo ld a ound us? Empi ical
esea ch using psychophysical asks has demons a ed ha ou pe cep ual decisions a e in luenced by
pas choices, a phenomenon known as he “choice his o y bias” e ec . This decision-making p ocess
sugges s ha he b ain adap s o en i onmen al unce ain ies based on his o y. Howe e , single-
subjec expe imen ask design is p e alen ac oss he wo k on choice his o y bias, hus limi ing he
implica ions o he empi ical e idence o indi idual decisions. He e, we explo e he choice his o y
bias e ec using a dual-pa icipan app oach, whe e dyads pe o m a sha ed pe cep ual decision-
making ask. We i s p opose wo compe ing hypo heses: he pa icipan s equally weigh hei own
and hei pa ne ’s decision his o y, o he pa icipan s do no weigh equally hei own and hei
pa ne ’s decision his o y. We hen use a s a is ical modeling app oach o i gene alized linea
models o he choice da a in a se ies o s eps and a i e a a model ha bes i s he obse ed da a.
Ou esul s indica ed ha he own and pa ne ’s ial his o y canno be ea ed independen ly. The
indings sugges an in e ac ion o ac o and decision a 1-back, leading o a choice al e na ion bias
a e a pa ne ’s decision in con as o a choice epe i ion bias a e an own decision. A simila e ec
is obse ed a 2-back, in addi ion o an addi i e choice epe i ion bias o simila size. The e ec s o
ac o and decision a 2-back do no depend on he p ope ies o he 1-back ial. Toge he , hese
indings suppo he idea ha he pa icipan s do no igno e hei pa ne ’s decisions bu ea hese
quali a i ely di e en ly om hei own.
In daily li e, people pe cei e and p ocess unce ain senso y in o ma ion o make decisions ha lead o use ul
ac ions. Fo example, medical p o essionals examine X- ay scans o de e mine signs o abno mali ies, o
badmin on playe s judge whe he he shu le du ing a double-playe ma ch landed inside o ou side he cou
line. This abili y o make pe cep ual judgmen s is cen al o human cogni ion1. In pa icula , i in ol es mapping
noisy senso y in o ma ion as inpu and ans o ming i in o decision esponses as ou pu . As such, classical
psychophysical me hods a e o en used o desc ibe his pe cep ual p ocess o unde s and cogni ion be e 2,3.
No ably, ex ensi e wo k on pe cep ual p ocessing has demons a ed ha pas choices in luence cu en
decisions, a phenomenon e e ed o as “choice his o y bias”4,5. This e ec has been shown using pe cep ual asks
such as a wo-al e na i e o ced-choice (2AFC) ask in which pa icipan s a e asked o disc imina e he di ec ion
o mo ion in isual s imuli6,7. A choice his o y bias e ec is also ound when he s imuli p esen ed on successi e
ials a e unco ela ed8. Such empi ical e idence sugges s he his o y bias e ec pe sis s as a subop imal decision-
making p ocess in which he b ain adap s o en i onmen al unce ain ies9. The e o e, pe cep ual decisions a e
in luenced by expe imen ial his o y e en when he ask is no adap i e.
Consis en ac oss he s udies on he choice his o y bias e ec is he use o single-subjec designs independen ly
o social se ings. Fo ins ance, Ab ahamyan and colleagues examined he adap abili y o choice his o y bias
using da a collec ed om indi iduals ac oss h ee labo a o ies4. U ai e al. analyzed choice da a collec ed om
mul iple pe cep ual expe imen s ac oss di e en senso y modali ies conduc ed a he le el o single subjec s7
None heless, in eali y, people a e no isola ed decision-make s. Ra he , people o en in e ac wi h o he s and
in eg a e exis ing in o ma ion a ailable o hem, such as when looking a maps oge he o na iga e physical
su oundings. In his scena io, one can be in luenced by he social cues o o he s o hei own bias in he decision
p ocess. The e o e, when s anda d psychophysical ask designs do no accoun o in e ac ion, insigh s d awn
om hese wo ks emain limi ed o indi idual decisions.
Resea ch on join a en ion implica ed he in luence o social cues and sha ed a en ion on pe cep ual
judgmen s. Fo example, Seow and Fleming expe imen ed o es whe he pe cep ual sensi i i y depends on
social con ex 10. By asking pa icipan s o de ec low-con as Gabo pa ches, hey disco e ed ha pa icipan s’
de ec ion pe o mance imp o ed when he pe cep ion was sha ed wi h a i ual human, o an a a a . This indica es
1Ins i u e o Cogni i e Science, Uni e si y o Osnab ück, Wachsbleiche 27, 49090 Osnab ück, Ge many. 2Social
Neu oscience Lab, Ins i u e o Psychology, Polish Academy o Sciences, Wa saw, Poland. 3Depa men o
Neu ophysiology and Pa hophysiology, Uni e si y Medical Cen e Hambu g-Eppendo , Hambu g, Ge many.
email: [email p o ec ed]
OPEN
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ha indi iduals conside he isual pe spec i e o o he s when making pe cep ual judgmen s. Expe imen al
wo k by Wahn and colleagues used join isual-spa ial asks and linea modeling analyses o in es iga e how
social ac o s, e.g., in o ma ion abou he co-ac o ’s ac ions o pe o mance eedback, migh accoun o g oup
bene i s11,12. The esul o hei s epwise modeling app oach showed an accu a e p edic ion o collabo a i e
bene i s and con ibu ed owa ds unde s anding join ac ion in social cogni ion. Thus, pe cep ion and ac ion a e
no solely indi idualis ic p ocesses bu can be shaped by he dyadic na u e o human in e ac ions13–16.
He e, we aim o explo e how he choice his o y bias e ec migh be modula ed in a social con ex . Speci ically,
we examine he pa icipan s’ choice beha io while hey ake u ns pe o ming a sha ed pe cep ual ask, wi h
s imuli p esen ed in a andom sequence, wi h hei dyadic pa ne . The ask allows he pa icipan s o obse e
each o he ’s choice esponse on each ial, which could, in u n, in luence hei decision-making p ocess. This
o m o in e ac ion in which he e is no ac ual collabo a ion o eedback has been shown o in luence one’s own
cogni i e p ocessing17,18.
Ou esea ch objec i e is o de e mine whe he pe cep ual decision-making is mo e o an indi idualis ic
(independen o he co-ac o ’s ac ion) o collec i e (con ingen on he co-ac o ’s ac ion) p ocess despi e he
co-ac o ’s ac ions being i ele an o he p esen decision. Fo his, we o mula e and es compe ing hypo heses
ha e lec sepa a e assump ions ega ding he choice his o y bias e ec in a social con ex . The null hypo hesis
(H0) s a es ha he pa icipan s equally weigh hei own and hei pa ne ’s decision his o y. This sugges s ha
he choice his o y bias e ec is no limi ed o a speci ic ac o in he dyad bu ela es o he combined sequence
o decisions by he dyad. The al e na i e hypo hesis (H1) s a es ha he pa icipan s do no equally weigh hei
own and hei pa ne ’s decision his o y. This assumes he choice his o y e ec is in luenced by he speci ic
ac o . I H1 is suppo ed, we examine how he choice his o y e ec depends on he speci ic ac o . In pa icula ,
he pa icipan s could ei he ollow o de ia e om hei pa ne ’s decision. To ollow he decision means i
he dyadic pa ne esponded le , he pa icipan is likely o choose le , and ice e sa o igh esponse (i.e.,
a “choice epe i ion”, eg ession coe icien es ima e β > 0). To de ia e om he decision means i he dyadic
pa ne esponded le , he pa icipan is likely o espond opposi ely om his by choosing igh , ice e sa o
igh esponse (i.e., a “choice al e na ion”, eg ession coe icien es ima e β < 0). We examine he i o gene alized
linea models co esponding o he di e en hypo heses o ial-by- ial choice esponse in a se ies o s eps.
The goal is o a i e a a model ha bes i s he beha io al da a and, in u n, explains he ex en o which he
hypo heses a e suppo ed. He e, we es which hypo hesis bes i s ou obse a ions.
Ma e ials and me hods
Pa icipan s
Se en y-eigh indi iduals, g ouped in hi y-nine dyads, we e ec ui ed o he p esen s udy. Twel e pa icipan s
(six dyads) we e excluded om pe o ming he main expe imen al ask due o excep ionally poo pe o mance
du ing he p ac ice block. This lea es 33 dyads, o 66 indi iduals (N = 66, 44 emales, 21 males, one non-bina y,
M = 25yea s old, SD = 5yea s). All pa icipan s had no mal o co ec ed- o-no mal ision wi hou a his o y o
neu ologic o psychia ic illnesses. All pa icipan s p o ided w i en in o med consen be o e he expe imen .
The s udy was conduc ed in acco dance wi h he Decla a ion o Helsinki and app o ed by he E hics Commi ee
o he Uni e si y o Osnab ück.
Expe imen p o ocol
A speeded andom do mo ion (RDM) disc imina ion ask was used (Fig.1a). The ask in ol ed iewing a cloud
o mo ing do s and de e mining whe he he e was cohe en mo emen igh wa d o le wa d by p essing he
wo colo ed bu ons (blue = igh , yellow = le ) on he cus om keyboa d (Black Box Toolki USB Response Pads
[URP48/URPVK], blackbox oolki .com) acco dingly. Be o e he pa icipan s began he ask, he expe imen e
ga e bo h w i en and e bal ins uc ions on he expe imen p ocedu e. The expe imen e also demons a ed
how o make a esponse by using he keyboa d bu ons. Pa icipan s we e ins uc ed o pe o m he ask as
quickly and as accu a ely as possible. In addi ion, pa icipan s we e ins uc ed o ixa e hei eyes on he cen e
o he s imulus p esen ed as a g een c oss when pe o ming he ask.
All s imuli we e c ea ed in Py hon ( e sion 3.9.2) using he Psychophysics Toolbox e sion 2021.1.319. The
s imuli’s le wa d and igh wa d mo emen di ec ions we e equip obable and andomly selec ed ac oss ials.
The do s (N = 328) we e whi e wi h a size o 3 × 3 pixels, ci cula ape u e o 5° diame e , speed o 9.95°/s,
and densi y o 16.70 do s/deg ee2. They we e p esen ed agains a black backg ound. The cohe ence o he
s imuli, de ined as he p opo ion o do s mo ing in he signal di ec ion, was p e-de e mined. Fo ins ance,
a a cohe ence le el o 0.5, hal o all he do s mo ed in he ial’s di ec ion, which was se o ei he 0 o 180
deg ees (le wa d o igh wa d) on e e y ame. These do s cons i u ed he “signal do s’'. The emaining hal was
e e ed o as he “noise do s”, whe e each ollowed a andom bu cons an di ec ion on each ame. In o de
o di ec he pa icipan ’s gaze a he s imuli and keep any in olun a y eye mo emen s o d i o a minimum
o ex ended ime pe iods, a bullseye ixa ion c oss was used20. Fo e e y ial, he ixa ion c oss colo changed
om g een o ei he blue o yellow o 700ms pos - esponse o indica e he ac ing pa icipan ’s choice esponse
(yellow i esponded ‘le ,’ blue i esponded ‘ igh ’). Du ing his eedback in e al, he do s we e s a iona y. The
pa icipan ’s pa ne also saw such eedback in o ma ion in he main expe imen .
In gene al, ou ask design and p ocedu e closely eplica ed es ablished wo k on pe cep ual decision-making,
pa icula ly ha o 6 whe e hey quan i ied he decision-making pa ame e s. Ou s udy consis ed o wo sessions:
es ing and he main expe imen . In he es ing session, he pa icipan s indi idually and sepa a ely pe o med
he p ac ice block ollowed by he i a ion block. The p ac ice block consis ed o 40 ials o mo ing do s a
a ixed cohe ence o 0.4. The i a ion block consis ed o 240 ials wi h andomly selec ed do cohe ences (0,
0.05, 0.1, 0.2, 0.4, 0.8, 40 ials each). While one pa icipan o a gi en dyad was pe o ming he p ac ice and
i a ion blocks, he o he pa icipan was ins uc ed o wai quie ly ou side he expe imen oom. The e was a
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sho b eak be ween he p ac ice and he i a ion blocks. I he pa icipan s did no achie e an accu acy le el o
75% du ing p ac ice, hey we e a o ded ano he oppo uni y (3 p ac ices in o al) o epea he p ac ice block
be o e p oceeding o he i a ion block. In he i a ion block, he indi idual cohe ence h eshold was es ima ed
om a psychome ic unc ion i o yield a goal accu acy le el o 75%6. I he pa icipan s ailed o each he
Fig. 1. (a) A depic ion o he expe imen ask p ocedu e. In each ial, an audio one cues he pa icipan o
espond o he do s ha mo ion dominan ly o he le o igh . The ixa ion c oss colo changed om g een
o blue o yellow acco ding o he choice esponse. (b) The diag am p esen s an example sequence o one
expe imen block pe o med by one dyad, consis ing o pa icipan s ”A” and “B.” The choice esponse, o he
decision on each ial, was ei he igh o le . In each ial, ei he pa icipan A o pa icipan B is he “ac o ”
who pe o ms he ask. He e, ial 9, highligh ed in ed, is shown as an example o an “ac i e ial,” in which
pa icipan A is he “ac ing pa icipan ,” while pa icipan B is he “obse ing pa icipan .” The p e ious ial
wi h he ac o and decision a e highligh ed in blue. The ac o and decision wo ials ago a e highligh ed
in yellow. Speci ically, ial 8 e e s o he ial a “1-back”, in which he obse ing pa icipan (“pa ne ” o
“o he ”) ga e a “ igh ” esponse. T ial 7 e e s o he ial a “2-back”, in which he ac ing pa icipan (“own” o
“sel ”) ga e a “le ” esponse. O e all, he decisions and ac o s a bo h delay o one and delay o wo om he
ac i e ial a e depic ed.
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goal accu acy o highe , hey we e excluded om pa icipa ing in he main expe imen , and he expe imen was
abo ed.
The main expe imen consis ed o 10 blocks wi h 100 ials each. In he main expe imen , he wo pa icipan s
o a dyad sa in sepa a e expe imen al ooms o pe o m he ask. They al e na ed andomly o espond o
he s imuli p esen ed on a 24-inch-wide Dell U2412M moni o wi h a esolu ion o 1920 × 1200 pixels and a
e esh a e o 60Hz a a iewing dis ance o 60cm. On each ial, only one dyad membe was assigned o
espond o he s imulus. No e ha while he pa icipan s sa in sepa a e ooms, each iewed s imuli mo ing in
an iden ical di ec ion h ough an ex ended window display. Howe e , he s imuli di icul y le el was ailo ed o
each pa icipan ’s beha io al da a, and i was upda ed a e e e y block (see Supplemen a y Me hods o de ails
on he adap i e p ocedu e). The iewing dis ance was measu ed om he pa icipan ’s eye o he cen e o he
moni o . The pa icipan s sel -adjus ed he chai ’s heigh o iew he cen e o he s imulus com o ably and
placed hei index inge s on he cus om keyboa d o make a esponse. The chai was ixed o he loo wi h he
help o he expe imen e . A e e e y wo blocks o he expe imen , he expe imen e measu ed he pa icipan ’s
iewing dis ance again o keep he iewing dis ance equal.
A he beginning o he main expe imen , he dyads unde wen sound amilia iza ion ials. They we e
ained o ecognize hei own and hei pa ne ’s ones as cues o espond in a gi en ial. The wo dis inc
ones in he sound amilia iza ion ials we e musical no es “C” a oc a e 5 and “F” a oc a e 4. Each no e had
a du a ion o 0.5s and was played o he pa icipan s 5 imes. Lexical ins uc ions accompanied he playing o
he ones: “When you hea his, i ’s you u n o espond” and “When you hea his, you pa ne will espond.”
No e ha while he es ing session consis ed o lexical eedback on he esponse co ec ness, i.e., a g een
“Co ec ” o a ed “Inco ec ” wo d was p esen ed below he s imulus a e e e y ial, such eedback was absen
du ing he main expe imen . In addi ion, ollowing he decision in e al o 1500ms a e s imulus onse as used
in6, we also se lexical wa nings o esponse ime < 100ms (“Too Fas ”) and > 1500ms (“Too Slow”). Simila ly,
du ing he main expe imen , lexical wa nings “Pa ne Too Slow” and “Pa ne Too Fas ” we e indica ed o he
obse ing pa icipan in he dyad.
A e comple ing he expe imen , he pa icipan s we e asked o comple e ques ionnai es on hei demog aphic
da a and how well hey know hei pa ne on a 100-poin scale. The es ing session o each pa icipan las ed
abou 30min. The main expe imen ook a ound 2h; he e o e, he en i e expe imen ook abou 3h o each
pai o pa icipan s. O e all, he expe imen se -up ollowed closely pas empi ical wo k, whe e he in e ac ion
be ween he dyads is solely wi hin he pe cep ual ask.
Me hod o da a analysis
Te minologies and a iable coding
He e, we desc ibe he a iable names and e minologies used h oughou he s udy. O e all, he objec i e o
c ea ing he ollowing a iables was o build a model ha could i s cap u e any linea e ec on he cu en
choice up o he delay o wo. This allowed an unbiased da a-d i en in es iga ion o he choice his o y bias in
dyadic decision-making. In discussing he de ails o he cu en ial, he a iable
Sn
coded o he s imulus;
u he mo e, he a iable
An
coded o he iden i y o he pa icipan ac ing, while he a iable
Dn
coded o he
decision, o choice esponse. As illus a ed in Fig.1b, he ac o s and decisions a 1-back and 2-back a e in ela ion
o he ac i e ial. In discussing he ial a 1-back, he a iables
An−1
and
Dn−1
coded o in o ma ion abou
he p e ious ial ac o iden i y and decision, espec i ely. Simila ly, o he ial a 2-back, he a iables
An−2
and
Dn−2
coded o in o ma ion abou he iden i y o he ac o and decision a wo ials ago, espec i ely. + 1
and − 1 we e used in he coding o he decision (+ 1 = igh ; − 1 = le ), s imulus (+ 1 = igh ; − 1 = le ), and ac o
iden i ies (+ 1 = own; − 1 = “pa ne ”).
In discussing ial his o y up o he delay o wo, we combined he ac o and decision a 2-back wi h he
de ails o he ac o and decision a 1-back. Speci ically, we c ea ed a iables con aining such in o ma ion
using condi ional e ec coding, o “one ho encoding”. + 1, − 1 and 0 we e used o indica e he ca ego ies o he
condi ions me . Fo example, he a iable
(
A
+1
n−1)(
D
−1
n−1)∗(
A
n−2)
codes o he ac o a 2-back, bu only unde
he condi ion ha 1-back was pe o med by “own” wi h decision “le ”. The e o e,
(
A
+1
n−1)(
D
−1
n−1)∗(
A
n−2)
is + 1 indica es “own” a 2-back, and − 1 indica es pa ne a 2-back, condi ioned on he ac ha 1-back was
pe o med by “own” wi h decision “le ”. I he 1-back condi ion o “own” and decision “le ” is no me , he
a iable
(
A
+1
n−1)(
D
−1
n−1)∗(
A
n−2)
is 0. Simila ly, he a iable
(
A
+1
n−1)(
D
−1
n−1)∗(
D
n−2)
codes o he decision
a 2-back, bu only unde he condi ion ha 1-back was pe o med by “own” wi h a decision “le ”. As such,
(
A
+1
n−1)(
D
−1
n−1)∗(
D
n−2)
is + 1 indica es decision “le ” a 2-back, and -1 indica es decision “ igh ” a 2-back,
condi ioned on he ac ha 1-back was “own” and “le ”. I he 1-back condi ions o “own” and decision “le ”
was no me ,
(
A
+1
n−1)(
D
−1
n−1)∗(
D
n−2)
is 0. Table 1 p esen s he a iable names and desc ip ions un il 2-back.
No e ha we did no c ea e a iables ha coded he combina ion o ac o and hei di ec ional decision a
1-back (e.g., 1-back pe o med by own wi h le decision), esul ing in a o al o 4 combina ions. Fu he mo e,
we did no c ea e a iables ha combined he ac o iden i y and di ec ional decision a 1-back wi h hose a
2-back (e.g., 1-back pe o med by own wi h le decision, combined wi h 2-back pe o med by own wi h le
decision), esul ing in a o al o 16 combina ions. This is because he use o a iables coded as such leads o
mul icollinea i y which in oduces complexi ies in in e p e a ions. Fo logis ic eg ession modeling es ima ion,
he dependen a iable is he pa icipan s’ esponse choices, which we e bounded be ween 0 and 1, e lec ing he
p obabili y o selec ing igh wa d, ising om 0 (le ) o 1 ( igh ).
Gene alized linea modeling
To es ou hypo heses, we i ed gene alized linea models (GLMs) wi h logi link unc ion o quan i y he
in luence o ial his o y on choice beha io . Following p io wo k on modeling choice his o y biases7,21, we
used he Akaike In o ma ion C i e ion (AIC) alues22 o o mal model compa isons. Gi en he la ge numbe
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o ials, we also used he Bayesian In o ma ion C i e ion (BIC) alues, which penalizes model complexi y mo e
s ongly han AIC23. To assess he model pe o mance, we conduc ed c oss- alida ion by pa i ioning he da a
in o aining and es ing se s. We e alua ed he models using c oss- alida ed accu acy and mean squa ed e o
(MSE). The binomial logis ic eg ession es ima ed he p obabili y o selec ing he igh decision esponse based
on he weigh ing o bo h senso y (i.e., cu en s imulus) and nonsenso y pa ame e s (e.g., pas ial esponses).
The model dis inguished esponse biases, such as when he pa icipan s p e e ed o epea o swi ch hei choice
esponse. We chose o use e ec coding o easie in e p e a ion o he coe icien es ima es as hey di ec ly
indica e he di e ence in he mean ou come a iable be ween he wo le els o he p edic o a iables.
Resul s
Explo a o y da a analysis
Fi s , we p ocessed and examined he eco ded esponses in he main expe imen o check o any missing
esponses and po en ial le / igh bias in he pa icipan s. In o al 33,000 esponses we e eco ded, i.e., no missing
esponses obse ed. Following his, only ials wi h eac ion ime (RT) g ea e han 0.1s and less han 1.5s we e
included in he subsequen analysis, esul ing in a emo al o 1795 ials ou o 33,000 ials (5.44% o o al
ials). The numbe o ac i e ials pe pa icipan anged om 338 o 523, wi h a mean o 472 ials (SD = 30).
One dyad had a di e ence o 129 ials in e ms o he numbe o ac i e ials. The a e age numbe o igh
esponses pe pa icipan was 240 ( ange = 161–350, SD = 39), while he a e age numbe o le esponses was
232 ( ange = 107–324, SD = 39). On he dyad le el, he a e age numbe o le esponses was 465 ( ange = 348–
545, SD = 54.57), and he a e age numbe o igh esponses was 480 ( ange = 410–581, SD = 45). To examine
any le / igh bias i.e., a p e e ence o a o one esponse o e ano he , we calcula ed he di e ence be ween he
p opo ion o igh choice esponses and he p opo ion o igh wa d-mo ing s imulus o he wo pa icipan s
wi hin he same dyad. A esul ing posi i e alue indica es a endency o espond igh , and nega i e alue
indica es a endency o espond le . The mean bias alues ac oss he pa icipan s is 0.007 ( ange = − 0.159–0.249,
SD = 0.073). Figu e2 shows a isualiza ion o he bias alues be ween he wo pa icipan s o he same dyad.
Pea son’s co ela ion be ween he bias alues o he wo pa icipan s wi hin he dyads showed no signi ican
co ela ion o an i-co ela ion, which allows o subsequen in es iga ion on he in luence o choice his o y bias
wi hou adjus men s o po en ial e ec o le -biased pa icipan pai ing wi h igh -biased pa icipan , o ice
e sa.
We analyzed he RT, pe o mance accu acy, and cohe ence le el da a o check o a ia ions ac oss he blocks.
The a e age RT was 0.87s (SD = 0.25s), and he a e age pe o mance accu acy was 73.6% (SD = 5.87%). The
indi idual cohe ence h eshold le el ange was 0.20–0.23, wi h a mean o 0.21 (SD = 0.012). Figu e3 shows he
pa icipan ’s mean RT, accu acy, and adap ed cohe ence le el changes h oughou he main expe imen . Pea son’s
co ela ion be ween he accu acy and s imuli cohe ence shows a signi ican posi i e bu weak co ela ion
( = 0.12, p < 0.001). The co ela ion be ween RT and accu acy was nega i e and signi ican ( = − 0.23, p < 0.001);
u he mo e, he co ela ion be ween cohe ence and RT was nega i e and signi ican ( = − 0.18, p < 0.001). The
Va iable name Desc ip ion
Sn
The cu en ial s imulus
An
The cu en ial ac o
Dn
The cu en decision o choice esponse
An−1
Ac o a 1-back
Dn−1
Decision a 1-back
An−2
Ac o a 2-back
Dn−2
Decision a 2-back
(
A
+1
n−1)(
D−
1
n−1)∗(
An
−
2
)
Ac o a 2-back, unde he condi ion ha 1-back was “own” and decision “le ”
(
A
+1
n−1)(
D−
1
n−1)∗(
Dn
−
2
)
Decision a 2-back, unde he condi ion ha 1-back was “own” and decision “le ”
(
A
+1
n
−
1
)(
D
+1
n
−
1
)∗(
An
−
2
)
Ac o a 2-back unde he condi ion ha 1-back was “own” and decision “ igh ”
(
A
+1
n
−
1)
(
D
+1
n
−
1
)∗
(Dn
−
2
)
Decision a 2-back, unde he condi ion ha 1-back was “own” and decision “ igh ”
(
A
−1
n
−1)(
D
−1
n
−1)∗(
An
−
2
)
Ac o a 2-back, unde he condi ion ha 1-back was “pa ne ” and decision “le ”
(
A−
1
n−1)(
D−
1
n−1)∗(
Dn
−
2
)
Decision a 2-back, unde he condi ion ha 1-back was “pa ne ” and decision “le ”
(
A−
1
n−1)(
D
+1
n−1)∗(
An
−
2
)
Ac o a 2-back, unde he condi ion ha 1-back was “pa ne ” and decision “ igh ”
(
A−
1
n
−
1
)(
D
+1
n
−
1
)∗(
Dn
−
2
)
Decision a 2-back, unde he condi ion ha 1-back was “pa ne ” and decision “ igh ”
Table 1. Va iable names and he desc ip ions o wha hey code o . The able shows he coding o he cu en
ial s imulus and decision, ollowed by he ac o s and decisions up o he delay o wo. The le e s “S”, “A” and
“D” s and o “s imulus”, “ac o ” and “decision”, espec i ely. The as e isk indica es he condi ioning be ween
wo ac o s.
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consis ency in he mean RT and pe o mance wi h a sligh ly dec easing end o s imuli cohe ence sugges ed
he adap i e p ocedu e wo ked easonably well.
Modeling choice his o y biases
The modeling app oach began wi h a no-his o y baseline model, ollowed by inco po a ing ial ac o s and choice
his o y da a up o a delay o wo. Building on pas empi ical wo k ha showed p e ious decisions in luenced he
pa icipan ’s choice in he absence o single- ial eedback and i espec i e o p e ious choice co ec ness7, we
assumed ha each dyadic pa icipan iewed hei decisions as co ec . This modeling logic a oided in oducing
quali a i ely di e en models ha could e.g., accoun o he pa icipan ’s pe cei ed co ec ness o bo h
hei own and hei pa ne ’s decisions, which kep he modeling app oach simple and consis en wi h pas
con en ions. We assessed he models in ela ion o he hypo heses, wi h an objec i e o a i e a one a guably
less complex model ha is simple o in e p e and assumed he bes i . In he ollowing, we epo he esul s
o each modeling s ep.
Fi s , we examined a ask-only model, whe e only he cu en ial s imulus was included as a p edic o o
model he pa icipan s’ pe o mance wi hou any addi ional cons ain s, such as wha he p e ious esponse was
o he iden i y o he p e ious ial ac o :
P (Dn= 1) ∼Sn
This Model 0 se ed as a baseline model and assumed he es ima ion o he cu en esponse depends solely on
he cu en ial s imulus, which was he ac ual ask. The esul s showed a s a is ically signi ican e ec o he
Fig. 2. A sca e plo o he le / igh bias alues o wo pa icipan s wi hin he same dyad when gi ing a
esponse. Each do ep esen s a dyad, wi h he bias alue o one pa icipan shown on he x-axis and he bias
alue o he o he pa icipan shown on he y-axis. Pea son co ela ion showed no signi ican co ela ion o
an ico ela ion in he obse ed pa e n.
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cu en s imulus on he cu en esponse (β = 1.04, 95% CI [1.01, 1.06], SE = 0.03, p < 0.001). S anda d e o s
we e clus e ed a he pa icipan le el o accoun o he non-independence o obse a ions wi hin indi iduals.
The c oss- alida ed accu acy o he model’s p edic ion was 73.8%, wi h an MSE o 0.1933. The accu acy alue
was compu ed by compa ing he model’s p edic ed p obabili ies (in alues 0s and 1s) agains he ue labels
o he ou come a iable. The MSE alue was calcula ed as he a e age squa ed di e ence be ween he p edic ed
and he ue alues. The h eshold o ans o ming he p edic ed p obabili ies in o p edic ed labels was se a
0.5. I he p edic ed p obabili y o a igh wa d esponse exceeded 0.5, we in e p e ed i as a p edic ion o class
1 ( igh wa d esponse). O he wise, he p edic ed p obabili ies below 0.5 we e classi ied as a p edic ion o class
0 (le wa d esponse). The p edic ed p obabili y o a igh wa d esponse gi en a igh wa d-mo ing s imulus
de i ed om he model’s es ima es was 73.8%, which aligned wi h ou in en ion o he ask design o yield a
goal o abou 75% accu acy pe o mance. The signi ican and posi i e associa ion be ween he p edic o and he
esponse sugges ed he pa icipan s ollowed ask ins uc ions and beha ed as hey should.
To in es iga e how ial his o y could in luence he pa icipan ’s choice, we buil on he baseline model o
include he a iables ha accoun ed o he possible sequences o ac o s and he decisions up o he delay o wo:
Fig. 3. Changes in he majo dependen a iables h oughou he main expe imen . (a) The RT ac oss he
expe imen blocks. (b) The mean accu acy pe o mance h oughou he expe imen . (c) The main expe imen ’s
mean cohe ence le el (upda ed a e e e y block o each pa icipan ).
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P (D
n
= 1) ∼S
n
+A
n−1
+D
n−1
+A
n−1
×D
n−1
+(A+1
n−1)(D−1
n−1)∗(An−2)+(A+1
n−1)(D−1
n−1)∗(Dn−2
)
+(A+1
n−1)(D−1
n−1)∗(An−2)×(A+1
n−1)(D−1
n−1)∗(Dn−2
)
+(A+1
n−1)(D+1
n−1)∗(An−2)+(A+1
n−1)(D+1
n−1)∗(Dn−2
)
+(A+1
n−1)(D+1
n−1)∗(An−2)×(A+1
n−1)(D+1
n−1)∗(Dn−2
)
+(A−1
n−1)(D−1
n−1)∗(An−2)+(A−1
n−1)(D−1
n−1)∗(Dn−2
)
+(A−1
n−1)(D−1
n−1)∗(An−2)×(A−1
n−1)(D−1
n−1)∗(Dn−2
)
+(A−1
n−1)
(
D+1
n−1
)
∗(An−2)+(A−1
n−1)
(
D+1
n−1
)
∗(Dn−2
)
(A−1
n−1
)
(
D+1
n−1)∗
(An
−
2)
×
(A−1
n−1
)
(
D+1
n−1)∗
(Dn
−
2)
This Model 1 included he ial his o y up o 2-back and accoun ed o he comple e combina ions o he sequences
o pas ac o s and choices, i.e., whe he he p eceding 1- and 2-back ials we e pe o med by onesel o he o he
gi ing a igh o a le esponse when p edic ing he choice o be made. The esul s showed signi ican and posi i e
main e ec s o he a iables
Sn
(β = 1.04, 95% CI [1.02, 1.07], SE = 0.03, p < 0.001),
(
A
+1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(β = 0.08, 95% CI [0.01, 0.15], SE = 0.04, p < 0.05) and
(
A
+1
n−1)(
D
+1
n−1)∗(
Dn
−
2
)
(β = 0.08, 95% CI [0.01, 0.14],
SE = 0.03, p < 0.05). The model also showed all he in e ac ion a iables posi i e and signi ican :
An−1×Dn−1
(β = 0.11, 95% CI [0.07, 0.14], SE = 0.02, p < 0.001),
(
A
+1
n−1)(
D
−1
n−1)∗(
An
−
2
)×(
A
+1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(β = 0.27, 95%, CI [0.17, 0.38], SE = 0.06, p < 0.001),
(
A
+1
n−1)(
D
+1
n−1)∗(
An
−
2
)×(
A
+1
n−1)(
D
+1
n−1)∗(
Dn
−
2
)
(β = 0.22, 95% CI [0.12, 0.32], SE = 0.06, p < 0.001),
(
A
−1
n−1)(
D
−1
n−1)∗(
An
−
2
)×(
A
−1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(β = 0.19, 95% CI [0.09, 0.30], SE = 0.07, p < 0.001), and
(
A
−1
n
−1)(
D
+1
n
−1)∗(
An
−
2
)×(
A
−1
n
−1)(
D
+1
n
−1)∗(
Dn
−
2
)
(β = 0.14, 95% CI [0.04, 0.24], SE = 0.06, p < 0.01). The model exhibi ed an AIC alue o 31,314.15 (ΔAIC = − 139
uni s om Model 0), as well as a BIC alue o 31,453.83 (ΔBIC = − 15.72 uni s om he Model 0). The c oss-
alida ed accu acy o he model was 73.8%, wi h an MSE alue o 0.1923. No e, howe e , ha he accu acy alue
was compu ed based on p edic ions h esholded a 0.5, hus no ully e lec ing he a ia ions in he model’s
ac ual p edic ion alues. O e all, Model 1 demons a es he impac o pas decisions and ac o s ha bias he
decision-making.
As a nex s ep, we in es iga ed whe he he his o y o own and pa ne ’s decisions can be conside ed
independen ly. Tha is, does i ma e whe he he las own decision occu ed di ec ly be o e o a e he las
pa ne ’s decision? Speci ically, we calcula ed he p edic ed in luence based on he speci ic combina ion o ac o
sequences o de e mine i he o de o own o pa ne ac ion ma e s. In o he wo ds, gi en he es ima es om
Model 1 we compu ed he p edic ions o each speci ic case and checked he e ec o ac o and di ec ional decisions.
Fo example,
(
A
+1
n−1
D
−1
n−1)(
A
−1
n−2
D
−1
n−2)
is own le decision a 1-back, combined wi h pa ne le decision
a 2-back, which is calcula ed by he ollowing: (β o
An−1
)(own) + (β o
Dn−1
)(own a 1-back)(decision le a
1-back) + (β o
(
A
+1
n−1)(
D
−1
n−1)∗(
An
−
2
)
)(pa ne a 2-back) + (β o
(
A
+1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(decision le
a 2-back) + (β o
(
A
+1
n−1)(
D
−1
n−1)∗(
An
−
2
)×(
A
+1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(pa ne a 2-back x decision le a
2-back). This is compa ed wi h
(
A
−1
n−1
D
−1
n−1)(
A
+1
n−2
D
−1
n−2)
, which is pa ne le decision a 1-back ollowed by
own le decision a 2-back, and is calcula ed by he ollowing: (β o
An−1
)(pa ne ) + (β o
Dn−1
)(pa ne a 1-back)
(decision le a 1-back) + (β o
(
A
−1
n−1)(
D
−1
n−1)∗(
An
−
2
)
)(own a 2-back) + (β o
(
A
−1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(decision le a 2-back) + (β o
(
A
−1
n−1)(
D
−1
n−1)∗(
An
−
2
)×(
A
−1
n−1)(
D
−1
n−1)∗(
Dn
−
2
)
(own a 2-back x
decision le a 2-back). Accoun ing o he ials up o he delay o wo i.e., 1-back and 2-back, his makes a
o al o 4 di ec ional decision combina ions: 1) le /le , 2) igh / igh , 3) le / igh , and 4) igh /le . Fo each o
he ou cases, we calcula ed and compa ed he esul s when swapping he ac o o de (own s. pa ne ). The
de ails o he manual calcula ions a e epo ed in he Supplemen a y Resul s. O e all, we obse e de ian esul s
o he es ima e in he cu en ial depending on whe he he own o pa ne ’s las decision occu ed ea lie
(Case 1: 0.08 s -0.12; Case 2: -0.04 s. 0.03; Case 3: -0.30 s. 0.32; Case 4: 0.30 s. -0.29). Addi ionally, swapping
he ac o ’s o de in each decision case shows sign lips. Thus, he his o y o one’s own decisions and he his o y
o pa ne ’s decisions canno be ea ed independen ly, a he , he own and pa ne ’s ials wi h how a ious
decisions in e digi a e ha e o be conside ed.
Based on he p e ious esul s, we u n ou a en ion o po en ial simpli ica ions o he model ela ed o
he dependencies o ials a 1-back and 2-back. Speci ically, we es ed whe he he ac o and he di ec ional
decision a 2-back a e independen o he di ec ional decision a 1-back. Fo his, we de eloped Model 2 which
is simpli ied:
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P (D
n
= 1) ∼S
n
+A
n−1
×D
n−1
+(A+1
n−1)∗(An−2)+(A+1
n−1)∗(Dn−2
)
+(A+1
n−1)∗(An−2)×(A+1
n−1)∗(Dn−2
)
+(A−1
n−1)∗(An−2)+(A−1
n−1)∗(Dn−2
)
+(A
−1
n−1)∗(An−2)×(A
−1
n−1)∗(Dn−2)
The a iables inco po a ed assume he ac o o decision a 2-back is condi ional on he ac o a 1-back bu
do no depend on he decision a 1-back. The esul s showed signi ican and posi i e main e ec s o he
a iables
Sn
(β = 1.04, 95% CI [1.02, 1.07], SE = 0.03, p < 0.001),
(
A
+1
n−1)∗(
D
n−2)
(β = 0.11, 95% CI [0.17, 0.16],
SE = 0.02, p < 0.001), and
(
A
−1
n−1)∗(
D
n−2)
(β = 0.07, 95% CI [0.02, 0.11], SE = 0.03, p < 0.01). Fo he in e ac ion
a iables,
An−1×Dn−1
showed posi i e and signi ican (β = 0.11, 95% CI [0.09, 0.14], SE = 0.02, p < 0.001).
Bo h
(
A
+1
n−1)∗(
An
−2)×(
A
+1
n−1)∗(
Dn
−2)
and
(
A
−1
n−1)∗(
An
−2)×(
A
−1
n−1)∗(
Dn
−2)
showed e y simila
posi i e and signi ican es ima es (β = 0.15, 95%, CI [0.09, 0.22], SE = 0.04, p < 0.001 and β = 0.15, 95% CI [0.09,
0.21], SE = 0.04, p < 0.001, espec i ely). The model’s p edic ed alues, i.e., es ima ed ma ginal means o he
a iable
(
A
+1
n−1)∗(
An
−2)×(
A
+1
n−1)∗(
Dn
−2)
showed ha unde he condi ion ha 1-back was own, when
he decision a 2-back was igh and he ac o a 2-back was own, he likelihood o epea ing he decision was
0.81, as compa ed o a lowe likelihood o 0.75 when he ac o a 2-back was pa ne . Simila ly, he model’s
p edic ed alues o he a iable
(
A
−1
n−1)∗(
An
−2)×(
A
−1
n−1)∗(
Dn
−2)
showed ha unde he condi ion ha
1-back was pa ne , when he decision a 2-back was igh and he ac o a 2-back was own, he likelihood o
epea ing he decision was 0.80, compa ed o a lowe likelihood o 0.74 when he ac o a 2-back was he pa ne .
This indica es ha , whe he 1-back was own o pa ne , he pa icipan exhibi ed a choice epe i ion bias when
hei sel ac ed a 2-back. Las ly, Model 2 exhibi ed an AIC alue o 31,294 (ΔAIC = -20.15 uni s om Model 1),
as well as a BIC alue o 31,368.08 (ΔBIC = − 85.75 uni s om he Model 1). The c oss- alida ed accu acy o he
model was 73.8%, wi h an MSE alue o 0.1921. This sugges s he quan i a i e e ec o he ac o a 2-back does
no depend on he di ec ional decision a 1-back.
Nex , we u he simpli ied he model o es whe he he e ec o he ac o a 2-back is independen o he
ac o and di ec ional decisions a 1-back:
P (D
n
= 1) ∼S
n
+A
n−1
+D
n−1
+A
n−1
×D
n−
1
+
A
n−2+
D
n−2+
A
n−2×
D
n−2
This Model 3 e lec s ha while he ac o and decision a 1-back and 2-back a e ele an , he in luence o 2-back
ac o s and decisions is no di ec ly dependen on he 1-back ac o and decision. The esul s showed posi i e and
signi ican e ec o
Sn
(β = 1.05, 95% CI [1.02, 1.07], SE = 0.03, p < 0.001) and
Dn−2
(β = 0.13, 95% CI [1.10, 1.16],
SE = 0.02, p < 0.001). The esul s also showed posi i e and signi ican e ec s o he in e ac ion
An−1×Dn−1
(β = 0.11, 95% CI [0.08, 0.14], SE = 0.02, p < 0.001) and
An−2×Dn−2
(β = 0.12, 95% CI [0.09, 0.14], SE = 0.02,
p < 0.001). This model exhibi ed an AIC o 31,240 (ΔAIC = − 54.13 uni s om he Model 2) and a BIC o 31,305.46
(ΔBIC = − 62.62 uni s om Model 1). The c oss- alida ed accu acy alue o he model was 73.8%, wi h a MSE
alue o 0.1917. Table 2 p esen s a summa y o he eg ession models. Toge he , he u he implica ions e ealed
ha Model 3 be e i s he obse ed da a. No ably, his model, which does no accommoda e any dependence
o he e ec o 2-back on he de ails o wha happened a 1-back, indica ed signi ican in e ac ion e ec s o he
ac o s and decisions o bo h 1-back and 2-back. This sugges s he decision and ac o join ly in luence he choice
o be made, showing suppo o H1. Fo example, he likelihood o epea ing a choice is in luenced by he ac ing
pa icipan ’s esponse a 2-back, wi h he likelihood inc easing o dec easing depending on whe he he ac ing
pa icipan esponded le o igh .
Discussion
In he p esen s udy, we in es iga ed he choice his o y bias e ec in a social con ex . Speci ically, pa icipan s
we e g ouped in dyads o pe o m a sha ed pe cep ual decision-making ask ha allowed each pa icipan
o obse e hei pa ne ’s esponses. Using a s epwise eg ession app oach, we es ed he ex en o which he
modeling esul s suppo ou wo p oposed hypo heses. Compa isons be ween he models led o Model 3 as
he be e - i ing model, which speci ies an e ec o he ask s imulus, he combined in luence o he ac o and
decision a 1-back, he decision a 2-back, and he combined in luence o he ac o and decision a 2-back.
Speci ically, he model exhibi ed lowes AIC and BIC, which indica es a be e balance be ween he model i
and complexi y. The educ ion in he c oss- alida ed MSE also sugges s a dec ease in p edic ion e o . Thus,
while he p edic i e accu acy appa en ly emained cons an , likely due o he classi ica ion h esholding a 0.5
no e lec ing he ull a ia ions in he model’s ac ual p edic ion alues, he imp o emen s in AIC, BIC, and
MSE indica e ha he model be e i s he da a. O e all, ou indings indica e a dyadic dependency in which
he pa icipan did no igno e hei pa ne ’s decisions; ye , hey ea ed hei pa ne ’s decisions di e en ly om
hei own i.e., de ia ed om hei pa ne ’s decision.
The cu en s udy is explo a o y and has limi a ions. One limi a ion is ha he pa icipan s sa in sepa a e
expe imen al ooms and did no sha e he same pe ipe sonal space. This physical sepa a ion may ha e limi ed
he in e ac ion e ec ypically accoun ed o in a sha ed space15. The pa icipan s did no communica e bu
only obse ed each o he ’s esponses on each ial. While his ac o was pa o he expe imen design, i could
educe a sense o social p esence ha in luences pe cep ual judgmen s24. On he lip side, hese design choices
allowed a clean and unambiguous analysis o he dyadic decision p ocess.
Scien i ic Repo s | (2025) 15:11420 9
| h ps://doi.o g/10.1038/s41598-025-96182-5
www.na u e.com/scien i ic epo s/