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ORIGINAL RESEARCH ARTICLE
published: 20 March 2015
doi: 10.3389/fpsyg.2015.00240
Arbitrary numbers counter fair decisions:
trails of markedness in card distribution
Philipp A. Schroeder1* and Roland Pfister2
1Department of Psychiatry and Psychotherapy, Neurophysiology and Interventional Neuropsychiatry, University of Tübingen, Tübingen, Germany
2Department of Psychology III, University of Würzburg, Würzburg, Germany
Edited by:
Hans-Christoph Nuerk, University of
Tübingen, Germany
Ann Dowker, University of Oxford,
UK
Reviewed by:
Stefan Huber, Knowledge Media
Research Center, Germany
Tobias Loetscher, University of
South Australia, Australia
*Correspondence:
Philipp A. Schroeder, Department of
Psychiatry and Psychotherapy,
Neurophysiology and Interventional
Neuropsychiatry, University of
Tübingen, Calwerstrasse 14,
D-72076 Tübingen, Germany
e-mail: philipp.schroeder@
uni-tuebingen.de
Converging evidence from controlled experiments suggests that the mere processing of
a number and its attributes such as value or parity might affect free choice decisions
between different actions. For example the spatial numerical associations of response
codes (SNARC) effect indicates the magnitude of a digit to be associated with a spatial
representation and might therefore affect spatial response choices (i.e., decisions between
a “left” and a “right” option). At the same time, other (linguistic) features of a number
such as parity are embedded into space and might likewise prime left or right responses
through feature words [odd or even, respectively; markedness association of response
codes (MARC) effect]. In this experiment we aimed at documenting such influences in a
natural setting. We therefore assessed number-space and parity-space association effects
by exposing participants to a fair distribution task in a card playing scenario. Participants
drew cards, read out loud their number values, and announced their response choice,
i.e., dealing it to a left vs. right player, indicated by Playmobil characters. Not only did
participants prefer to deal more cards to the right player, the card’s digits also affected
response choices and led to a slightly but systematically unfair distribution, supported by
a regular SNARC effect and counteracted by a reversed MARC effect. The experiment
demonstrates the impact of SNARC- and MARC-like biases in free choice behavior through
verbal and visual numerical information processing even in a setting with high external
validity.
Keywords: embodied cognition, numerical cognition, SNARC effect, MARC effect, and justice for all, linguistic
markedness, free choice
INTRODUCTION
Like nothing else, numbers are regarded as pure and objective.
They are the cornerstone of scientific progress in terms of mea-
surements and statistics and they similarly shape global business
in various ways—from defining monthly salaries to describing
trends at the stock market. But does this objectivity survive when
numbers come in contact with human agents? In fact, there
seems to be good reason for a positive answer to this question.
Numbers obviously allow for rule-based decisions between com-
peting options, and a decision that is based on numbers is readily
accepted as fair and impersonal (Porter, 1996). At the same time,
however, research on human decision making has documented
that numbers can systematically bias an agent’s choice behavior
via anchoring and adjustment heuristics (Mussweiler and Englich,
2003; Furnham and Boo, 2011). For instance, when asked to
estimate the value of a property, laymen and professionals alike
rated the price of a real estate higher when they were told a higher
listed price before (Northcraft and Neale, 1987). This anchoring
bias was found in numerous contexts and research in this domain
has shown that heuristic decisions might even integrate nominally
irrelevant anchors like telephone and social insurance numbers
(Tversky and Kahneman, 1974).
Such anchoring effects are of course driven by memory
processes rather than by the numbers themselves. Still, recent
research on numerical and embodied cognition suggests that
the mere presence of a number alone might be sufficient to
invoke biases in thoughts and actions (Barsalou, 1999; Fischer,
2006, 2012). These biases built on well-documented associations
between numerical magnitude and spatial locations that indicate
smaller numbers to be associated with left locations and larger
numbers to be associated with right locations [spatial numerical
associations of response codes (SNARC) effect; Dehaene et al.,
1993; Wood et al., 2008]. Most importantly for the present study,
such spatial-numerical associations also affect response choices
(Tschentscher et al., 2012; Shaki and Fischer, 2014). That is, when
being confronted with smaller numbers, participants showed a
preference for choosing a left vs. a right response key (Daar
and Pratt, 2008) and, similarly, such small numbers involuntarily
prompted left-oriented gaze directions (Ruiz Fernández et al.,
2011) and small numbers were produced more likely while turn-
ing or gazing to the left (Loetscher et al., 2008, 2010). These
automatic biases document that the mere presence of a number
is sufficient to bias choices and behavior. Sensory and motor
biases induced by the SNARC effect can be considered of high
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Schroeder and Pfister Arbitrary numbers counter fair decisions
FIGURE 1 | Experimental setup. Participants started each trial by leaving
the central home key. They then drew a card, named its value and
announced to assign the card to either the left or the right player
(represented by two female Playmobil® characters). Card values were
predefined according to the rummy game rules and explicitly instructed to
the participants. A fair distribution was to be achieved without explicitly
counting the values assigned to each player. The experimenter coded each
announcement and we analyzed (i) how many cards and points were
distributed to each player and (ii) whether digit features (magnitude and
parity) affected single response choices.
diagnostic merit for the understanding of grounded, embodied,
and situated cognition (Fischer, 2012). Findings pertinent to this
point range from culture-dependent finger counting habits that
influence magnitude representations (Domahs et al., 2010) to
bodily postures (Eerland et al., 2011) or even “unusual bodies”
(Keehner and Fischer, 2012) that introduce peculiarities in spatial
tasks. Together, these studies indicate that numerical associations
reliably alter spatial response choices in deliberately employed
highly controlled settings where the agent does not pursue any
other goals except for deciding spontaneously for a spatially coded
response.
As a first aim, the present study investigated whether the
described bias would also occur in a more externally valid setting
such as in situations where the agent aims at fairly and objectively
distributing value among other people. We operationalized this
situation in terms of a card distribution task in which participants
were asked to deal cards of a given value to a player to the left or
to the right and additionally announce their value-space choice
(Figure 1). If spatial-numerical biases do indeed generalize to this
situation, participants should deal more cards with higher values
to the right player than to the left player.
Of course, these biases do not work in an all or none fashion,
but gradually. That is, even though participants prefer choices
that are congruent to a number’s spatial association (e.g., a left
response to a small number), they also tend to show a fair amount
of incongruent choices (e.g., a right response to a small number;
Daar and Pratt, 2008). In the natural card playing setting of this
study, however, both spatial-numerical associations and marked-
ness of parity and space [markedness association of response
codes (MARC) effect; Nuerk et al., 2004] might affect choice
probabilities for each single card, summing up to an overall biased
and therefore unfair bias in value distribution. As both, high and
even numbers (such as the target card value “8” or “10”) are
usually associated with right responses and with more points in
the rummy card setting at hand, our main hypothesis was that
participants would be biased to deal overall more points to the
right than to the left player.
MATERIALS AND METHODS
PARTICIPANTS AND APPARATUS
Twenty-five participants (19 females, mean age =24.3, range:
18–52 years, 3 left-handed)1were invited to participate in a
15-min experimental session. They were seated in front of the
apparatus displayed in Figure 1. This apparatus mainly consisted
of a 60 ×40 cm cardboard box, the surface of which was
covered with blue and white paper. Two Playmobil® characters
represented the players and were positioned at the rear edge of
the card box surface with an inter-player distance of 50 cm. The
players were matched for various attributes such as size, age,
beauty, and orientation toward the participant. A slot in front
of each player allowed the participants to insert a card in a box
beneath the surface of the apparatus, restricting visual feedback
of the current distribution. A central key was positioned at the
front edge to allow for a standardized trial procedure, and the
1As pointed out by a reviewer, individual variations of age, handedness or sex
might play a role in marked decisions about numbers (see the discussion for
an elaboration). However, also following the reviewer’s suggestion, fitting a
model on right-handed female participants aged 30 or less did not substan-
tially alter the results and only marginally improved the model fit.
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Schroeder and Pfister Arbitrary numbers counter fair decisions
card deck was placed 10 cm from the key onto a predefined
mark. One participant decided to distribute cards by color and
thereby achieved a totally fair distribution; this participants’ data
was excluded from the analysis and we refer to the remaining
N=24 participants in the following. The study was conducted
in accordance with the Declaration of Helsinki and the guidelines
of the ethics committee at the University of Würzburg.
PROCEDURE
The basic task of the participants was to draw a card and deal it to
either the left or the right player. Each participant received three
random training cards, then a complete 52 Anglo-American style
rummy card pack. We ensured that the card icons were printed in
all four corners of each card to avoid systematic influences origi-
nating from the specific stimulus set (Figure 1). Card values were
defined following standard rummy game rules, that is: number
cards (2–10) counted their printed value (i.e., two points for a
“2,” three points for a “3,” and so on), royal cards (jack, queen,
and king) counted 10 points, and aces counted 11 points. The
deck was professionally shuffled prior to the experiment. During
the instructions, we emphasized that participants should aim for a
fair distribution of values across players by intuition and without
using any explicit strategies (such as counting points across the
experiment).
To start a trial, participants pressed and released the start
button. They then drew the top card from the deck, read out
loud the card’s face (e.g., “Ace of Spades”), its value (“11”), and
announced the side they wanted to distribute it to (always in this
order). They then inserted the card into the right or left card
slot. The experimenter registered the information and also coded
invalid trials (i.e., illegal use of the left hand, reading out the
wrong number or value, or naming the card’s attributes and the
corresponding choice in the wrong order; 4.4% trials in total).
DATA TREATMENT
For the main analysis, both the number of cards and the resulting
scores for each player and participant were computed. Note that
although the two measures are confounded, they still allow for
distinct evaluation of choice preference and influences of the
SNARC or the MARC effect: Even without an overall preference
of one player in terms of the number of cards, a difference in
scores can arise from a SNARC-like distribution of high-value
cards to the right player and low-value cards to the left player.
Both measures were controlled for homogeneity and normal
distribution and subjected to one-tailed paired t-tests to assess our
main hypothesis of a preference for the right player.
In a second, exploratory analysis, we aimed at dismantling
underlying SNARC and MARC influences to the free, binary
choice at a trial-wise level. Therefore, we used generalized mixed-
effects models to predict the likelihood of a left response from the
two first-level fixed factors parity and magnitude.
RESULTS
SCORES AND NUMBER OF CARDS
Mean scores and number of cards for each player are depicted
in Figure 2. Tests for normal distribution (Kolmogorov Smirnov:
ps>0.23) and homogeneity of the sample were conducted prior
to the analysis and showed the data to be suitable for analyses via
parametric tests.
Whereas 188 (SE =3.33) points on average were assigned
to the right player, only 172 (SE =3.76) points were assigned
to the left player, and this difference in scores was significant,
t(23) =2.52, p=0.010, d=0.53 (Figure 2A). A similar effect
emerged for the number of cards dealt to the left and right player,
respectively, t(23) =1.92, p=0.034, d=0.40 (Figure 2B), as par-
ticipants assigned about two cards more (dN=1.71, SE =0.48)
to the right player. The effects on points and card numbers were
FIGURE 2 | Mean scores and standard errors of paired difference (cf.
Pfister and Janczyk, 2013) in the card distribution task. Participants overall
preferred the right player which resulted in a significant difference in scores
(A), and a similar effect in overall card numbers (B). Note that both Playmobil
players acted earnest without any particular facial expression during the
experiment, unlike the displayed emotions in panel (A). *p<0.05, **p<0.01.
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Schroeder and Pfister Arbitrary numbers counter fair decisions
Table 1 | Probabilities of left response choices as a function of target card value.
Single-digit cards Royal cards
Target card value 2 3 4 5 6 7 8 9 10 11
P(left) [%] 57.3 50.4 48.3 42.0 52.8 40.6 48.5 42.4 49.4 47.2
correlated significantly across participants, r=0.85, p<0.001,
indicating that the difference in cards accounted for about 71% of
the effect on distributed points.
EXPLORATORY ANALYSIS: SNARC AND MARC EFFECTS
More fine-grained analyses targeted the outcome of individual
decisions rather than the overall number of points or cards dealt
by each participant (Table 1). More precisely we aimed at ana-
lyzing the impact of magnitude and parity on the outcome of
a decision (i.e., the likelihood for a card to be dealt to the left
or to the right). To this end, we employed generalized linear
mixed-effects models to model the binary outcome of the choice.
Magnitude and parity were entered as fixed factors into the model
(first level predictors), which further included individual subjects
as random effects on the second level. The model was fitted
in R by using the glmer function of the lme4 package (Bates
et al., 2014; binomial family and logit link function). We further
restricted the analysis to single-digit values (2–9) due to the actual
different pictorial presentation of royal card values and possibly
different representational format of values that would imply a
two-digit numerical notation (Nuerk and Willmes, 2005; Nuerk
et al., 2011).
In a first step, we evaluated each predictor individually (each
being coded as centered variable). As suggested by the main analy-
ses above, higher magnitudes were indeed associated with a higher
preference for right responses (fixed effect estimate =0.055/num-
ber, SE =0.032), z=1.70, p=0.045, ppb =0.036.2Surprisingly,
even numbers were more likely to be dealt to the left side as com-
pared to odd numbers (fixed effect estimate =0.281, SE =0.147),
indicating a reliably reversed MARC effect, z= −1.91, p=0.028,
ppb =0.030.
For model comparisons, we fitted a null model including
only an intercept on the first level, an additive model with value
and parity as independent predictors, and a saturated model
with main effects as well as the two-way interaction. In a first
step, we compared the null model to the additive model. This
comparison yielded a marginally significant effect in favor of the
additive model χ2(2) =5.42, p=0.067, ppb =0.069, indicating
that the two additional parameters did indeed add explanatory
value. Further including the interaction effect, however, did
not improve model fit significantly, χ2(1) =0.01, p=0.941,
ppb =0.929.
DISCUSSION
We investigated the effects of different characteristics of numbers
(values of playing cards) on biases in fair distribution behavior.
Indeed, we found evidence for such systematic biases in a free
2Based on the comments of a reviewer, the model comparison was repeated
using parametric bootstrapping with 1000 simulations, using the PBmod-
comp() function of the R package pbkrtest (Halekoh and Højsgaard, 2014).
choice experiment: Participants read out loud a rummy card’s
value and announced their spatial assignment to a leftward or
rightward positioned player. Without applying explicit strategies,
participants failed to distribute cards in a statistically fair way and
assigned a mean benefit of two cards or 16 points to the right
player. In line with recent findings from the linguistic markedness
and spatial-numerical associations of response codes effects, we
hypothesized such a pattern to be partly driven by odd and
high numbers being associated with rightward oriented action
codes.
In the following exploratory analyses, we aimed at disman-
tling SNARC and MARC-like effects on response decisions at
an individual, trial-wise level. Indeed, we found some evidence
for the regular SNARC effect, but the data also indicated a
reversed MARC effect with odd numbers being more likely to
be distributed to the right player and even numbers being more
likely to be distributed to the left player. Although this latter
finding certainly comes unexpected, several recent studies cast
doubt on a stable left-right association of odd and even numbers.
Rather, the direction of the MARC effect seems to depend on task
rules, i.e., affirmative answers seem to be generally compatible
with right response codes and might override the parity-driven
code of an odd number (Cho and Proctor, 2007). Further, Nuerk
et al. (2005) observed the MARC effect to be altered by stimulus
and experimental settings: Whereas participants showed a usual
MARC effect for number words when the experiment started
with Arabic notation digits, this effect was reversed when the
experiment started with dice-dot patterns. In light of the apparent
similarity of dice patterns and the patterns printed on the play-
ing cards of the current experiment (see Figure 1), one might
speculate that such gambling-related stimuli might generally elicit
a reversed linguistic markedness of parity; however, Chang and
Gibson (2011) found a regular odd-even effect in Sudoku puzzles
and future studies are needed to clarify these speculations and
investigate the underlying mechanisms.
Such flexibility of the MARC effect further seems likely in
light of various findings on flexible coding of the related SNARC
effect. For instance, the SNARC effect is influenced by inter-
individual characteristics such as finger counting habits (Fischer,
2008), cultural aspects such as reading direction (Shaki et al.,
2009; Domahs et al., 2010) as well as sex (Bull et al., 2013) and
age (Wood et al., 2008). The MARC effect, similarly, was recently
found reversed for left-handers (Huber et al., 2014), which sup-
ports a body-specificity account (Casasanto, 2009) rather than a
linguistic markedness account (Nuerk et al., 2004). Furthermore,
the SNARC effect is also modulated by short-term, contextual
factors such as recently encountered episodes (sequence effects:
Pfister et al., 2013), number usage (number placement in text:
Fischer et al., 2010; on a ruler vs. clock face: Bächtold et al.,
1998) and current number range (Dehaene et al., 1993; Fias et al.,
1996).
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Schroeder and Pfister Arbitrary numbers counter fair decisions
GENERAL PLACEMENT PREFERENCES
Of course, the overall preference for the right card slot of our
mostly right-handed participants also reminds of robust phe-
nomena unrelated to the processing of numerical stimuli such as
turning biases when confronted with a decision to take either a left
or a right turn (Liederman and Kinsbourne, 1980; Güntürkün,
2003; cf. Shaki and Fischer, 2014, for the interplay of number
processing and turning during walking). Furthermore, physical
positioning was shown to produce more positive attitudes for
rightward placed items (Nisbett and Wilson, 1977; Choi and
Myer, 2012). Vice versa, positive abstract concepts were associated
with right space for right-handed participants (Casasanto, 2009).
In fact, a vast amount of marketing literature is concerned with
devaluation of laterally placed items (Dittrich and Klauer, 2012),
which is at times confounded with a desirable perception of
magnitude (i.e., heaviness perception; Deng and Kahn, 2009) or
automatic price and quality inferences (i.e., expensive and high-
quality items on the right end; Valenzuela and Raghubir, 2009).
For free choice actions, goal keepers were found more likely to
dive to the right during shoot-outs and under pressure (Roskes
et al., 2011; but see Price and Wolfers, 2014), which was taken to
document approach motivation (Roskes et al., 2014).
HANDEDNESS-DEPENDENT PLACEMENT PREFERENCES
Already for spontaneous turning biases, stronger right-sided
head-turning was documented for right-handed than for left-
handed participants (Ocklenburg and Güntürkün, 2009). Sim-
ilarly, positive abstract concepts were associated with rightward
space for right-handers, but left-handed participants with similar
linguistic experience (i.e., use of metaphors) showed a reversed
association of abstract concepts and space (Casasanto, 2009),
suggesting that bodily experiences might shape valence-specific
placement preferences. In a large Moroccan sample that exhibited
strong taboos against the use of left hands, the implicit space-
valence association was found effectively identical compared to
a Spain sample (de la Fuente et al., 2014), but explicit measures
(i.e., good-is-right rating and ratio of right/left-handers) were
larger in the Arab population. Thus, handedness and according
interactions with the external world appear to be valid can-
didates in explaining general and explicit spatial mappings of
valence.
Given the data at hand, we cannot provide evidence for culture
or hand-experience specific modulations. However, valence-space
and value-space associations are not necessarily interchange-
able, despite a possible positive connotation of playing cards or
numbers in general. For mere numbers, reversing the polarity
of a response side through response eccentricity did not affect
spatial-numerical associations (Santiago and Lakens, 2014), sug-
gesting that the link between numbers and space is not (exclu-
sively) driven by their value-valence correspondence (i.e., polarity
correspondence; Proctor and Cho, 2006). Another study even
suggested magnitude to underlie spatial valence representations
(Holmes and Lourenco, 2011). Furthermore, number-space asso-
ciations are manifold regarding the number’s features (see Patro
et al., 2014, for a recent taxonomy proposal at an early age), and
we next discuss the possible interpretation of SNARC and MARC
effects in terms of linguistic markedness.
LINGUISTIC MARKEDNESS IN NUMBER PROCESSING?
It is widely accepted that number processing includes a verbal
component, as suggested by the triple-code model (Dehaene et al.,
1993; Klein et al., 2014). Semantic features of the number (parity
and magnitude) are activated automatically and can deteriorate
unrelated task processing already in children of 10 years of age
(Berch et al., 1999). As such, linguistic markedness of a verbal
number-code, i.e., in form of the non-marked even parity fea-
ture, might facilitate equally non-marked responses, i.e., right
actions (Nuerk et al., 2004). Arguably, in this experiment, the
number of cards dealt to a player can be regarded an unspecific
placement preference and explained a substantial proportion, but
not all variance of differences in scores. Rather, the results from
our exploratory analysis suggest that space-number associations
further biased the distribution outcome, and that reversed space-
parity associations supported but space-magnitude associations
counteracted the fair distribution.
For linguistic influences in the SNARC effect, instead of
assuming an oriented mental number line (i.e., Göbel et al.,
2001), it is similarly possible that magnitude is coded by opposed
small/large polar or linguistic representations (c.f. Nuerk et al.,
2004; Proctor and Cho, 2006). Facilitated left/right responses
can be accounted for by corresponding pairs of markedness:
The adjectives large and small are lexical opposites with large
as the non-marked adjective (Jakobson, 1931; see also: Lehrer,
2008). Similarly, the adjective right is linguistically non-marked
(Zimmer, 1964), and the correspondence of both non-marked
(i.e., large and right) and marked (i.e., small and left) pairs
would lead to the SNARC effect. Homogenous marked and non-
marked pairs should be responded to faster and they should
more often be selected in a free choice paradigm. Consequently,
with a decreasing marked property of small, the marked left
response side was chosen less frequently. However, it is not clear
how linguistic markedness can account for flexible magnitude-
space and reversed parity-space associations; instead, a flexible,
body-specific conceptual layer, i.e., in form of polarity or space,
seems more likely. Obviously, participants were more cautious in
distributing high-value (i.e., royal) cards more equally in order
to distribute the cards fairly; nevertheless, magnitude-response
correspondence, as indexed by the regular SNARC effect, could
have effectively led to the observed right-bias.
Crucially, the interpretation of the SNARC effect in terms
of polarity correspondence (Proctor and Cho, 2006) or verbal
codes (Gevers et al., 2010) does not exclude the possibility of
a visuo-spatial representation of magnitude. In line with the
dual-coding framework of Paivio (1986), non-verbal and verbal
representations can be processed referentially and activate each
other. The observed SNARC effect in verbal and following motor
responses can be attributed to such a referential activation. Pos-
sibly, a visuo-spatial representation was pronounced because our
participants performed actual hand movements in a well-defined
space, namely over a card-playing table.
We excluded two-digit and royal card stimuli from the mixed-
effects SNARC and MARC models as too little is known about
these indirectly magnitude-related stimuli at this time: Do they
extend the mental number line similar to 0 (Pinhas and Tzelgov,
2012)? How are nominal two-digit numbers processed when part
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Schroeder and Pfister Arbitrary numbers counter fair decisions
of this specific number range (Dehaene et al., 1993; Nuerk and
Willmes, 2005; Nuerk et al., 2014) and does the pictorial presenta-
tion, i.e., of a king vs. a jack, trigger marked representations other
than the rule-based card value?
Notwithstanding these open issues, a range of recent papers
addressed the linkages of brain mechanisms devoted to language
and action, respectively, and elaborated these linkages in several
frameworks to accommodate for SNARC and MARC effects (e.g.,
Pulvermüller, 2005; Barsalou, 2008; Fischer, 2012). In case of
the SNARC effect, interestingly, language or number processing
is most likely only indirectly associated with motor system acti-
vations through magnitude processing (Fias et al., 1996) and
magnitude-related spatial codes (Gevers et al., 2006) or verbal
codes (Gevers et al., 2010). Still, this indirect loop was demon-
strated sufficient to modulate deliberate action selection (Daar
and Pratt, 2008; Ruiz Fernández et al., 2011). In this experiment,
we further show that this bias even transfers to a more natural card
playing scenario and is able to interfere with a fair distribution
task.
FAIR DECISIONS IN CARD DISTRIBUTION
Although statistically the goal of fair distribution was not met,
participants were mostly confident about their choices during
debriefing and reported to have achieved the goal by deciding
upon a subjective feeling of just distribution. This finding is in line
with results on the egocentric fairness bias (Tanaka, 1999), stating
that especially just world believers (Rubin and Peplau, 1975)
consider their own behavior as fairer than other people’s behavior.
In relation to these findings, the perception of fairness might
be considered biased by social demands (Blair, 2002), whereas
actual fair behavior was counter-acted here by automaticity, i.e.,
number-space associations.
Several alternative explanations might also account for the
observed general preference for the right player. In this regard,
some limitations of the study have to be considered: Both the table
coloring and the player characters were not counterbalanced and
could have implied unidentified response tendencies3. The study
sample was rather diverse regarding participants’ age, sex, and
handedness, which likely increased the variance of number-space
associations. Future studies should more closely examine these
characteristics’ interactions with number-driven action decisions.
By including the rummy card set, the stimuli used were, on one
hand, of high external validity and allowed for instructing and
investigating fair distribution behavior. On the other hand, the
stimulus set by nature included two-digit and pictorial cards and
thereby differs from previous studies. Nevertheless, we focused on
single digits only in the mixed effects models analysis and thereby,
the results of this analysis must be regarded exploratory and might
underestimate the SNARC effect for the entire number range.
A closer look at single digits in the exploratory analy-
sis pointed towards regular magnitude-space associations, but
reversed parity-space associations. As such, automatic number
magnitude processing emphasized a possible pre-existing pref-
erence bias by suggesting rightward (leftward) choices for high
3For effects of color on cognition, see Elliot and Maier (2014). We thank a
reviewer for drawing our attention to this point.
(low) value cards, resulting in higher scores. Given the full
standard rummy card set, a regular MARC effect would have
further emphasized responses favoring the right player. Placement
preferences were increasingly identified in the literature, and the
same is true for number-space associations. In a natural setting, it
is likely that both types of bias affect choices, and our analysis
confirms this view by the combination of identity-unspecific
results (number of cards) and number specific results (scores and
single-digit decision outcomes).
In conclusion, the results of our study support current views
of actions as being influenced by language processing. During
card distribution and while aiming at a fair and equal distribu-
tion, the participants’ choices were still affected by linguistic or
conceptual features of actual rummy cards, namely digit parity
and magnitude. A regular SNARC and a reversed MARC effect
emerged and ultimately supported the overall preference of a right
player avatar. The successful transfer of these effects to a more nat-
ural setting emphasizes the importance of further understanding
the (neural) mechanisms behind indirectly and directly action-
related linguistic and conceptual influences on number process-
ing. Understanding these mechanisms will allow for identifying
in which situations number associations can systematically bias
behavior and, consequently, a better understanding will allow for
countering these biases.
AUTHOR CONTRIBUTIONS
PS and RP designed research; PS performed research; PS and RP
analyzed data and wrote the paper.
ACKNOWLEDGMENTS
We acknowledge support by Deutsche Forschungsgemeinschaft
and Open Access Publishing Fund of Tübingen University. We
are grateful to Julia Schönrock for casting and recruiting suitable
Playmobil® characters for the study.
REFERENCES
Bächtold, D., Baumüller, M., and Brugger, P.(1998). Stimulus-response compatibil-
ity in representational space. Neuropsychologia 36, 731–735. doi: 10.1016/S0028-
3932(98)00002-5
Barsalou, L. (1999). Perceptions of perceptual symbols. Behav. Brain Sci. 22, 637–
660. doi: 10.1017/S0140525X99532147
Barsalou, L. W. (2008). Grounded cognition. Annu. Rev. Psychol. 59, 617–645. doi:
10.1146/annurev.psych.59.103006.093639
Bates, D., Maechler, M., Bolker, B., and Walker, S. (2014). Linear Mixed-Effects
Models Using Eigen and S4. R Package version 1.1-7. Available at: http//CRAN.R-
project.org/package=lme4
Berch, D. B., Foley, E. J., Hill, R. J., and Ryan, P. M. (1999). Extracting parity
and magnitude from Arabic numerals: developmental changes in number
processing and mental representation. J. Exp. Child Psychol. 74, 286–308. doi:
10.1006/jecp.1999.2518
Blair, I. V. (2002). The malleability of automatic stereotypes and prejudice. Personal.
Soc. Psychol. Rev. 6, 242–261. doi: 10.1207/S15327957PSPR0603_8
Bull, R., Cleland, A. A., and Mitchell, T. (2013). Sex differences in the spatial repre-
sentation of number. J. Exp. Psychol. Gen. 142, 181–192. doi: 10.1037/a0028387
Casasanto, D. (2009). Embodiment of abstract concepts: good and bad in right-
and left-handers. J. Exp. Psychol. Gen. 138, 351–367. doi: 10.1037/a0015854
Chang, H.-S., and Gibson, J. M. (2011). The odd-even effect in Sudoku puzzles:
effects of working memory, aging, and experience. Am. J. Psychol. 124, 313–324.
doi: 10.5406/amerjpsyc.124.3.0313
Cho, Y. S., and Proctor, R. W. (2007). When is an odd number not odd? Influence
of task rule on the MARC effect for numeric classification. J. Exp. Psychol. Learn.
Mem. Cogn. 33, 832–842. doi: 10.1037/0278-7393.33.5.832
Frontiers in Psychology | Developmental Psychology March 2015 | Volume 6 | Article 240 |6
Schroeder and Pfister Arbitrary numbers counter fair decisions
Choi, J., and Myer, D. W. (2012). The effect of product positioning in a comparison
table on consumers’ evaluation of a sponsor. Mark. Lett. 23, 367–380. doi:
10.1007/s11002-012-9162-9
Daar, M., and Pratt, J. (2008). Digits affect actions: the SNARC effect and response
selection. Cortex 44, 400–405. doi: 10.1016/j.cortex.2007.12.003
Dehaene, S., Bossini, S., and Giraux, P. (1993). The mental representation of parity
and number magnitude. J. Exp. Psychol. Gen. 122, 371–396. doi: 10.1037/0096-
3445.122.3.371
de la Fuente, J., Casasanto, D., Román, A., and Santiago, J. (2014). Can culture
influence body-specific associations between space and valence? Cogn. Sci. doi:
10.1111/cogs.12177 [Epub ahead of print].
Deng, X., and Kahn, B. (2009). Is your product on the right side? The “location
effect” on perceived product heaviness and package evaluation. J. Mark. Res. 46,
1–48. doi: 10.1509/jmkr.46.6.725
Dittrich, K., and Klauer, K. C. (2012). Does ignoring lead to worse evaluations? A
new explanation of the stimulus devaluation effect. Cogn. Emot. 26, 193–208.
doi: 10.1080/02699931.2011.570313
Domahs, F., Moeller, K., Huber, S., Willmes, K., and Nuerk, H.-C. (2010). Embod-
ied numerosity: implicit hand-based representations influence symbolic num-
ber processing across cultures. Cognition 116, 251–266. doi: 10.1016/j.cognition.
2010.05.007
Eerland, A., Guadalupe, T. M., and Zwaan, R. A. (2011). Leaning to the left makes
the Eiffel Tower seem smaller: posture-modulated estimation. Psychol. Sci. 22,
1511–1514. doi: 10.1177/0956797611420731
Elliot, A. J., and Maier, M. A. (2014). Color psychology: effects of perceiving color
on psychological functioning in humans. Annu. Rev. Psychol. 65, 95–120. doi:
10.1146/annurev-psych-010213-115035
Fias, W., Brysbaert, M., Geypens, F., and D’Ydewalle, G. (1996). The importance
of magnitude information in numerical processing: evidence from the SNARC
effect. Math. Cogn. 2, 95–110. doi: 10.1080/135467996387552
Fischer, M. H. (2012). A hierarchical view of grounded, embodied, and situated
numerical cognition. Cogn. Process. 13(Suppl. 1), S161–S164. doi: 10.1007/
s10339-012-0477-5
Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associa-
tions. Cortex 44, 386–392. doi: 10.1016/j.cortex.2007.08.004
Fischer, M. H. (2006). The future for SNARC could be stark. . ..Cortex 42, 1066–
1068. doi: 10.1016/S0010-9452(08)70218-1
Fischer, M. H., Mills, R. A., and Shaki, S. (2010). How to cook a SNARC: number
placement in text rapidly changes spatial-numerical associations. Brain Cogn.
72, 333–336. doi: 10.1016/j.bandc.2009.10.010
Furnham, A., and Boo, H. C. (2011). A literature review of the anchoring effect.
J. Socio Econ. 40, 35–42. doi: 10.1016/j.socec.2010.10.008
Gevers, W., Ratinckx, E., De Baene, W., and Fias, W. (2006). Further evidence that
the SNARC effect is processed along a dual-route architecture: evidence from
the lateralized readiness potential. Exp. Psychol. 53, 58–68. doi: 10.1027/1618-
3169.53.1.58
Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., et al.
(2010). Verbal-spatial and visuospatial coding of number-space interactions. J.
Exp. Psychol. Gen. 139, 180–190. doi: 10.1037/a0017688
Göbel, S., Walsh, V., and Rushworth, M. F. (2001). The mental number line and the
human angular gyrus. Neuroimage 14, 1278–1289. doi: 10.1006/nimg.2001.0927
Güntürkün, O. (2003). Human behaviour: adult persistence of head-turning asym-
metry. Nature 421, 711. doi: 10.1038/421711a
Halekoh, U., and Højsgaard, S. (2014). A Kenward-Roger approximation and
parametric bootstrap methods for tests in linear mixed models–the R package
pbkrtest. J. Stat. Softw. 59, 1–30.
Holmes, K. J., and Lourenco, S. F. (2011). Common spatial organization of number
and emotional expression: a mental magnitude line. Brain Cogn. 77, 315–323.
doi: 10.1016/j.bandc.2011.07.002
Huber, S., Klein, E., Graf, M., Nuerk, H.-C., Moeller, K., and Willmes, K. (2014).
Embodied markedness of parity? Examining handedness effects on parity judg-
ments. Psychol. Res. doi: 10.1007/s00426-014-0626-9 [Epub ahead of print].
Jakobson, R. (1931). “The structure of the Russian verb,” in Russian and Slavic
Grammar Studies, eds L. Waugh and M. Halle (Berlin: Mouton), 1–14.
Keehner, M., and Fischer, M. H. (2012). Unusual bodies, uncommon behaviors:
individual and group differences in embodied cognition in spatial tasks. Spat.
Cogn. Comput. 12, 71–82. doi: 10.1080/13875868.2012.659303
Klein, E., Suchan, J., Moeller, K., Karnath, H.-O., Knops, A., Wood, G., et al. (2014).
Considering structural connectivity in the triple code model of numerical
cognition: differential connectivity for magnitude processing and arithmetic
facts. Brain Struct. Funct. doi: 10.1007/s00429-014-0951-1 [Epub ahead of
print].
Lehrer, A. (2008). Markedness and antonymy. J. Linguist. 21, 397. doi: 10.1017/
S002222670001032X
Liederman, J., and Kinsbourne, M. (1980). The mechanism of neonatal rightward
turning bias: a sensory or motor asymmetry? Infant Behav. Dev. 3, 223–238. doi:
10.1016/S0163-6383(80)80028-2
Loetscher, T., Bockisch, C. J., Nicholls, M. E. R., and Brugger, P. (2010). Eye
position predicts what number you have in mind. Curr. Biol. 20, R264–R265.
doi: 10.1016/j.cub.2010.01.015
Loetscher, T., Schwarz, U., Schubiger, M., and Brugger, P. (2008). Head turns bias
the brain’s internal random generator. Curr. Biol. 18, R60–R62. doi: 10.1016/
j.cub.2007.11.015
Mussweiler, T., and Englich, B. (2003). Adapting to the Euro: evidence from bias
reduction. J. Econ. Psychol. 24, 285–292. doi: 10.1016/S0167-4870(03)00015-1
Nisbett, R., and Wilson, T. (1977). Telling more than we can know: verbal
reports on mental processes. Psychol. Rev. 84, 231–259. doi: 10.1037/0033-295X.
84.3.231
Northcraft, G. B., and Neale, M. A. (1987). Experts, amateurs, and real estate: an
anchoring-and-adjustment perspective on property pricing decisions. Organ.
Behav. Hum. Decis. Process. 39, 84–97. doi: 10.1016/0749-5978(87)90046-X
Nuerk, H.-C., Iversen, W., and Willmes, K. (2004). Notational modulation of the
SNARC and the MARC (linguistic markedness of response codes) effect. Q. J.
Exp. Psychol. A 57, 835–863. doi: 10.1080/02724980343000512
Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., and Fischer, M. H. (2011).
Extending the mental number line: a review of multi-digit number processing.
Z. Psychol. 219, 3–22. doi: 10.1027/2151-2604/a000041
Nuerk, H.-C., Moeller, K., and Willmes, K. (2014). “Multi-digit number process-
ing,” in Oxford Handbook of Mathematical Cognition, eds R. Cohen Kadosh and
A. Dowker (Oxford: Oxford University Press), 1–20.
Nuerk, H.-C., and Willmes, K. (2005). On the magnitude representations of two-
digit numbers. Psychol. Sci. 47, 52–72.
Nuerk, H.-C., Wood, G., and Willmes, K. (2005). The universal SNARC effect: the
association between number magnitude and space is amodal. Exp. Psychol. 52,
187–194. doi: 10.1027/1618-3169.52.3.187
Ocklenburg, S., and Güntürkün, O. (2009). Head-turning asymmetries during
kissing and their association with lateral preference. Laterality 14, 79–85. doi:
10.1080/13576500802243689
Paivio, A. (1986). Mental Representations: A Dual-Coding Approach. New York:
Oxford University Press.
Patro, K., Nuerk, H.-C., Cress, U., and Haman, M. (2014). How number-space
relationships are assessed before formal schooling: a taxonomy proposal. Front.
Psychol. 5:419. doi: 10.3389/fpsyg.2014.00419
Pfister, R., and Janczyk, M. (2013). Confidence intervals for two sample means:
calculation, interpretation, and a few simple rules. Adv. Cogn. Psychol. 9,
74–80.
Pfister, R., Schroeder, P. A., and Kunde, W. (2013). SNARC struggles: instant control
over spatial-numerical associations. J. Exp. Psychol. Learn. Mem. Cogn. 39, 1953–
1958. doi: 10.1037/a0032991
Pinhas, M., and Tzelgov, J. (2012). Expanding on the mental number line: zero is
perceived as the “smallest.” J. Exp. Psychol. Learn. Mem. Cogn. 38, 1187–1205.
doi: 10.1037/a0027390
Porter, T. M. (1996). Trust in Numbers: The Pursuit of Objectivity in Science and
Public Life. Princeton, NJ: Princeton University Press.
Price, J., and Wolfers, J. (2014). Right-oriented bias: a comment on roskes,
sligte, shalvi, and de dreu (2011). Psychol. Sci. 25, 2109–2111. doi: 10.1177/
0956797614536738
Proctor, R. W., and Cho, Y. S. (2006). Polarity correspondence: a general principle
for performance of speeded binary classification tasks. Psychol. Bull. 132, 416–
442. doi: 10.1037/0033-2909.132.3.416
Pulvermüller, F. (2005). Brain mechanisms linking language and action. Nat. Rev.
Neurosci. 6, 576–582. doi: 10.1038/nrn1706
Roskes, M., Sligte, D., Shalvi, S., and De Dreu, C. K. W. (2014). Does approach
motivation induce right-oriented bias? Reply to price and wolfers (2014).
Psychol. Sci. 25, 2112–2115. doi: 10.1177/0956797614547919
Roskes, M., Sligte, D., Shalvi, S., and De Dreu, C. K. W. (2011). The right side?
Under time pressure, approach motivation leads to right-oriented bias. Psychol.
Sci. 22, 1403–1407. doi: 10.1177/0956797611418677
www.frontiersin.org March 2015 | Volume 6 | Article 240 |7
Schroeder and Pfister Arbitrary numbers counter fair decisions
Rubin, Z., and Peplau, L. A. (1975). Who Believes in a Just World? J. Soc. Issues 31,
65–89. doi: 10.1111/j.1540-4560.1975.tb00997.x
Ruiz Fernández, S., Rahona, J. J., Hervás, G., Vázquez, C., and Ulrich, R. (2011).
Number magnitude determines gaze direction: spatial-numerical association in
a free-choice task. Cortex 47, 617–620. doi: 10.1016/j.cortex.2010.10.006
Santiago, J., and Lakens, D. (2014). Can conceptual congruency effects between
number, time, and space be accounted for by polarity correspondence? Acta
Psychol. (Amst.) doi: 10.1016/j.actpsy.2014.09.016 [Epub ahead of print].
Shaki, S., and Fischer, M. H. (2014). Random walks on the mental number line.
Exp. Brain Res. 232, 43–49. doi: 10.1007/s00221-013-3718-7
Shaki, S., Fischer, M. H., and Petrusic, W. M. (2009). Reading habits for both words
and numbers contribute to the SNARC effect. Psychon. Bull. Rev. 16, 328–331.
doi: 10.3758/PBR.16.2.328
Tanaka, K. (1999). Judgments of fairness by just world believers. J. Soc. Psychol. 139,
631–638. doi: 10.1080/00224549909598423
Tschentscher, N., Hauk, O., Fischer, M. H., and Pulvermüller, F. (2012). You
can count on the motor cortex: finger counting habits modulate motor cor-
tex activation evoked by numbers. Neuroimage 59, 3139–3148. doi: 10.1016/
j.neuroimage.2011.11.037
Tversky, A., and Kahneman, D. (1974). Judgment under uncertainty: heuristics and
biases. Science 185, 1124–1131. doi: 10.1126/science.185.4157.1124
Valenzuela, A., and Raghubir, P. (2009). Are top-bottom inferences conscious and
left-right inferences automatic? implications for shelf space positions. HEC Paris
INSEAD Fontainebleau. 19, 185–196.
Wood, G., Willmes, K., Nuerk, H.-C., and Fischer, R. (2008). On the cognitive link
between space and number: a meta-analysis of the SNARC effect. Psychol. Sci.
Q. 50, 489–525.
Zimmer, K. E. (1964). Affixal negation in English and other languages: an investi-
gation of restricted productivity. Word 20(2), Monograph No. 5.
Conflict of Interest Statement: The authors declare that the research was con-
ducted in the absence of any commercial or financial relationships that could be
construed as a potential conflict of interest.
Received: 22 November 2014; accepted: 16 February 2015; published online: 20 March
2015.
Citation: Schroeder PA and Pfister R (2015) Arbitrary numbers counter fair
decisions: trails of markedness in card distribution. Front. Psychol. 6:240. doi:
10.3389/fpsyg.2015.00240
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