How to Model Heterogeneity in Costly Punishment: Insights from
Responders’ Response Times
URS FISCHBACHER
1,2
, RALPH HERTWIG
3
* and ADRIAN BRUHIN
4
1
Thurgau Institute of Economics, Kreuzlingen, Switzerland
2
University of Konstanz, Germany
3
Max Planck Institute for Human Development, Center for Adaptive Rationality, Berlin, Germany
4
University of Lausanne, Lausanne, Switzerland
ABSTRACT
We investigate what processes may underlie heterogeneity in social preferences. We address this question by examining participants’ decisions
and associated response times across 12 mini-ultimatum games. Using a finite mixture model and cross-validating its classification with a
response time analysis, we identified four groups of responders: one group takes little to no account of the proposed split or the foregone al-
location and swiftly accepts any positive offer; two groups process primarily the objective properties of the allocations (fairness and kindness)
and need more time the more properties need to be examined; and a fourth group, which takes more time than the others, appears to take into
account what they would have proposed had they been put in the role of the proposer. We discuss implications of this joint decision–response
time analysis. Copyright © 2013 John Wiley & Sons, Ltd.
key words ultimatum game; response time; finite mixture model; heterogeneity; altruistic punishment; response time; heuristics
Our collective folklore is populated with characters, such as
Zorro, Robin Hood, and the Lone Ranger, who fight to right
what they perceive of as injustice and in the process punish
norm violators. Dirty Harry, the screen cop made famous by
Clint Eastwood, even tells the norm violators “Go ahead, make
my day,” thus informing them that he will derive satisfaction
from punishing them. Clearly, these characters are figments
of our imagination, although some may have historical origins.
The willingness to enforce norms even if doing so exacts costs
to one, however, is not a prerogative of fictional characters but
can also be observed in ordinary people. Take, for example, the
legion of whistleblowers, such as Daniel Ellsberg, risking their
career and retaliation to expose the misconduct on the part of
an agency, organization, or a company.
Not everybody, however, finds a Robin Hood in himself or
herself or finds satisfaction in punishing norm violators. Do
economists and psychologists therefore have to assume funda-
mentally different character or personality traits to explain
people’s varying predilections to punish norm violators?
Calling upon such distinct traits is indeed the predominant
approach in moral philosophy (see Doris, 2002). Alternatively,
however, these differences across people could be differences
in degree, not kind. The same issue also arises concerning the
cognitive processes underlying our choices, which are social
in the sense that they also affect other people apart from the
decision maker. When making these choices, do all people
process the same chunks of information and motives similarly,
except that they may weight them differently? Or, do some
people recruit processes that are different in kind?
We will be concerned with heterogeneity in social choices.
People are able to display an amazing range of behaviors
towards others. In particular, there is a rich body of empirical
evidence showing that humans care about others. They are
generous, and they reward the kind actions of others and
punish unkind behavior. Their responses, however, can also
betray envy and sometimes even spite (e.g., Berg, Dickhaut,
& McCabe, 1995; Falk, Fehr, & Fischbacher, 2005; Fehr &
Gächter, 2000; Güth, Schmittberger, & Schwarze, 1982).
Observations of diverse other-regarding preferences challenge
a frequent assumption in economic models, namely, that
humans are assumed to be rational decision makers and to
harbor purely self-regarding preferences (see Camerer &
Fehr, 2006).
Several theories have been proposed to accommodate the
panoply of other-regarding preferences. All retain the utility
framework and account for other-regarding behaviors by
either discarding or modifying the assumption of purely
self-regarding preferences. Social preference theories mod-
ify it by stipulating that, in additi on to the material payoff,
people’s choices may be guided by the outcomes and beha-
viors of others. Those other-regarding preferences (hence-
forth, social motives) are incorporated as additional terms
into the utility function. The most prominent among these
theories are those by Bolton and Ockenfels (2000), Charness
and Rabin (2002), Dufwenberg and Kirchsteiger (2004), Falk
and Fischbacher (2006), Fehr and Schmidt (1999), Kirchsteiger
(1994), Levine (1998), and Rabin (1993). Common to all is
the acknowledgement that humans are heterogeneous in
the extent to which they are guided by selfish and social
motives. The theories, however, differ in the motives (repre-
sented by parameters) that they postulate and in how they
combine them. For ex ample, the theories by Bolton and
Ockenfels (2000) and Fehr and Schmidt ( 1999) assume that
people value equali ty and dislike inequit y, whereas the
theories by Charness and Rabin (2002), Dufwenberg and
Kirchsteiger (2004), Falk and Fischbacher (2006), Levine
*Correspondence to: Ralph Hertwig, Max Planck Institute for Human Develop-
ment, Lentzeallee 94, 14195 Berlin, Germany. E-mail: hertwig@mpib-berlin.mpg.de
Copyright © 2013 John Wiley & Sons, Ltd.
Journal of Behavioral Decision Making , J. Behav. Dec. Making, 26: 462–476 (2013)
Published online 24 January 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/bdm.1779
(1998), and Rabin (1993) assume that people like to recipro-
cate and hence reward kind and punish unkind behavior.
Each theory aspires to describe all humans, capturing hetero-
geneity by param eterization of the assumed motives. In
practice, each theory succeeds in explaining some data but
fails in explaining all (see, e.g., Brandts & Sola, 2001;
Engelmann & Strobel, 2004; Falk, Fehr, & Fischbacher,
2003, 2008; Falk et al., 2005). I n this article, we take a
different approach to shed light onto the phenomenon of
heterogeneity. Specifically, we take advantage of response
times (RTs) in the mini-ultimatum game, a variant of the
classic and frequently studied ultimatum game (Güth
et al., 1982). Next, we briefly introduce these games
and then turn t o the standard approach of modeling het-
erogeneity in social games. Note that a companion piece
to the present article is that of Hertwig, F ischbacher,
and Bruhin (2013). Their theoretical and empirical analy-
ses focus on models of sequential decision trees. Here, we
extend this work by reporting more detailed tests and anal-
yses of people’s behavior and RTs. Furthermore, the pres-
ent focus is on establishing evidence for heterogeneity be-
tween people’s decision s in the mini-ultimatum game and
how it can be mapped onto underlying psychological
processes.
THE ULTIMATUM GAME AND THE
MINI-ULTIMATUM GAME
The ultimatum game involves two parties who play a single
round in which one person, the proposer, suggests how to split
a fixed monetary pie, typically provided by the experimenter.
This proposed split represents a take-it-or-leave-it offer (an
ultimatum) that the other person, the responder, chooses to
accept or reject. The interaction between the players is anony-
mous. If the responder chooses to accept the offer, the division
will be implemented. Should the responder decide to reject the
proposed division, both players will go away empty-handed. In
theory, a purely self-interested responder will accept any
proposed positive payoff, no matter how small. Anticipating
this choice, a self-interested proposer will offer nothing more
than the smallest amount possible. The equilibrium offer (i.e.,
the division for which no player has anything to gain by doing
something differently) thus allocates the smallest positive
payoff to the responder and the lion’s share to the proposer.
This, however, is not what is typically observed in the labora-
tories. More than 30 years of research on the ultimatum game
has consistently found that responders tend to reject low
offers and thus behave at odds with the assumption that they
simply maximize their self-interest (see Camerer, 2003; Güth
& Tietz, 1990).
In our investigation, we employed a variant of this classic
social game. The mini-ultimatum game is a sequential two-
player game. The first mover can choose between two fixed
allocations. Then, the second mover can accept or reject
this choice. Acceptance means that the allocation will be
implemented, whereas rejection means that both players will
receive zero. We presented our participants with 12 different
mini-ultimatum games and classified them according to their
rejection behavior. Subsequently, we used this classification
in the analysis of participants’ RTs.
HOW TO MODEL HETEROGENEITY?
Most theories of social preferences capture only one social
motive, be it, for example, inequity aversion (Bolton &
Ockenfels, 2000; Fehr & Schmidt, 1999) or reciprocity
(Levine, 1998; Rabin, 1993). Moreover, all the models fail to
explain the behavior of all participants (e.g., Engelmann &
Strobel, 2004). Within parameterized social preference
theories, there are at least two ways to respond to this state of
affairs. Accepting that the existing theories explain only a
subset of respondents, one could model heterogeneity using
distinct models for different people. Alternatively, one may
aim for a unifying theory that encompasses multiple social
motives and that explains heterogeneity by assuming that
people differ in the strength and combinations of these motives,
as has been done, for example, by Charness and Rabin (2002),
Cox, Friedman, and Gjerstad (2007), Cox, Friedman, and
Sadiraj (2008), or Falk and Fischbacher (2006).
The interpretation of degenerated parameter values illus-
trates how these two approaches differ. Degenerated values
(mostly zero values), for instance, for parameters capturing
social motives could be interpreted to mean that the person,
in reality, operates on the basis of a selfish preference function.
Consequently, the person’s choices can be accommodated in
terms of a simpler model that altogether omits parameters
capturing social motives. The same seemingly selfish behavior,
however, could also be consistent with very low values on
these social
parameter(s). Consequently, such parameters
would not be zero but only close to zero; hence, such a person
may indeed behave unselfishly in some other situations. The
first interpretation of degenerated parameter values implies that
heterogeneity is categorical in nature; the second assumes its
nature to be gradual. Which is more appropriate?
To investigate the nature of heterogeneity in social choice,
we use behavioral data and, in addition, a process measure,
namely, RT. Our starting premise is as follows: A theory that
aims to accommodate all heterogeneity and assumes the
same set of parameters (although not parameter values) and
the same process (e.g., calculations) for all respond ents
implies, ceteris paribus, relatively homogeneous response
time patterns. Differences only arise to the extent that people
differ in terms of processing speed but not in terms of differ-
ent decision processes. If, however, observed RTs prove to
be systematically different across people and games, then
such heterogeneity suggests that across people, different
processes are at work.
The issue of how to model heterogeneity is of importance
far beyond research on social games. Take, for illustration,
the modeling of individuals’ risky choice between monetary
gambles. Expected utility theory assumes heterogeneity to be
a matter of degree, not kind, and recruits families of utility
functions (such as constant absolute or relative risk aversion)
to describe it. Similarly, cumulative prospect theory (Tversky
& Kahneman, 1992) captures heterogeneity in terms of
Heterogeneity in Costly Punishment 463U. Fischbacher et al.
Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 26, 462–476 (2013)
DOI: 10.1002/bdm
different parameter values of its value and probability
weighting functions (Glöckner & Pachur, 2012). Applying
a finite mixture model (McLachlan & Peel, 2000) to choices
in monetary gambles, Bruhin, Fehr-Duda, and Epper (2010),
however, observed two distinct types of decision makers.
One group’s parameter values represented rational and risk-
neutral choices; the other group’s values revealed loss
aversion and an S-shaped probability weighting. Even
though there is heterogeneity within the second group (see,
e.g., also Booij & van de Kuilen, 2009), their decision
process is qualitatively different from that of members of
the rational, risk-neutral group (e.g., overweighting of rare
events and underweighting of common events versus linear
treatment of probabilities).
Also, investigating risky choices, Brandstätter, Gigerenzer,
and Hertwig (2006, 2008) turned to models of lexico-
graphic heuristics. Within this framework, heterogeneity
can also be described either parametrically (e.g., aspira-
tion levels can be parameterized; see Rieskamp, 2008)
or in terms of distinct heuristics (e.g., heuristics that
completely ignore probability information s uch as mini-
max or those that sequentially process outcome and prob-
ability information such as the priority heuristic; see
Brandstätter et al., 2006. Regarding the latter approach
to modeling heterogeneity, it appears fair to conclude:
Although the evidence for specifi c heuristics is often con-
troversially debated (see, e.g., the extensive w ork on the
priority heuristic; Ayal & Hochman, 2009; Birnbaum &
Gutierrez, 2007; Birnbau m & LaCroix, 2008; Cokely &
Kelley, 2009; Fiedler, 2010; Glöckner & Herbold, 2011;
Johnson, Schulte-Mecklenbeck, & Willemsen, 2008;
Rieger & Wang, 2008; Rieskamp; 2008 but also Brandstätter
& Gussmack, 2012; Arieli, Ben-Ami, & Rubinstein, 2011), a
widely accepted view in psychological research on behavioral
decision making is that different people recruit different
cognitive strategies to respond to the same t ask.
RESPONSE TIME: A WINDOW ON THE
UNDERLYING PROCESS
Unlike in economics, in psychology, RT has often been
employed as a measure of human behavior in its own right.
Models of, for example, human categorization—how people
assign a set of stimuli to a number of different groups or
concepts—are often required to predict not only behavior but
also the RTs (Lafond, Lacouture, & Cohen, 2009; Lamberts,
2000). Temporal dynamics have also played a crucial role in
the long-lasting debate in psychology on the serial or parallel
nature of information processing (Townsend, 1990). Moreover,
in investigations of human decision making, RT has regularly
been used to test a choice or inference model’s predictions
(e.g., Pachur & Hertwig, 2006) or to discriminate between the
predictions of competing models (e.g., Brandstätter et al., 2006;
Bröder & Gaissmaier, 2007; Payne, Bettman, & Johnson, 1993).
Bergert and Nosofsky (2007), for example, tested RT
predictions of a lexicograph ic inference heuristic, the take-
the-best heuristic (Gigerenzer & Goldstein, 1996), against
the predictions of a weighted-additive model, embodying
rational decision making. In making a decision about
which of two alternatives scores higher on some quantitative
dimension (e.g., which of two companies has higher annual
revenues), the take-the-best heuristic considers the properties
(cues) of the alternatives (e.g., information about number
of employees, the type of industry) in order of their diagnos-
ticity (cue validity) and arrives at an inference based on the
first one that distinguishes between the alternatives. The
weighted-additive model, in contrast, assigns to each cue a
weight, calculates the summed total evidence in favor of each
alternative, and chooses the alternative with more total evi-
dence. The models—one embodying restricted search, the
other exhaustive search—imply distinct RT patterns, depend-
ing on the choices in question (only in the most extreme case,
when merely the lowest-ranked cue distinguishes, do the
models’ RT predictions converge). As Bergert and Nosofsky
showed, generalizations of both models yield formally iden-
tical predictions of choice probabilities but “embody dramat-
ically different decision making processes” (p. 116). They, in
turn, imply very different RTs, with take-the-best terminating
search once a cue inspected discriminates and the weighted-
additive model always inspecting all cues. The observed RT
pattern pointed toward a search pattern consistent with the
search-restricting take-the-best heuristic.
Economists have only recently begun to take advantage of
RT as a window on cognitive processes. Rubinstein (2007),
for example, proposed distinguishing between instinctive
and cognitive choices, and used RT to investigate which
decisions, for example, in the beauty contest game, require
cognitive effort and which require no or little cognitive effort
(thus counting as instinctive in Rubinstein
’s view). Record-
ing RTs in the context of the ultimatum game, Brañas-Garza,
Léon-Mejia, and Miller (2007) found that selfish responders
decide faster. Relatedly, Piovesan and Wengström (2009)
found that selfish dictators decide faster and that selfish deci-
sions are made more swiftly.
The latter two investigations are related to ours insofar as
they classify respondents on the basis of their overt decisions
and then record ed RTs. We, however, go beyond the obvious
distinction between selfish and non-selfish players. To
preview, we collect choices and RTs in a series of mini-
ultimatum games, and using a finite mixture model analysis,
we classify participants according to their choices. The clas-
sification suggests four distinct types of participants, who
differ in whether and how social motives matter for their
decisions. Importantly, this heterogeneity maps onto system-
atic RT pattern: First, we find distinct behavioral classes to
be reflected in distinct average RT. Second, RTs relate to
the interaction of participant types and games. This becomes
most obvious when comparing parti cipants who appear to act
on the basis of social motives to those without. Regardless of
the details of a specific offer, the strictly selfish respondents
can quickly accept it (given our games), with no RT differ-
ence between games. In contrast, a person who takes social
motives into account will have to appraise a given offer in
light of these motives. This takes time, and because different
games evoke these motives to different degrees, game-
specific RTs result. We indeed find di stinct patterns of RTs
between behavioral classes and games, suggesting that
464 Journal of Behavioral Decision Making
Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 26, 462–476 (2013)
DOI: 10.1002/bdm
qualitatively different processes are at work. Interestingly,
however, some of these distinct patterns of RT could, in prin-
ciple, also be predicted by social preference model. In what
follows, we show how and contrast those predictions to those
derived from models of heuristics.
RESPONSE TIME PREDICTIONS BASED ON
SOCIAL PREFERENCE THEORIES AND
LEXICOGRAPHIC HEURISTICS
We begin with a disclaimer: The aim of our investigation is
not to test between different social preference theories.
Rather, we will assess the relative importance of the postu-
lated social motives on an individual level. Moreover, we
will examine to what extent the social preference theories
and a heuristic processing account can accommodate the ob-
served RTs. We use the following terminology when analyz-
ing rejection behavior. The payoffs for the proposer (P) and
responder (R) in the chosen (c) and the forgone (f) allocation
are as follows: P
c
,R
c
,P
f
, and R
f
. We assume that all payoffs
are positive but refrain from further assumptions. In particu-
lar, we do not assume that the sum of the payoffs is constant
(as in the standard ultimatum game). Let us now discern be-
tween three social motives, each one could cause rejection of
a positive payoff.
Assuming rationality and selfish preferenc es, no offer in
the mini-ultimatum games will ever be rejected as long as
the responder’s payoff (R
c
) is positive. In the present games,
R
c
payoffs were always positive. Starting with Güth et al.
(1982), however, rejections of low offers have been often
demonstrated. Various social preference theories have been
proposed that recruit different social motives causing such
rejections. Arguably, the most prominent motive for rejection
is inequity aversion as invoked in Bolton and Ockenfels
(2000) and Fehr and Schmidt’s (1999) models.
Inequity aversion
Applied to the mini-ultimatum games, inequity aversion
means that if the responder fares worse than the proposer,
one will have a reason to reject the allocation offered. Conse-
quently, there is a trade-off between the responder’s disutility
resulting from inequity and the utility resulting from the ab-
solute payoff. For people who behave according to inequity
aversion, only the two payoffs of the chosen alternative are
relevant, that is, R
c
and P
c
. We say that an allocation is unfair
(i.e., inequitable) if the responder receives less than the pro-
poser and that an offer will be rejected if it is unfair (i.e.,
R
c
P
c
< 0).
Kindness
Lack of equity or fairness, however, appears to be not the
only reason motivating rejection. Brandts and Sola (2001)
and Falk et al. (2003) showed that the rejection rate of an
offer also depends on the counterfactual allocation (i.e., the
one that could have been chosen but was not). Taking it into
account, a responder can evaluate an offer’s kindness.
Kindness is a social motive that is featured prominently in
Dufwenberg and Kirchsteiger’s (2004) and Rabin’s (1993)
reciprocity theories. An offer is said to be unkind if it is smal-
ler than the counterfactual allocation, and an offer will be
rejected if it is unkind (i.e., R
c
R
f
< 0).
1
By rejection, the
responder can reduce the proposer’s payoff, and this act
can be a term in the responder’s utility function.
2
Mirror
As a third criterion for the acceptance or rejection of an offer,
we investigate the possibility that the offer is evaluated by tak-
ing the role of the proposer and probing oneself as to whether
one would have deemed the allocation acceptable and thus also
proposed it. We do not suggest a normative measure. We take
an empirical approach and assume that people differ in their
norm of what is an (still) acceptable division of resources
(see López-Pérez, 2008, for a formal theory of such an
approach). They themselves abide by the norm and punish
others who violate it. Stimulating the possible dilemma the pro-
poser faces is tantamount to taking an honest look in the mirror
and asking oneself: What would I do? Applied to the mini-
ultimatum game, this social motive predicts that responders
consider an offer as more acceptable if they also would have
made it.
How can one find out what a person would do to others?
Naturally, a person’s choices as a proposer could reveal
one’s personal norm. Therefore, all our participants played
both roles, that of the responder and proposer. The proposer,
however, is likely to reckon with the fact that an offer could
be rejected. So, in the example earlier, a person could
consider the 800:200 offer as perfectly acceptable but never-
theless refrain from proposing it for fear of rejection. Hence,
we expected choices in the dictator game might be better
proxies of a person’s norm of acceptability and therefore
asked people also to respond in the same games as a dictator.
To conclude, we expect that a person is more likely to reject
an offer if one would not make that offer oneself (in an
ultimatum or dictator game).
In sum, we distinguish between three non-exclusive social
motives for rejections: unfairness, unkindness, and m irror
(i.e., I would not have proposed this allocation). If a responder
has any or all of these concerns, rejections will become more
likely, relative to a responder who derives one’schoice
exclusively from one’s narrow self-interest. On the basis of
these social motives, we can now derive RT predictions for
social preference theories and for lexicographic heuristics.
1
A kind offer refers to the kinder of the possible offers. The kind offer is thus
a relative construct and not necessarily kind in an absolute sense. For exam-
ple, choosing 800:800 over 200:500 is kinder but not in essence kind.
2
Strictly, the theories do not compare the allocations but the expected alloca-
tions taking into account the responder’s second-order beliefs about one’s re-
jection. There are two problems with equilibria based on this assumption:
First, there are many equilibria, thus making it nearly impossible to test
the theories. Second, some of these equilibria are rather implausible. For ex-
ample, an offer could be rejected because the responder thinks the proposer
expects a rejection and, therefore, by choosing this offer, intends a payoff of
zero for the responder. However, why would the proposer make an offer
with the intention of having it rejected?
Heterogeneity in Costly Punishment 465U. Fischbacher et al.
Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 26, 462–476 (2013)
DOI: 10.1002/bdm
Response times and social preference models
Economic models have little to no pretension of making pre-
dictions about processes. Notwithstanding this fact, one can
derive—based on the auxiliary assumption that increasing
complexity requires more time (e.g., Payne et al., 1993)—the
following two qualitative RT predictions. First, if responders
invoke a utility calculation to evaluate the proposed split, and
if they merely differ in how they weight their motives (self-
interest vs. social motives) that are arguments in this function,
then all people should display the same RT or at least the same
pattern of RTs. Second, if for some people only a single motive
matters (e.g., self-interest), their calculation will be simpler,
relative to others who need to trade-off self-interest and social
motives. Consequently, the former group’s RTs should, on
average, be shorter than the latter ones.
Let us illustrate what these predictions mean using Fehr
and Schmidt’s (1999) theory of inequity aversion. According
to this theory, people experience, next to satisfaction with
their material payoffs, disutility from advantageous and from
disadvantageous social inequality. These two concepts are
included in terms of two arguments in a more complicated
(relative to a neoclassical utility function) social utility func-
tion, as described in Equation (1):
U
i
¼ p
i
a
i
N 1
X
j
max p
j
p
i
; 0
b
i
N 1
X
j
max p
i
p
j
; 0
(1)
Disutility is subtracted from the utility stemming from the
material payoff p
i
. Disadvantageous inequality has a weight
of a
i
, and advantageous inequality has a weight of b
i
. Both
parameters are assumed to be nonnegative. Finally, N
denotes the number of players (two in our case).
Applied to our mini-ultimatum games, three behavioral
predictions follow: First, if b
i
< 1 (this assumption is made in
the model), then no offer with advantageous inequality will
be rejected. Thus, advantageous inequality is not relevant for
the rejection decision. Second, an offer (P, R) involving disad-
vantageous inequality will be rejected if R/(P + R) < a
R
/
(1 + 2a
R
). Third, the response to an offer depends only on the
offer made, regardless of the alternative. How do these behav-
ioral predictions translate into RT predictions? A naïve initial
assumption would be that complexity and, by extension, RTs
are identical across responders. There is, however, heterogene-
ity in the parameters, and some heterogeneity could affect RTs.
Specifically, for those responders with a parameter value of
zero, the corresponding argument in the complex utility
function can be canceled. On a process level, the calculations
therefore become simpler and RTs, assuming serial processing,
faster. That is, should one or both weighting parameters equal
zero, one could argue that people behave according to a simpler
variant of the complex utility function.
Assuming that in Fehr and Schmidt’s (1999) theory, dis-
advantageous disutility needs to be considered only when
disadvantageous inequality occurs, we can derive a simple
RT prediction. To the extent that it can be swiftly determined
whether an offer implies advantageous or disadvantageous
inequality, then participants with a
i
> 0 can be expected to
have a longer RT for offers with disadvantageous inequality
than participants with a
i
=0.
Response times and lexicographic heuristics
There is an alternative to the assumption that individuals
maximize a more complicated utility function that includes
social motives. On this view, social motives are ordered
according to, for example, their importance and players process
them sequentially, making a decision as soon as a decision
criterion is met. We briefly describe this modeling approach
in terms of heuristics (Gigerenzer, Hertwig, & Pachur, 2011).
There are several classes of heuristics, one obvious candidate
for two-alternative choice problems (i.e., rejecting vs. accept-
ing an allocation) being lexicographic rules. These rules order
decision dimensions (e.g., aspects, reasons, cues, motives)
according to some criterion, search through m ≥ 1 dimensions,
and render an immediate decision based on the first dimension
that discriminates. Two prominent examples of lexicographic
decision rules are elimination-by-aspects (Tversky, 1972) and
the take-the-best heuristic (Gigerenzer & Goldstein, 1996).
Because very little is known about what kind of heuristics
people may use—if they use them at all—in the context of
mini-ultimatum games or ultimatum games in general, we do
not estimate heuristic models in a behavioral econometric
analysis. We take a different approach. Specifically, we use
people’s choices to classify them into different types of respon-
ders. These types, in turn, suggest possible lexicographic
heuristics that responders could be using. Equally important,
even the generic forms of the heuristics give rise to qualitative
response time predictions. We then use empirical RT to test the
predictions of the generic lexicographic heuristics and those
suggested by the social preferences models. We assume that
the heuristics process one or more of the three social motives
identified before (unfairness, unkindness, and mirror), except
that they, unlike the social preference models, process the
different motives sequentially. For illustration, consider the
following generic heuristic consisting of three motives:
Step 1. If a responder receives more than the proposer, one
will accept the offer without further ado.
Step 2. If one receives less than the proposer, one will consider
whether the offer was nevertheless kind and will accept
it if it proves kind.
Step 3. If the offer turned out to be unkind, the responder probes
oneself: “Would I have made this offer?” If the answer
is yes, one will accept the proposed allocation,
otherwise one will reject it.
This generic lexicographic heuristic assumes that strong
social motives (i.e., those that imply low behavioral variance,
and in which, in the extreme case, all offers that pass or fail a
test are accepted or rejected, respectively) have priority over
weaker motives. Specifically, let us suggest that inequality
aversion precedes kindness, and kindness precedes the kind
of perspective taking as embodied in the mirror criterion.
From this ensues, for example, the following key prediction:
One and the same person will respond swifter when alloca-
tions meet the inequality aversion test relative to those allo-
cations failing this test and the kindness test and that are,
466 Journal of Behavioral Decision Making
Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 26, 462–476 (2013)
DOI: 10.1002/bdm
