Stuck in the Middle: The Psychophysics of Goal Pursuit

Abstract

The classic goal-gradient hypothesis posits that motivation to reach a goal increases monotonically with proximity to the desired end state. However, we argue that this is not always the case. In this article, we show that motivation to engage in goal-consistent behavior can be higher when people are either far from or close to the end state and lower when they are about halfway to the end state. We propose a psychophysical explanation for this tendency to get "stuck in the middle." Building on the assumption that motivation is influenced by the perceived marginal value of progress toward the goal, we show that the shape of the goal gradient varies depending on whether an individual monitors progress in terms of distance from the initial state or from the desired end state. Our psychophysical model of goal pursuit predicts a previously undiscovered nonmonotonic gradient, as well as two monotonic gradients.

Full text

Psychological Science
22(5) 607 –612
© The Author(s) 2011
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DOI: 10.1177/0956797611404899
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Achieving a goal often requires engaging in goal-consistent
behavior for an extended period. For instance, losing weight
requires sticking to a diet and resisting temptations over many
months. The classic goal-gradient hypothesis (Hull, 1932,
1934) posits that motivation to reach a goal increases mono-
tonically with proximity to the desired end state. Similarly,
Lewin (1935, 1951) suggested that effort increases as people
near their goals. Spatial and temporal goal gradients have been
observed in animals (Brown, 1939, 1948; Miller, 1944, 1959;
Rigby, 1954) and in humans (Förster, Higgins, & Idson, 1998;
Kivetz, Urminsky, & Zheng, 2006; Losco & Epstein, 1977;
Nunes & Drèze, 2006; Smith, 1965; Wipf, 1964).
However, we suggest that motivation is not always
monotonically related to distance from the desired end state
(cf. Louro, Pieters, & Zeelenberg, 2007). In particular, we
hypothesize that motivation can decrease about halfway to the
end state. We propose a psychophysical model of goal pursuit
that accounts not only for this tendency to get “stuck in the
middle,” but also for the classic goal gradient. The psycho-
physics of goal pursuit is based on three elements: (a) motiva-
tion as a function of perceived marginal value of progress,
(b) adoption of a reference point to monitor progress, and
(c) diminishing sensitivity.
Heath, Larrick, and Wu (1999) showed that motivation to
engage in a certain behavior is influenced by the perceived
marginal value of progress produced by such behavior.
Consider a student with a 500-page reading assignment. At
any one time, the perceived marginal value of reading the next
page may substantially influence motivation to keep reading.
The perceived marginal value of progress is influenced by the
reference point adopted to monitor progress. In general, peo-
ple monitor progress in terms of distance from a standard of
reference (Carver & Scheier, 1998). Specifically, they can use
either their initial state as the standard of reference to monitor
progress and to consider what they have achieved so far (i.e.,
to-date frame), or they can use the desired end state and con-
sider what they still need to achieve (i.e., to-go frame; Koo &
Fishbach, 2008). Thus, to monitor progress, the student could
count either the number of pages read thus far or the number
of pages remaining.
Building on the psychophysical power law (Stevens, 1975)
and the principle of diminishing sensitivity (Kahneman &
Tversky, 1979; Tversky & Kahneman, 1991), we suggest that
the perceived value of a given unit of progress changes as a
function of distance from the standard of reference. When a
person uses the desired end state as the reference point for
monitoring progress, the perceived marginal value of progress
Corresponding Author:
Andrea Bonezzi, Kellogg School of Management, Department of Marketing,
Northwestern University, 2001 Sheridan Rd., Evanston, IL 60208
E-mail: a-bonezzi@kellogg.northwestern.edu
Stuck in the Middle: The Psychophysics of
Goal Pursuit
Andrea Bonezzi1, C. Miguel Brendl1, and Matteo De Angelis2
1Department of Marketing, Kellogg School of Management, Northwestern University, and
2Department of Economics and Business, Luiss Guido Carli University
Abstract
The classic goal-gradient hypothesis posits that motivation to reach a goal increases monotonically with proximity to the
desired end state. However, we argue that this is not always the case. In this article, we show that motivation to engage in
goal-consistent behavior can be higher when people are either far from or close to the end state and lower when they are
about halfway to the end state. We propose a psychophysical explanation for this tendency to get “stuck in the middle.”
Building on the assumption that motivation is influenced by the perceived marginal value of progress toward the goal, we show
that the shape of the goal gradient varies depending on whether an individual monitors progress in terms of distance from
the initial state or from the desired end state. Our psychophysical model of goal pursuit predicts a previously undiscovered
nonmonotonic gradient, as well as two monotonic gradients.
Keywords
motivation, goal gradient, self-regulation, monitoring progress
Received 6/14/10; Revision accepted 1/21/11
Research Report

608 Bonezzi et al.
increases: Reading one more page is perceived as yielding
more progress when 50 pages remain (1:50) than when 200
pages remain (1:200). Hence, motivation increases as distance
from the end state decreases (Fig. 1a). In contrast, when a per-
son uses the initial state as the reference point for monitoring
progress, the perceived marginal value of progress decreases:
Reading one more page is perceived as yielding less progress
after having read 200 pages (1:200) than after having read 50
pages (1:50). Hence, motivation decreases as distance from
the initial state increases (Fig. 1b). Overall, the motivation
functions shown in Figure 1 are marginal benefit curves of
moving toward (to-go frame) and moving away from (to-date
frame) a reference point, obtained as the first derivatives of
their respective value functions (Heath et al., 1999).
We suggest that people tend to adopt their initial state as the
reference point at the beginning of goal pursuit and the desired
end state as their reference point when nearing the goal. Simi-
lar attentional shifts have been observed in other domains
To-Go Frame
a
bTo-Date Frame
Perceived Value
of Progress
Motivation
Motivation
Perceived Value
of Progress
∆V2
∆V2
∆V1
∆V1
∆D2
∆D2
∆D1
∆D1
Initial
State
Initial
State
Distance From
Standard of Reference
(End State)
Distance From
Standard of Reference
(Initial State)
Distance From
Standard of Reference
(Initial State)
Distance From
Standard of Reference
(End State)
End
State
End
State
Fig. 1. Illustration showing how the frame of reference adopted to monitor progress influences the perceived marginal value of progress and
thus motivation. When an actor monitors progress in terms of distance (D) from the desired end state (a; to-go frame), the perceived value
(V) of an additional unit of distance (ΔD1 = ΔD2) increases the closer the actor is to the end state (ΔV1 < ΔV2; left graph). As a consequence,
motivation increases as distance from the end state decreases (right graph). When an actor monitors progress in terms of distance from the
initial state (b; to-date frame), the perceived value of an additional unit of distance (ΔD1 = ΔD2) decreases the further the actor is from the
initial state (ΔV1 > ΔV2; left graph). As a consequence, motivation decreases as distance from the initial state increases (right graph).

The Psychophysics of Goal Pursuit 609
(Elster & Loewenstein, 1992; Loewenstein, 1994). Moreover,
our hypothesis is consistent with the idea that the initial state
is more salient at the beginning of goal pursuit, whereas the
desired end state is more salient toward the end of goal pursuit
(Liberman & Dar, 2009). A switch in reference points, in com-
bination with the principle of diminishing sensitivity, predicts
decreased motivation in the middle of goal pursuit (Fig. 2). To
illustrate, a student who begins reading a book initially moni-
tors progress by counting pages read. As the student reads fur-
ther, the value of reading each additional page decreases, thus
decreasing motivation. As the end of the book nears, the stu-
dent switches reference points and starts monitoring progress
by pages remaining. The value of reading each additional page
now increases, thus increasing motivation.
Overall, the psychophysics of goal pursuit predicts a previ-
ously undiscovered nonmonotonic motivational pattern (i.e., a
U-shaped gradient). Moreover, it accounts for two monotonic
patterns: the classic increasing goal gradient and a novel
decreasing goal gradient.
Experiment 1
In Experiment 1, we tested whether motivation can decrease
halfway through goal pursuit.
Procedure
Students (N = 126) played a “words in a word” game: Each stu-
dent was presented with a word (e.g., manager) and was asked
to create as many other words as possible using the letters con-
tained only in that word (e.g., gear, range). Participants worked
on a series of nine words, each presented for 2 min. Each word
was identified by a serial number, by which participants were
able to track their progress. Those who scored within the 90th
percentile could win $50. Three target words were rotated
between participants in Positions 2, 5, or 8 according to a Latin
square design. The order of all other words was randomized.
Results and discussion
A quadratic within-participants effect of position, t(373) = 2.97,
p = .004, indicated that participants found fewer solutions when
a target word was presented fifth (M = 7.13, SD = 3.81) than
when it was presented second (M = 8.39, SD = 4.86), t(373) =
3.36, p = .001, d = 0.35, or presented eighth (M = 8.45, SD =
4.46), t(373) = 3.51, p = .001, d = 0.36. The Word × Position
interaction was not significant, t < 1.
These data suggest that respondents exerted less effort when
halfway through goal pursuit than when closer to the end or the
beginning; this finding is consistent with our hypothesis of
decreased motivation in the middle. However, this decrease
could also be due to depletion (Baumeister, Bratslavsky,
Muraven, & Tice, 1998) rather than to the proposed perceptual
mechanism. Depleted people tend to perform poorly on self-
control tasks (Muraven, Tice, & Baumeister, 1998) because they
focus on their fatigue rather than on the goal (Vohs & Schmei-
chel, 2003). However, when an external standard of reference for
monitoring goal pursuit is made salient, depleted individuals are
able to restore self-regulation by focusing on the standard rather
than on their fatigue (Wan & Sternthal, 2008). Decreased perfor-
mance when halfway to the goal could then result from fatigue
being difficult to overcome in the middle of goal pursuit, when
both external standards of reference for monitoring goal pur-
suit—beginning and end—are distant, hence least salient.
Experiment 2
Although we do not exclude the possibility that depletion
might produce a similar motivational pattern as the one we
found in Experiment 1, we argue that depletion is not neces-
sary to account for our results and that a perceptual mecha-
nism might provide a more parsimonious explanation. In
Experiment 2, we tested our psychophysical explanation by
manipulating the reference point used to monitor progress
(Koo & Fishbach, 2008) in a context that does not involve
depletion. Our psychophysical model of goal pursuit predicted
two pure monotonic gradients: increasing motivation when
progress is monitored with respect to the desired end state and
decreasing motivation when progress is monitored with
respect to the initial state (Fig. 2).
Procedure
At the end of an experimental session unrelated to the
present experiment, students (N = 137) received an envelope
containing $15 remuneration and information about a charity
Motivation
To-Date
Frame
Initial
State
End
State
Distance From
Standard of Reference
(Initial State vs. End State)
To-Go
Frame
Fig. 2. Predicted motivational patterns as a function of the standard of
reference adopted to monitor progress toward the goal. Motivation decreases
monotonically when an actor monitors progress relative to the initial state
(to-date frame), whereas motivation increases monotonically when an actor
monitors progress relative to the end state (to-go frame). The stuck-in-the-
middle pattern results when an actor initially adopts a to-date frame and then
switches to a to-go frame during goal pursuit.

610 Bonezzi et al.
project. A description of the project specified the charity’s goal
($300) and the current level of progress toward the goal,
manipulated between participants as either money collected so
far (to-date frame; $55, $155, or $245) or money still to be
collected (to-go frame; $245, $145, or $55). Participants were
instructed to leave part of their compensation in the envelope
if they wished to contribute.
Results and discussion
The predicted Frame × Progress interaction emerged, F(2,
131) = 3.525, p = .032. The classic goal gradient was repli-
cated for respondents who read about money still needed.
They donated more money when the collection was close to
the end (M = $2.86, SD = $2.59) than when it was in the mid-
dle (M = $1.10, SD = $1.59) or at the beginning (M = $1.05,
SD = $1.54). Consistent with the psychophysical power law,
results showed that contributions increased significantly when
comparing the middle with the end, t(131) = 2.13, p = .03, d =
0.37, but not when comparing the beginning with the middle,
t < 1; this suggests a nonlinear goal gradient.
The opposite gradient emerged for respondents who read
about money already collected. They donated more money
when the collection was at the beginning (M = $2.68, SD =
$3.94) than when it was in the middle (M = $1.12, SD = $2.05)
or near the end (M = $1.50, SD = $3.16). Consistent with the
psychophysical power law, findings indicated that contribu-
tions decreased significantly when comparing the beginning
with the middle, t(131) = 2.08, p = .04, d = 0.36, but not when
comparing the middle with the end, t < 1; this again suggests a
nonlinear gradient.
Experiment 2 allows two important conclusions. First, it pro-
vides evidence for a perceptual mechanism following the psy-
chophysical power law (Stevens, 1975) that is independent of
depletion. Specifically, it shows that different motivational gra-
dients can emerge, depending on the reference point adopted to
monitor progress. Second, it suggests that the stuck-in-the-middle
U pattern results from a switch in reference points during goal
pursuit, because when a single reference point was made salient,
a monotonic motivational pattern emerged.
Experiment 3
In Experiment 3, we tested whether the motivational U pattern
results from an attentional shift from the starting point to the
end point during goal pursuit. Across three conditions, we
measured and manipulated attentional focus to reference
points. When no frame to monitor progress was provided, we
expected the attentional measure to shift from the starting
point to the end point and performance to exhibit the stuck-in-
the-middle U pattern found in Experiment 1. However, we
expected that an explicit frame to monitor progress would
undermine this attentional shift, focusing to-date respondents
on the starting point and to-go respondents on the end point
throughout goal pursuit. Focus on one single reference point
should then produce the monotonic performance patterns
found in Experiment 2.
Procedure
Students (N = 69) proofread a series of nine essays for typo-
graphical errors. Three target essays were randomly rotated
between participants in Positions 2, 5, or 8. All other essays
were randomly rotated in the remaining positions. Above each
essay, a diagram illustrated the student’s progress on the task,
thus allowing us to manipulate the standard of reference for
monitoring progress. In the to-go condition, participants ini-
tially saw a row of nine icons, each representing one of the
essays to be reviewed. One icon at a time would disappear
from left to right after an essay was reviewed. In the to-date
condition, participants initially saw an empty row, to which
one icon at a time would be added from left to right after an
essay was reviewed. In the no-frame condition, participants
always saw a row of nine washed out icons, of which the one
corresponding to the essay being reviewed was highlighted.
For each essay, we measured the number of typos identified
and the time spent reviewing the essay. We computed a perfor-
mance index as the ratio of these two measures (i.e., typos
found per second). To measure attentional focus, we asked
participants to report where they currently were on the task
immediately after they completed the third and sixth essays.
Two coders blind to hypotheses and conditions then coded
whether the answers indicated a focus on essays completed
(to-date frame) or on essays to be completed (to-go frame; see
Koo & Fishbach, 2010).
Results and discussion
Our attentional measure confirmed that respondents adopted
different standards to monitor progress across conditions. Spe-
cifically, 80.9% of to-date respondents maintained a focus on
essays completed, and 79.1% of to-go respondents maintained
a focus on essays to be completed. Moreover, 75% of respon-
dents in the no-frame condition switched their focus from
essays completed to essays to be completed.
Performance exhibited the three expected patterns (Fig. 3).
To-go participants’ performance exhibited the classic goal gra-
dient, increasing monotonically as fewer essays remained. Per-
formance was highest when participants were close to the end of
the task (M = 0.13 typos per second, SD = 0.036) and lower
when either halfway (M = 0.098 typos per second, SD = 0.019)
or close to the beginning (M = 0.088 typos per second, SD =
0.024). Consistent with the psychophysical power law, findings
showed that the increase in performance was not significant
when comparing the beginning of the task with the middle,
t(198) = 1.58, p = .12, but was significant when comparing the
middle with the end, t(198) = 3.67, p = .001, d = 0.52.
To-date participants exhibited the opposite gradient: Their
performance decreased monotonically as the number of
essays reviewed increased. Performance was highest when

The Psychophysics of Goal Pursuit 611
participants were close to the beginning of the task (M = 0.123
typos per second, SD = 0.033) and lower when either halfway
(M = 0.095 typos per second, SD = 0.029) or close to the end
(M = 0.104 typos per second, SD = 0.028). The decrease in
performance was significant when comparing the beginning
with the middle, t(198) = 3.89, p < .001, d = 0.55, but it was not
significant when comparing the middle with the end, t(198) =
1.61, p = .11; this again suggested a nonlinear gradient.
In the no-frame condition, the stuck-in-the-middle U pattern
emerged. Pair-wise comparisons showed that performance
was higher when participants were close to the beginning of
the task (M = 0.122 typos per second, SD = 0.046) or near the
end (M = 0.124 typos per second, SD = 0.034) than when
they were halfway (M = 0.092 typos per second, SD = 0.026),
t(198) = 3.86, p < .001, d = 0.55; t(198) = 4.46, p < .001, d = 0.63.
Performance near the beginning and near the end of the task
did not differ, t < 1.
Overall, Experiment 3 provides evidence that the stuck-in-
the-middle U pattern is due to an attentional shift from the
starting point to the end point during goal pursuit. Further-
more, this experiment shows that three different goal gradients
can emerge, depending on the standards of reference adopted
to monitor progress.
General Discussion
Despite the widely accepted belief that motivation to reach a
goal increases as people approach the desired end state (Hull,
1932), the psychophysics of goal pursuit suggests that this is
not always the case. Because motivation is influenced by the
perceived marginal value of progress (Heath et al., 1999), dif-
ferent motivational gradients can emerge depending on the
standard of reference used to monitor progress. The classic
increasing motivational gradient occurs when individuals
focus on the desired end state throughout goal pursuit, whereas
a decreasing motivational gradient occurs when individuals
focus on the initial state throughout goal pursuit.
Our findings point to a previously undiscovered vulnera-
bility occurring about halfway to a goal. We showed that
participants exhibited a tendency to focus on the initial state as
the standard of reference at the beginning of goal pursuit, but
then shifted their focus to the desired end state as the end
neared. The observed stuck-in-the-middle pattern resulted
from this switch in reference points, in combination with the
psychophysics of utility perception. Therefore, the psycho-
physics of goal pursuit provides a parsimonious theoretical
explanation that accounts for the stuck-in-the-middle pattern,
as well as for other motivational gradients.
Acknowledgments
The authors would like to thank Brian Sternthal for his support and
his insightful comments on earlier drafts of this manuscript, Editor
Robert V. Kail and Associate Editor Thomas Mussweiler for their
guidance in the review process, and two anonymous reviewers for
their constructive comments.
Declaration of Conflicting Interests
The authors declared that they had no conflicts of interest with
respect to their authorship or the publication of this article.
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