1. Research Methodologies
Probability of Acknowledgment on Sproul Plazaa)
N. Eldifrawy1, b)
UC BerkeleyCompass Project
(Dated: 21 July 2015)
In a study of the application of decision theory, this project is centered around the observation of subjects
as they traverse the length of Sproul plaza, and the probability of a mutual interaction between two distinct
members.
Keywords: UC Berkeley, Sproul Plaza, Interactions, Decision Theory
I. INTRODUCTION
The goal of this project is to determine the likelihood
of encountering and having a mutual interaction with
an acquaintance and friend as one walks through Sproul
plaza and the neighboring areas. Many times, one walks
through, pondering as to whether or not they’ll meet
someone they know, sometimes hoping they do, and other
times in apprehension. By studying and measuring the
flow of people, while taking into account various different
variables that effect flow rate and interaction percentage,
this project will hopefully be capable of making such pre-
dictions with a certain degree of certainty.
II. METHODOLOGY
In order to attempt to measure and analyze interac-
tions in all of Sproul, a statistical model was developed.
First, the flow of people through Sather gate during a two
minute period was measured. It was measured that the
average total time that it would take to walk through
Sproul plaza was two minutes, so in counting the flow
of people for 2 minutes, the amount of people passing
by theoretically was equivalent to total amount of peo-
ple on Sproul during a given time. Then, for another
2 minute period, the interactions were measured in an
area that was approximated to be an eighth of the total
area of Sproul plaza. An interaction was considered a
mutual form of acknowledgement, including but not lim-
ited to smiling, handshakes, hugs, waves, head nods and
screaming hello from large distances. Missed interactions
were considered any attempt at an interaction that was
not reciprocated. Attempts at forced interactions, such
as people flyering, were not taken into considerations.
Various other variables were taken into consideration,
like the weather and the time of the day, as well as general
campus events going on at the same time that might alter
the results (ie elections, Cal day, dance performances).
a)And directly neighboring areas such as Golden Bear Cafe and
Sather Gate
b)Also at Materials Science and Engineering Department, UC
Berkeley University.
III. RESULTS
Various trends can be deduced from the data. General
flow of people is indicated in blue, with mutual inter-
actions in green and missed interactions in red (refer to
methodology for what falls into each category).
Figure 1 indicated the general flow of people with re-
spect to interactions and missed interactions, on a day by
day progression, starting from March 4th to March 18th,
2015. Measurements were not taken every day, and some
days have multiple measurements.
FIG. 1. Data organized with respect to date taken
Temperature seemed to have a large effect on the
amount of interactions. Figure 2 shows the effect. Bad
weather, such as rain or cold, resulted in a much lower
flow and percentage of interactions overall. In fact, some
days, there were no interactions at all, missed or mutual,
as indicated by the graph. The coldest days are the small-
est to the center, and the outer rings are representative
of measurements taken during warmer weather.
Furthermore, the magnitude of the flow corresponds
to the amount of people missing interactions. With an
increase of people on Sproul Plaza, there is a clear in-
crease of missed interaction. Figure 3 shows that exact
correlation, with the days with least amount of flow on
the inside, and the days with the most on the outside.
Another interesting correlations can be observed be-
tween the missed interactions and the number of people,
as well as the time of the day. During the top of the hour,

2. Research Methodologies 2
FIG. 2. Interactions organized with coldest temperature on
the inside
FIG. 3. Interactions organized with smallest number of inter-
actions in center
there are clear spikes in the amount of interactions, as in-
dicated by figure 4. The thick ring around the outmost
layer is indicative of the average, with 15% of the people
who walked through Sproul plaza having a mutual inter-
action, at any time of the day, while 2% of the total flow
was missed interactions, resulting in a 14% of attempted
interactions missed, with 86% of them being responded
to.
FIG. 4. Interactions organized with smallest number of inter-
actions in center
IV. DISCUSSION
The results indicate a series of interesting trends and
correlations. The reasoning behind these correlations are
perhaps even more interesting. In terms of the reason-
ing behind the ebb and flow of students during various
times, days, and weather patterns, it is clear that stu-
dents will often skip out on school at the slightest dis-
comfort, such as weather. Furthermore, the majority of
students seem to have classes during the afternoon, re-
sulting in the largest rush during that time. At the top
of the hour, such as 12:00, 1:00 and 2:00, there was the
greatest flow of people. secondary to that was the half
hour intervals, with the flow being nearly non existent at
anytime in between, which corresponds directly to class
timings.
In terms of specific interactions, there are many rea-
sons as to why certain interactions were acknowledged
and others were not. On rainy days, most people had
umbrellas and were bundled up and seemed to be rushed
to get from one destination to another, so the number
of interactions was often minimal and at times zero. On
days with bad weather, such cold or fog, people were
still aware of their surroundings, but would not mind ac-
knowledging someone they saw directly in front of them.
During times with large flow, there was a large num-
ber of missed interactions. This can be attributed to two
things. The first is that often people are attempting to
walk through Sproul without being flyered to, and so keep
their head down and their eyes glued to the end, so often
they dont see the person waving/smiling/greeting them.
Often, when people are making spectacles on Sproul ev-
eryones eyes are glued to them, and so they don’t notice
others.Furthermore, often during rush hours people walk
together in crowds with friends and classmates they are
in the middle of conversing with, so it provides too much
of a hassle to interrupt their own conversations to ac-
knowledge the other.
However, annoyances such as flyering do sometimes
provide a positive effect on interactions. Many people
avoid the center lane of Sproul, and tend to travel in the
more narrow ends, resulting in people bumping into and
acknowledging one another there.
V. CONCLUSION
Through the analysis of the data, there comes to a clear
conclusion that there is a direct correlation between the
flow and ebb of people through Sproul and the amount of
interactions that occur, along with the effect of variables
such as weather, flyering, and on Sproul events have on
the flow, and through that, the amount of interactions.
Roughly 15% of the people who walk through Sproul will
have some form of interaction.
1Kazuhisa Takemura, Behavioral Decision Theory Psychologi-
cal and Mathematical Descriptions of Human Choice Behavior,
(Springer) (2014)

3. Research Methodologies 3
2Giudici, P. , Ingrassia, S. and Vichi M., Statistical Models for
Data Analysis (Springer)(2013)
3D. Bauso Game Theory: Models, Numerical Methods and Appli-
cations (University of Palimero)(2014)