The ght for courses: Documenting the Sciences-po's course registration ...econ.sciences-po.fr/...J_P-optimality_of_scpo_course_registration.pdf · The ght for courses: Documenting

The �ght for courses: Documenting the Sciences-po's

course registration system

Jérôme SANTOUL

May 20, 2014

Master EPP PhD Track - Sciences-po ; Polytechnique ; ENSAE

Supervisor: Sidartha Gordon

1

2

Abstract

This master thesis tries to document the course registration process in Sciences-po Paris.

The main goal is to �nd a way to model the actual system that has few equivalents in other

top-level universities in the world. The model should help understand the strategy pro�le

used by the students to prepare their course registration. Two types of data are used: a

survey conducted ex-post to assess the level of success and failure of the students as well as

understanding how they prepare their registration. The other data is a log-�le of the course

registration server, to observe the behaviour of the students in real time.

Résumé: Ce mémoire de master a pour objectif de documenter les inscriptions pédagogiques de

l'IEP de Paris. La �nalité est de formuler un modèle qui puisse représenter de façon plausible le

système actuel, qui n'a que peu d'équivalents dans le monde universitaire. Ce modèle doit aider à

comprendre comment les étudiants établissent des stratégies pour le jour des inscriptions. Deux

types de données sont utilisées dans ce mémoire. Un sondage a été conduit ex-post auprès des

étudiants de 2e année du collège universitaire pour mesurer leur degré de réussite ou d'échec, et

comprendre leur façon de préparer les inscriptions. L'autre ensemble de données est un �chier-

log extrait du serveur des insription pédagogiques, pour observer le comportement des étudiants

en temps réel.

Acknowledgements I would like to thank my supervisor Sidartha Gordon for his constant

support and guidance, as well as Utku Ünver, Scott Kominers and Alfred Galichon for the

precious insights they provided during the redaction of this master dissertation. Hélène Beaujet

and Thibauld Christin have my eternal gratitude for �nding the huge number the typos I made

while writing this dissertation.

CONTENTS 3

Contents

1 Literature review 5

1.1 Stable matching and e�cient matching: . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 The UMBS-like systems: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 The various STP systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 The Boston Draft Mechanism: . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.2 The HBS system: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 The Sciences-po's system: an example of RTA system . . . . . . . . . . . . . . . 9

1.4.1 The course requirements: . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.2 The registration Day: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Data and Methodology 12

2.1 The server log-�le: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 The survey: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Strategies and preparations for the course registration day: . . . . . . . . 14

2.2.2 The courses strictly preferred: . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.3 The compromises and limits: . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Model and results: 16

3.1 Documenting the data: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.1 The survey: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.2 The log-�le: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Modelling the RTA mechanism: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

A Additional activity plots for all 2nd year available lectures 29

B General activity for other registration days 32

C References 35

CONTENTS 4

Introduction :

For universities across the world, ensuring that their students get the courses that they desire

while maintaining equality of treatment is a constant struggle. Many systems have been

designed, involving, bidding, listing and more. Yet none of these systems have (nor will) be

at the same time ex-post pareto e�cient, clear the set of available courses, ensure equality of

equals, and be strategy proof 1. By equality of equals, we mean that students with the same

preferences should get ex-ante the same course allocation outcome.

Most of the actual literature dealing with the issues treats systems based on either bidding

or stated course preference lists.

The �rst system involves giving students at the beginning of the process an equal number of

"credits". During the bidding phase, students will place bids on some courses and the students

that bid the highest get registered in the course at the cost of their bid. The losers get their

credits back for further bidding rounds. I will refer to this type of system as the University of

Michigan Business Course allocation system (UMBS) following the work of Sömnez and Ünver

(2007)2

The second system requires each student to �le a preference list to the administration of the

university. The administration then applies an algorithm using the lists of stated preferences

of the students and attributes courses to them. Many di�erent methods are used to allocate

courses to students using their stated preferences (tiebreaker, �rst preference �rst etc....) I will

refer to this family of allocation systems as the STated Preferences systems (STP).

These many systems all su�er from the same type of weakness: they allow manipulation

by the students/parents/agents. A UMBS student can adapt his strategy and get a better

payo� by overbidding the courses that are generally popular and underbidding courses that

are unpopular 3. This intuition is also behind the manipulations of some of the STP systems:

agents do not order their preferences truthfully and tend to play around the allocation algorithm.

Yet the STP and UMBS type of course allocation systems are not the only one used by

universities. Other families of systems that are much simpler to understand and much more

uncommon are real time registration systems. In these types of systems, used by Sciences-po

Paris and a few other universities (UofT for undergraduates in Arts and Sciences) around the

world, courses are allocated on a "�rst come, �rst served" basis. Because everything happens in

real time, modelling, documenting and analysing these systems is a di�cult undertaking. I will

refer to the system as a Real-Time allocation system (RTA).

1Pathak and Sönmez (2013), "School Admissions Reform in Chicago and England: Comparing Mechanismsby Their Vulnerability to Manipulation", American Economic Review, 103(1): 80-106.

2Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International EconomicReview, Department of Economics, University of Pennsylvania and Osaka University Institute of Social andEconomic Research Association, vol. 51(1), pages 99-123, 02.

3Abdulkadiro§lu, Atila, and Tayfun Sönmez. 2003. "School Choice: A Mechanism Design Approach ."American Economic Review, 93(3): 729-747

1 LITERATURE REVIEW 5

The following dissertation will be organized in three parts :

• Part 1 presents a summary of the past literature about allocation systems and emphasizes

some intuitions that are useful for analysing RTA systems. A detailed description of the

Sciences-po's course registration procedure is also presented.

• Part 2 describes the available data in detail as well as their strengths as well as their

shortcomings

• Part 3 describes the main results obtained from the data and presents a model to formalize

the RTA systems.

1 Literature review

Before getting into the meat of the RTA systems, a small reminder about market design mech-

anisms, other multi-units allocation systems along with their strengths and weaknesses can be

of use. Some of their characteristics can also be found in RTA mechanism, for RTA presents

features that come from both UMBS and STP systems.

1.1 Stable matching and e�cient matching:

Among the large family of assignment mechanisms, there is a rule that remains constant: no

assignment mechanism has all the following properties at the same time4.

The properties are5

• Strategy-proof: Strategy-proofness means that no individual can manipulate the mecha-

nism to his advantage by misreporting his preference. This incentive-compatibility condi-

tion ensures that agents report truthfully and the allocation chosen by the rule is based on

true preferences.

• Pareto-Optimality: The �nal allocation is pareto optimal

• Non-Bossiness: Non-bossiness means that no individual can change the allocation without

changing his assigned object. This property prevents collusion among agents because if

a mechanism violates this condition, then an agent may be bribed by others in order to

change the allocation without changing his assigned object.

• Equality of Equals: Equality of Equals requires the mechanism to give the same allocation

to two agents who share the same set (or equal sets) of preferences.

4Anna Bogomolnaia and Hervé Moulin, "A Simple Random Assignment Problem with a Unique Solution",Economic Theory, Vol. 19, No. 3 (Apr., 2002), pp. 623-635

5The de�nition of these properties is taken from: Lars Ehlers, "Top Trading with Fixed Tie-Breaking inMarkets with Indivisible Goods", (2012), unpublished at the time of writing.


Some systems can have several of these properties at once but never all of them. The top

trading cycle algorithm for instance is Pareto-optimal, non bossy and strategy-proof, but relies

in di�erences of initial endowment to works, implying non equality of equals.

An other important property of allocative mechanism is the notion of stability. A

matching is stable if there is no blocking pair of agent that would prefer to be associated

together rather than with their current partners. For one sides matching, such as students

to course matching, the notion of priority and the right for one agent to claim a given course arise.

Of course, it is di�cult for an allocative mechanism to be both stable and e�cient, especially

if it involves a one side matching with priorities. Multiple systems try to deal with these issues

when it comes to allocate courses. Below are a few examples of such mechanisms.

1.2 The UMBS-like systems:

UMBS-like systems are based around some basic principles and the only variation between them

are usually numbers (i.e number of credits given to each students to bid). The example I will

describe in detail is the one used by the Ross' School of Business of the University of Michigan.

The registration follows the following steps6 :

• Students from the same promotion are assigned the same number of points to bid (either

500 or 1000)

• The students have a time window to place as many bids as they wish on any course they are

allowed to register in. Of course, their total points bid cannot exceed their initial number

of points.

• At the end of the time window, courses are allocated to the ones placing bids. If there are

more bidders than seats in a given course, only the n highest bids get a seat.

• If there are more persons placing a bid at the tie breaking value, the seats are allocated

randomly.

Sömnez and Ünver argue that, while the system looks like a market for courses, there is one

major di�erence between the two: in a standard auction, the bids are a tool to measure who

has the biggest claim on a good. Here it is used for both tie-breaking, but also to measure the

student's preferences. This property allows for manipulating the allocation, as stated in the "tip

and tricks" section of the UMBS website7

Q. How do I get into a course?

A. If you bid enough points to make market clear, a seat will be reserved for you in that section

of the course, up to class capacity.

6http://www2.bus.umich.edu/MyiMpact/academics/register/biddingtips7see: http://webuser.bus.umich.edu/Departments/Admissions/AcademicServices/CurrentUpdates/BiddingTipsTricks.htm


In the end, Sömnez and Ünver have proved that this type of system is not e�cient, because of

the con�icting roles of the bid. Students are encouraged to overbid popular courses and underbid

unpopular courses even if it is their favourite courses. This property of such system is interesting

for further analysing the RTA mechanism. Before this, I will focus on some STP systems in the

coming part.

1.3 The various STP systems

For this section I will focus speci�cally on two di�erent systems. There are many variations of

these systems and going in detail for all of them would be too time consuming. The �rst system

is the Boston mechanism which is widely used in the US to allocate children to schools8. The

other system is more limited in scope: it is the Harvard Business Schools allocation system,

studied in a recent paper9

1.3.1 The Boston Draft Mechanism:

This analysis is based on the paper by Pathak and Sönmez10. The Boston draft is a mechanism

that revolves around the principle of "First choice �rst". Namely, this draft tries to maximize

the number of agents that get their �rst choices. It works in a �nite number of rounds as follows:

• Agents/students/parents submit to the administration an ordered preference list of

items/courses/schools. The list must include at least two entries and is unlimited in length.

• Before the �rst round agents are ordered in priority according to some criteria (academic

results, income, anything that one can imagine)

• In the �rst round, the �rst entry of each list is read (i.e the administration only looks at

the �rst choice of each agent). Each agent is assigned his �rst choice following the priority

order, if there is still room left. If there is no room left, the agent gets nothing and the

administration moves on to the next agent.

• In the ith round, the administration reads the ith choice of the remaining agents and tries

to assign seats one at the time following the order of priority of the agents. Again, if a

choice has no seat left, the administration moves on.

The authors have noted that because some preference lists were sometimes too short, it was not

uncommon in Boston to have children una�ected to a school after all the rounds were completed.

It was also observed that the una�ected children usually had parents that were reporting only a

few extremely popular schools that were �lled up very quickly in the �rst rounds. On the opposite

8Trivia: it is not used in Boston any more since 20059Budish, Eric, and Estelle Cantillon. 2012. "The Multi-unit Assignment Problem: Theory and Evidence from

Course Allocation at Harvard." American Economic Review, 102(5): 2237-7110Pathak, Parag A., and Tayfun Sönmez. 2008. "Leveling the Playing Field: Sincere and Sophisticated Players

in the Boston Mechanism." American Economic Review, 98(4): 1636-52


side, some parents played the system and actually misreported their preference. Their strategy

is summarized by the following recommendation found in the board of one parents association:

One school choice strategy is to �nd a school you like that is undersubscribed and put it as a top

choice, OR, �nd a school that you like that is popular and put it as a �rst choice and �nd a

school that is less popular for a �safe� second choice.

Because the system punishes you very hard for failing (you are basically forgotten until the

beginning of the next round if your choice has no room left), sincere agents are severely dis-

advantaged compared to parents that play around the system (the authors call them "strategic").

They have demonstrated that, if all agents are strategic, this allocative system is equivalent

to the (Gale and Shapley 1962)11 allocation mechanism. However, since all agents are not

sophisticated in reality, sophisticated agents are weakly better with the allocation of the Boston

mechanism.

This system has some interesting features that one can �nd in an RTA system. Precisely:

• During a round, only the top choice is considered and all the others are ignored.

• Failing to get an allocation early is very detrimental

• Agents that play the system are weakly better than sincere agents

1.3.2 The HBS system:

This analysis is based on the paper by Eric Budish and Estelle Cantillon. 2012 and this part

will present their conclusion:

The HBS system is a draft system that is quite complicated12 Here is a rough presentation

on how the system works:

1. Phase one: stating preferences

(a) One student at a time chooses a single course and adds it to his "Rank-Order List"

(b) Students are then randomly given a priority order.

2. Phase two: allocating seats

(a) During the �rst round (and all subsequent odd rounds) students are taken in ascending

order of priority. Each taken student is given the highest course in his list where there

11Gale, David, and Lloyd Shapley. 1962. �College Admissions and the Stability of Marriage.� American Math-ematical Monthly, 69(1): 9-15.

12So complicated that Havard organizes a "mock registration" session to make sure that every students under-stands how things work.


is still room left (i.e, if your �rst choice is full, you get your second choice if there is

still room. If no room left in the 2nd choice, try 3rd etc...)

(b) During the second room (and all subsequent even rounds) students are taken in de-

scending order of priority. Allocation follows the same principle as above.

3. Phase three: add and drop (this is not di�erent from any other US university). One can

model this using a random serial dictatorship on the set of courses where there is still room

left.

As the authors have demonstrated both theoretically and empirically that this draft system

is more e�cient (i.e increases the total welfare) than some more classic strategy-proof systems

like the random serial dictatorship.

What they also showed is that some students are playing the system (this was expected) and

that this strategic over sincere play induces losses of welfare in general.

The optimal strategy the authors found for such a game is, again, to lie on your preferences

and place at the top of the Rank-Order list the courses that are popular, leaving the unpopular

(hence easily obtained even in later rounds) at the bottom of the list.

This is a major change compared to the Boston mechanism where the draft punishes you

for placing very popular choices at the top of your list. With the HBS draft, students are

encouraged to "go happy go lucky" with their stated preferences. The draft will not punish you

for not getting your �rst choice in the �rst round, because it will automatically give you your

next highest choice with room left.

The last feature the system presents is the randomized priority order, that one can �nd in

the RTA system that has no �xed criteria to draw priority.

There are many other allocating systems in the world. In the end, I believe that by covering

the UMBS, Boston and HBS mechanisms to allocate the course, we now have a broad view and

lots of tools to understand how the Sciences-po's registration system works.

1.4 The Sciences-po's system: an example of RTA system

In this section, I will present in detail not only the registration process, but also the courses

requirements of the 2nd year undergraduate students. Both of them are very complex to

describe. I advise a reader only interested in the results and the methodology to skip these

descriptions and go to the next part. For those interested in interpreting the results and

understanding all the constraints the analysis is facing, this is a must read.


1.4.1 The course requirements:

I am focusing on the spring semester of the 2nd year undergraduate students. During this

semester students were asked to take compulsory courses:

• One fundamental module (French: module fondamental) which is in this semester a pair

lecture-tutorial in history. Tutorials are usually in groups between 15 and 25. Lecture can

host up to hundreds of students.

• One seminary in either law, economics or history. A seminary is usually a lecture of up to

30 students and sometimes includes an associated tutorial.

• One seminary in either Sociology or political science. Same format as the other seminaries.

• One cross-�eld seminary: (French "séminaire interdisciplinaire") �ve to choose from. Topics

of courses are such that they cannot enter the other categories. No associated tutorial.

• Two electives: a 2 hours per week course in groups between 20 and 30.

• One artistic workshop: similar format as above. Themes ranging from drama to the art of

speech through jewellery.

I will refer to these courses types as fundamentals, seminaries, electives and workshops re-

spectively in this dissertation. On top of these compulsory courses, students are allowed to take

optional courses. Namely:

• Up to two language courses. Among these courses are e-learning courses (i.e courses with

unlimited capacities).

• One "dead language course", either Greek or Latin.

• Artistic activities (note: these include working for the "Bureau des Arts")

As one can see this abundance of courses format makes the analysis of the system as a whole

very di�cult. Modelling the preferences of the students as a simple ordered list is an idea

that can be challenged. One cannot freely swap courses in di�erent categories. Because of this

isolation between fundamentals, seminars etc. I do consider the market of fundamentals as an

almost completely separated from the other types markets, bar one exception. All these markets

registrations happen the same day. I will get deeper into this process in the next part.

1.4.2 The registration Day:

All the students at Sciences-po face the same system and the same procedure during their

registration. The only di�erence between a graduating students and a fresh �rst year bachelor

student is the course requirement (i.e freedom and/or complexity of choice). I detailed the 2nd

year university college spring semester course requirement in the previous part. Now let us delve


into the registration process in itself:

The students have a dedicated day for their registration depending on their year and master's

degree they are in. For the spring semester 2014, 2nd year university college students had their

registration on January 8th from noon to 6PM.

During this window of time, students can access a dedicated website, using a special

login and password. Once logged in, a front page acts as a reminder of the students courses

requirements. Hyper-links lead to the di�erent categories of courses available to the students.

Students have to click them and will access a list of all the courses available in the category13.

Students can then click in the list to get to the course's page. In this page, the course's available

conferences are shown. One can tick boxes at the left of a conference and then click on a

button submit to register the course. If a given conference/lecture/tutorial is full, the box

corresponding will be greyed out and replaced with the letter C (stands for "Complet" in French).

Once the registration for a given course is done, the seat is de�nitively attributed to the

student. At any time during the registration window, a student can freely drop a course and

select another one which is not yet full.

As one can see, the registration process involves quite some clicks. One needs to go through

3 di�erent pages (main, category, course) on the website to register in a course and repeat

the operation each time he wants to register in a new course. One can hardly register at two

courses at the same time. Moreover, because when a seat is granted it can only be released at

the discretion of the student (aka, �rst arrived �rst served), the entire registration process turns

into an arms race. The registration time window is up to 6 hours long, yet the majority of the

registrations happen in the �rst 5 minutes after the beginning because of this principle.

Failing to register in a given course is thus very costly for a student. One student has to load

3 webpages to see if a given course is full or not. It means that when a student discovers that

the course he wanted is full, he must restart the entire process for his secondary choice and is

now late for successful students could register in two courses where he could just get one. Time

is of the essence in the registration.

All these facts make me believe that this registration procedure is unlike any system

described in the literature before. There is no clear strategy pro�le for this system : it cannot

be reduced to a preference list. Courses are too varied to have clear preferences and surveys

support this claim. We can separate categories of courses to get real preference lists. However,

since the registration happens for all types at the same times, seeing the Sciences-po's system

as multiple parallel HBS-like STP is not possible either.

13Link to the list of available electives, a similar list appears on the website: http://college.sciences-po.fr/siteparis/enseignements-electifs-semestre-2

2 DATA AND METHODOLOGY 12

In part 3, I will de�ne what I believe is the best approximation model for this system and

will try to justify this representation by the information extrated from data about the course

registration. However, a description of these data should be conducted �rst, which is the point

of the next part.

2 Data and Methodology

The data I managed to obtain to conduct this dissertation are of two types. The �rst type of

data is a survey submitted to the Sciences-po's students at the beginning of the spring semester.

This survey covered students' strategies about the course registration period as well as courses

that were desired but not obtained.

The second type of data was an extract of the log-�le of the courses' registration server.

2.1 The server log-�le:

This �le is an important dataset that includes all the requests sent to the server since September

2013 up to and including the beginning of March 2014. Each line in the master �le contains a

unique request sent by a user to the master server.

Each user is identi�ed by a 10 digits called the PIDM. Students as well as sta� members all

have their own PIDM.

Each course in this database is identi�ed by a unique 6 digits number called the CRN. It is

important to remember that what is considered a "teaching module" for an ordinary student (i.e

combination of lecture and tutorial) is not with the database. Within the �le, a given lecture

at a given time has its own CRN number and all the associated tutorials have their own CRN,

that are di�erent from the one of the main lecture.

A single line in this master �le can be identi�ed with the PIDM of the user at the origin of the

request, the CRN of the course/tutorial/conference the student wants to register in or out and

the time at which the line was created in the log �le. Various other information are available as

well but I do not have a full understanding of it. Precisely, it was impossible to determine if a

line was a registration, a course drop or a failed attempt.

Because the database includes the registrations of all students, not just the 2nd year ones,

the database has been �ltered using a secondary �le. This �le is a database of all registered

students of Sciences-po for the year 2013-2014.

In order to respect the privacy of all students, all information allowing to identify the person

have been removed before any analysis could be made. This included characteristics such as

age, nationality, sex and name. I assumed that the Sciences-po's students are intelligent people

that, when facing a problem such as getting into desired courses, are using their intellectual


skills. I claim without justifying it that these intellectual skills should not be a�ected by sex

or age or any other comparable characteristics. It is a strong assumption that will need to be

veri�ed, however it will require agreements and additional time that I do not have14.

Last but not least, the CRN numbers are mapped to actual courses name and characteristics

using a third �le. This �le encompasses all the courses available to the second year students,

as well as exams. This �le is matched with the master �le using CRN keys. Because of the

complicated structure of the Sciences-po courses, the analysis about optimality will be restricted

to electives, artistic workshops and seminars.

Why such restriction about pareto optimality ? Multiple reasons can be invoked:

First of all, going in details about tutorials requires complementary data that are not available

now (more on this in the survey subsection).

Secondly, choices of elective/workshops and seminars are mostly driven by the module's theme,

because there is only one session available. There is no choice of timing. Same cannot be said

about the lectures and their tutorials. The only choice a student makes when he is registering

for an elective, a seminar or a conference, is a choice of a pair course theme & time schedule.

Thus one can assume (the survey supports this hypothesis) that we can strictly order the courses

by theme preferences for each student.

For fundamentals, this is a much stronger hypothesis. I do not believe one can order the lectures

and conferences on theme only. My hypothesis is not backed up by data, but it is reasonable to

assume that students universally prefer to have a tutorial from 14h45 to 16h45 rather than one

from 19h15 to 21h15.

Of course, the study of such preferences could help a lot the administration to provide a better

o�er of courses. A simple application to smooth demand consists in giving a given lecture,

two (or more) associated tutorials with schedules that are equally preferred on average among

students.

Let us take a lecture on Thursday with two tutorials, one should be on a Monday at 8AM and

the other one on Friday at 7PM (two equally hated schedules for students/anyone). It would

render the registration process smoother than a schedule with one tutorial on Monday 5PM and

the other at Friday 7PM.

However, the timetable of each course is not found within the database provided. One could

recreate the schedules but it would be an entirely new dissertation.

One should remember that when interacting with the course registration website and clicking

"register", the students (or any sta� member that recti�es mistakes etc...) sends a request to the

registration server. Because students usually pick a lecture, an exam and a tutorial at the same

14On an o�-topic note, I do want to remind the reader that the registration process is a stressful one and yieldspeople to do mistakes. To study how students handle mistakes under stress is not a micro economics problem(more a problem for psychology/sociology) but it remains interesting nonetheless


time during registration, it means that the website sends two requests with the same PIDM but

di�erent CRN at the same time to the server.

The �le has many lines that have the same PIDM and same add date. I chose to group lines

with the same PIDM and add date together for connexion analysis. I do however keep these

lines separated when I determine which courses students are registered in.

2.2 The survey:

The survey is a google form sent to all second year students of Sciences-po of the Paris campus

that are not involved in an exchange program. Students in region campus are not included

because of they face a very di�erent o�er of courses they face. The survey is written in French

and covers several aspects of the courses' registration procedures. The survey is divided in two

parts:

2.2.1 Strategies and preparations for the course registration day:

The �rst half of the survey is dedicated to understand how students prepare the course registra-

tion day. It included:

• Questions about the level of detail of the preparation (choose the lecture, or the lecture

and tutorial etc...)

• Questions about the criteria used to pick/plan to pick a course and their relative importance

• Questions about the preferred type of course.

2.2.2 The courses strictly preferred:

The second part of the survey was aimed at gathering enough information to perform a top

trading cycle algorithm with the students and their courses. For each course type (fundamen-

tals, seminars, electives and artistic workshops), students were asked if they got all their "�rst

choices" i.e the course they wanted at the time they desired the most. If for a given course type,

a student answers no, then the student is redirected to a list of all the available courses of the

said type. The student is asked to tick all the courses of the list that he strictly prefers over his

actual course(s).

The only exception was with the fundamental courses. I considered this type to be too di�cult

to examine because each course is a pair of lecture and tutorials. Because of the sheer volume

of available tutorial for a single lecture, it was impossible to have the students point to the

lectures they wanted and keep the entire survey human readable. To compensate, I only asked

the students to say if they had a problem getting the tutorial at the time they wanted or if they

could not get registered in the main lecture at all. The study of the demand for tutorial and

modelling this demand could be a dissertation in itself.


A last section was left at the end of the survey for comments.

2.2.3 The compromises and limits:

This survey su�ers several drawbacks for many di�erent reasons. First of all, as stated in the

paragraph above, one type of course does not have the relevant data to perform a top trading

cycle algorithm on it, for the sake of readability.

Secondly, if a student has more than one course in a given category (eg. electives), and ticks

at least one course in the preferred courses list, there is no way to tell which course is the one

the student wants to drop in favour of the ticked one(s). This is purely a technical limitation

imposed by the google form : it is impossible to mix a scale and a ticking list in the same

question. However, it remains possible to test for multiple combinations of preferences and

apply the top trading cycle on each of them.

Moreover, the survey did not include the language courses at all as well as Latin and Greek.

On the one hand, Greek and Latin are pure outliers and not compulsory courses. The demand

for these two courses is usually low compared to compulsory courses.

On the other hand, language courses at Sciences-po, while not o�cially compulsory are heavily

recommended for students, for an IELTS or equivalent language certi�cation test is required

to be admitted in an English speaking university for the exchange year. These courses are

organized and monitored independently of the other courses. Each semester, the language

department o�ers the same set of courses to every student of the IEP, regardless of their year,

�uency in a given language or degree. Students are then free to register in any of the proposed

course as long as there is no time con�ict and they meet the skill requirement. In concrete

terms, it means that the studied students (2nd year undergraduate) in this dissertation are

competing with all the other students in the IEP. There are way too many parameters entering

the equation and I have no clue on how to approach this issue. Thus it is left out of the board.

Finally, some students in the 2nd year undergraduate cohort are dual degree students that follow

courses in other universities. These are the SMASS (math major coupled with Sciences-po's

Bachelor), the SPIV (philosophy major coupled with Sciences-po's Bachelor) and the SCUBE

(read it S-cube, biology/physics/math major). These students have courses requirements that

are close to the ones of the normal students (they draw in a restricted pool of courses). However,

some of them were able to "bypass" capacity requirements of some courses through direct

intervention of their sta�. These students are not many but they present a potential bias toward

e�ciency of the system, since they were able to get their �rst choices when they should not have

under the normal procedure.

Naturally, the survey did not obtain a 100 % response rate, but with more than 560 responses

for about 900 students targeted, I consider the survey to be a success. While the network of

preferences is not complete, it allows to perform a serious TTC algorithm anyway.

3 MODEL AND RESULTS: 16

3 Model and results:

This part presents the two main contributions of this dissertation :

• To document my data as much as possible in order to provide micro-foundation for the

next sub-section.

• To propose a model that could represent more or less the actual RTA system, and acts as

a starting point for theoretical analysis.

3.1 Documenting the data:

3.1.1 The survey:

Students response to the question on how they prepared their registration were expected:

1. 93% of the students have a precise idea of the courses they want to take, including the

timing of the tutorial and they also have their 2nd choices ready, should something go

wrong.

2. The remaining percents are people who did not bother about the timing of their courses.

3. When choosing a course, the them/title of the course is the most important criteria for

almost all students.

4. Students are more picky when it comes to choose the timing of the tutorials of their electives

and seminars than when choosing tutorials for their fundamentals.

5. A minority of students (40%) do not use the students' magazine15 when choosing their

courses/preparing their list of choices. However, for 39% of students (i.e 63% of the users

of la péniche), it is only a minor criteria.

6. Finally, a large number of students declare they are plying the system. More precisely:

(a) 53% of the students declare to register �rst in the course they think are popular (i.e

�lls quickly)

(b) 21% of the students declare playing "truthfully" i.e they register �rst in the courses

they prefer.

15http://lapeniche.net/


(c) The remaining 19% do not bother about it and register in courses following their order

of appearance in the website16 (i.e fundamentals �rst, seminars second, electives third

and workshop last).

One fact is ba�ing: out of the 565 students who responded to the survey, only 96 got all their

�rst choices for every course type (and thus can brag about winning the "Just as Planned"

Prize). Results for students that were partially successful (but got most of their �rst choices)

are summarized below :

Fundamentals? Seminars? Electives? Workshops? Number FractionY Y Y Y 96 (125 w/ 2 major) 17.0% (22.1)N Y Y Y 41 7.26%Y N Y Y 9 1.59%Y Y N Y 28 4.96%Y Y Y N 21 3.72%

Students that were quite successful 195 (224) 34.5% (39.6)

Table 1: Table of success rate for students who performed well

A relatively high percentage of students did not have their �rst choice of fundamental. This

does not mean they did not get in the lecture but rather that they failed to get the tutorial they

wanted.

Some students were very unlucky or late and had courses that were only second choices or

even below (no dual degree included):

Fundamentals 1st choice? Seminars? Electives? Workshops? Number FractionN N N N 61 10.8%Y N N N 14 2.48%N Y N N 42 7.43%N N Y N 25 4.24%N N N Y 44 7.79%

Students very unsuccessful 186 32.9

Table 2: Table of success rate for students who performed poorly

Although the percentage of students falling in the "Not as Planned" category seems quite

high, one should remember that they are likely to be overrepresented because of self selecting bias.

This leaves us with a third of the students who performed well in two categories of courses.

It is also useful to note that some course categories tend to have a higher success rate than others:

16Joke aside, this is the category I belonged to


Course type: Global success rate Fraction who got courses they did not plan to take:Fundamentals 40% 20%Seminars 63% 15%Electives 50% 21%Workshops 61% 18%

Table 3: Table of success rate by types of courses

Again, the low success rate for the fundamental courses (lectures+ tutorials) should not be

over-interpreted: since tutorials' group are small, it is extremely di�cult to get in the one

one wants. This contrasts a lot with the interest that students have in fundamentals. When

asked "What type of course type do you value the most?", 53% of the students answered

"fundamentals", 27% the electives and only 13% preferred the seminars. The remaining 7%

showed strong enthusiasm for language courses or Greek.

Why such a di�erence between the success rate of the seminars and the interest in said

seminars? One reason is found within the wording of the question "What type of course do you

value the most?". It appears that 2nd year student believe that the choice of the fundamental

will strongly de�ne their later studies at Sciences-po.

The very high success rate for seminars and workshops leaves room for two hypotheses:

1. Lots of students tend to rush for these types of course and �nd themselves with their �rst

choice of tutorial already full (full of students that rushed to the tutorials) when they are

done with seminars.

2. Students are rushing for tutorials and those �ll up so quickly that a lot of students are left

with less favourable ones.

One statistic that puzzles me is the high number of people that ended up with courses they

did not plan at all to take. Could this indicate a lack of planned 2nd choices? Additional

input on the matter could help. As a �nal remark, one could do additional statistic based on

the preferences of students (success rate of student who prefer seminars vs the one who prefer

fundamentals). I did not do them because of time constraints and the incomplete nature of this

survey. If one could make such type of survey a compulsory part of the undergraduate studies,

it could yield much stronger results.

3.1.2 The log-�le:

Summarizing a survey is rather easy. However, constructing and designing summary statistics

for a log �le of requests was quite a challenge. I tried to �nd a compromise between generality,

readability and ease of representation. Since I was not able to make a di�erence between a


request to register in a course and a request to drop a course, I chose to represent the "activity"

of students or the "activity" of a course.17

The general activity of the cohort The term "activity" refers to the number of received

requests during a time interval. To limit redundancy, I sometimes eliminated lines with a du-

plicated PIDM, CRN and time triplet (i.e requests received at the same time, from the same

student and the same course).

Figure 1: The general activity of the server on January 8th 2014

The bottom graph is a regression of the log number of requests vs the log of time. A clear

correlation between the two appears. That supports the idea that the activity on the server

follows either an exponential distribution or a Pareto distribution. The regression parameters

given in the graph are obtained using the following regression equation :

log(”activity”) = log(Cst)− 1

τ× log(t) (1)

One can see that the constant parameter (that represents the number of requests sent during

the �rst minute of the registration process is abnormally large and the characteristic time is

extremely large as well. This suggests that in a fraction of seconds, the activity drops by half.

Pareto's regression equation on the other hand yields:

fP(x) = log(k) + k × log(xmin)− (k + 1) log(x) (2)

17Some regressions have detailed results in the annex.


This equation imposes a cumbersome requirement on the coe�cients (namely the constant and

the slope of the curve are linked since xmin is �xed, and the equation does not hold.

Things do become more interesting however when one shortens the length of the time interval:

Figure 2: The general activity of the server on January 8th (5sec interval)

The graph represents the same activity as the graph above, with a shorter time interval. It

shows an interesting phenomenon at the beginning of the registration: there is a warm-up time

during which not all students are connected. What can explain this? A simple reason comes

immediately in mind: not every student is smashing the refresh button to get in the registration

website as soon as possible. Some students are checking their clock which is not an optimal

process. What this implies is that students frenetically smashing their refresh button gain a time

advantage.

For the second log-log regression, I removed all the points that were representing the warm-up

part to diminish the disturbance. The �tting gives better but still unsatisfying results: were are

predicting over 10000 peak activity (there are only one thousand second year students so activity

cannot got over one thousand) and the "activity's half life" is around one second.

The pattern of exponential decrease is not speci�c of the Paris campus nor the 2nd year students.

Most of the other registration days seem to follow the same law (the plots are in the annex)

However, despite its unrealistic �tting results, I will consider that the activity follows an

exponential decrease after the maximum activity is reached.


The activity of speci�c courses: The exponential decrease of general activity is not equally

spread over the available courses. Some seminars clearly feature such behaviour while others are

following completely random patterns:

Figure 3: Activity for the tutorial number 55848

The course number 55848 (no course name or teacher name will be communicated in the

dissertation as part of an agreement with Sciences-po) has a peak of activity at the very beginning

of the registration period and very few requests after. On the other hand:

Figure 4: Activity for the tutorial number 55984

the conference number 55984 is heavily requested at the end of the registration procedure,

probably indicating a very low demand: it was probably picked because of the lack of room in

any other conference.


The observed patterns are also found with lectures18:

Figure 5: Activity for the lecture number 54137

The scheme above looks like a case study, with the exact same exponential decrease pattern.

However, some other lectures have a "smoother activity". This brings an explanation to the

persistence of activity even after the �rst 10 minutes of the registration window. This is the

manifestation of a not very well know practice of the administration. This practice is nicknamed

"plateau opening". The administration opens up additional seats during the registration window.

Combined with some students dropping some of their course to take other ones, this means that

�lled courses can still reopen during the window. In the survey, people reported to do "lurking"

opened seats during the entire registration window. This behaviour is re�ected in the activity

graphs.

The problem of doubloons: As stated during the data description, I have removed the

triplets with duplicated PIDM, CRN and time. This does a�ect the activity, sometimes by a

large quantitative factor. Here is an example:

This graph shows the activity of the lecture 54137. The activity is not exponentially decreas-

ing suggesting that this course was middle rated by students. Now below is the activity graph

of the same courses with all the duplicated triplets removed:

Qualitatively, there is no major change: the activity is still spread out. Quantitatively, the

lecture appears to include a lot of people in the end whereas with doubloons dropped, only

17 requests remain. This is puzzling and a better understanding on the log-�le mechanisms is

necessary.

18The plots for all lectures are in the annex


Figure 6: Activity for tutorial 59408 with duplicates:

Figure 7: Activity for the tutorial 59408 without duplicates :

Time interval between requests: Since the general activity of students follows an exponen-

tial distribution (this is my theory anyway), it implies a lot of things:

• The probability of a student to get into a course during a time interval is linear and

increasing with the length of the said interval: P(”register during dt”) = dtτ

• The probability of getting registered is not a�ected by the presence of other students (in

theory yes, in practice no because of server overloads that disturbs everyone).

• students starts the registration with a number of "course requirements" and try to evacuate

them as fast as possible (similar to radioactive nucleus evacuating extra proton/neutron).

Once they have evacuated their requirements, they leave the process.


It makes sense to suppose that the probability of a student getting registered (which translates

in "the server receives something") increases over times. To assess the phenomenon, I have

computed for each student a "time gap" between two requests.TO avoid data pollution, requests

that have been received in less than 3 seconds from the previous ones (for the same student)

have been cut out (nobody clicks through 4 very di�erent pages in 3 seconds) that are probably

caused by lags in the server (multiple registration bundles). Below is the plot:

Figure 8: Frequency of time intervals between two requests of the same student:

Blue crosses are original data. They do feature an extremely fat and extended right tail.

This was to be expected: this tail is generated by the "lurkers" that do connect sometimes

hours (the graph is truncated for the sake of readability) after the beginning of the registration

period. Thus a type II extreme value distribution �ts the data perfectly. This distribution has

the advantage of having a lower bound. In our case though, the �tted bound was negative which

is not realistic (and the distribution is di�cult to interpret).

To focus on the gaps during the "exponential decrease" phase, I had to cut out the requests

generated by the "lurking". My method was harsh but e�ective: I computed the mean gap

between requests for every student, then removed every datapoint whose associated gap was

more than one standard deviation away from the mean.

It is a rough method that removes a third of the available data but the results were here:

the purged gap distribution in red has a tail that is much thinner.

In the end, I �nd the following results:


Data used mean standard deviation

Original data 22.1435717 19.04684448

Purged Data 24.24396417 15.07888027

The standard deviation must be interpreted carefully for the data is highly skewed. On average,

during the "exponential decrease phase" (or burn phase), it takes 20 seconds for a student to

register in a course. This mean is purely theoretical because of the many accidents and errors

that might occur during the registration process and in�ate the average the gap.

3.2 Modelling the RTA mechanism:

This section presents what I believe is the best way to model the Sciences-po's RTA mechanism.

The properties of such a model are not detailed in the dissertation (it is not its goal) but it gives

a base to conduct further (and more theoretical) research.

Courses:

There are a �nite number Q of di�erent types of courses. Each course Cq can only belong to a

single type of course q. Each course has a capacity kC ∈ [0; 1]. The global capacity of all courses

is thus K ∈ [0; 1]A, where A is the total number of available courses.

Important note about categories: a course from any given category is fully substitutable

with courses from the same category but cannot be substituted with courses from any other

category.

I borrow this hypothesis from Budish and Cantillon 201219 that were working with a

continuum of students normalized to 1; the courses capacities are also normalized to 1. I assume

that the preferences of the students are common knowledge. Since everything is normalized, it

is equivalent to assume that the individual preferences are a private type of each student but

the general distribution of preferences is common knowledge20.

I am assuming that students do not communicate their preferences or choices in advance

to other students. This is absolutely unveri�ed in reality, and there are evidences of this

phenomenon in real life (i.e some students admitted in the survey to coordinate with their

friends to get in the same course). To keep the complexity under check, I ignore this aspect of

the process. One can of course add a cheap talk game in the model to make it look more realistic.

Each student can take at most one seat in a given course and at most mq ≥ 1 in each

category q (m stands for maximum).

19E. Budish and Cantillon, "Multi Unit assignment Problem, the case of the HSB mechanism", AER, 201220This follows from Mas-Colell (1984)


Preferences:

Each student s has a set Q sets of ordered preferences for all categories together. I choose this

representation since students have to take courses in every category, at the same time. It is easier

to consider preferences inside a given category. However the ultimate goal for each student is to

get his/her �rst choices in each category and maximizing the global welfare across all categories

of courses. The strict order can be imposed for applying a top trading cycle. However, what I

am trying to do with the data (�nd one instance of trading cycle within one course category)

does not require a strict ordering. I am not aiming at �nding the Pareto-Optimal allocation. I

am aiming at a Pareto improving allocation (I am aiming for better, not best).

Note: The data are too incomplete to support a model featuring this type of preferences. What

the survey contains is the set of preferred courses in each category (this set can be empty). This

is far from an ordered list.

Allocation:

All the N students (noted s) end up at the end of registration day with an allocation of courses

noted as. The only feasible allocation is where the student takes exactly the required number

of courses in each category. The allocation takes place in discrete time periods (lasting about

20-30 sec according to empirical data). During each time period, students can try to register in

any given course of any category. The attempt can succeed or not.

At each period, students are randomly given a priority order.

Strategy:

Each student (i.e player) is trying to maximize his utility by getting his topmost choice on each

course category.

A strategy σ for a student s thus has the following form:

• It is an ordered list of courses. It can have any size.

• The list is �xed at the beginning of the registration window and does not change during

the registration process.

• At the nth period, a student tries to register in the nth course in the list if he is allowed

to. If the nth item in the list is a course that cannot be taken because the student has

reached his maximum number of seats in the course's category, he immediately tries to

register in the next entry in his list (you do not lose a turn because you have met your

course requirements).

• If a student's attempt to register fails, he moves to the next item of the list in the next

period.

To represent the imperfect planning of some student, about a half of the students should play

this game normally and the other half should play it truthfully i.e their ordered list is the exact


copy of their preference list.

Lurking:

The lurking phase is modelled as a random serial dictatorship that happens in three phases:

1. Students release some seats in courses they are in

2. Students are randomly given a priority order

3. The serial dictatorship takes place over the set of free seats

Conclusion :

Real time allocation systems are a family of systems that are still not studied in detail for a

number of reasons. Among them are the huge number of parameters that interfere with the

game such as stress and technical di�culties. Nonetheless some properties can be inferred from

these systems:

They lead to an arms race between students, trying by any mean to gain a lead over their

fellows. This arms race translates into and exponential distribution of the activity of students

in the beginning of the process, followed by a a long quest for remaining opened seats. This

exponential distribution allows to build up some statistics over each course, provided one has

su�cient numbers of data points. The half life (time interval after which the activity over one

course is halved) of each course and the average level of activity can be a good proxy for its

popularity ex-ante.

After extensively browsing the literature on multi-unit assignment mechanism, I came to

the conclusion that no system can achieve a "perfect" allocation. Each has advantages and

drawbacks. In the case of Sciences-po, the systems has been proved extremely simple to grasp

for all students. Its major drawback however is its inherent stressful nature. This stress is

further ampli�ed by the technical problems encountered by servers during the "burn phase" of

the registration. Its second drawback is to force student to register in lots of di�erent course

markets (read: course categories) at the same time, forcing students to sacri�ce courses in one

category to have a better chance to get the course they want in another category. I propose the

following change for the 2nd year course registration:

Extend the system already used in the Paris School of International A�airs. Have di�erent

registration times for di�erent course categories (fundamentals and seminars in the morning,

electives and workshops in the afternoon).

Transform the real-time system in a discrete type system: give students 1-3 minutes to tick a

single course in the website and apply for registration. If the number of applicants for a course

exceed the course capacity, the system should randomly select the one who should be accepted

and notify the student about it. Although it will make the registration last longer, it will induce


less stress and encourage students to spread out to maximize their chances to get in.

Finally, conduct preliminary surveys about the students �rst choices and publish some results. It

will allow people to realize that some courses are overcrowded and hopefully limit the magnitude

of this rush during the d-day. There is no need to do it fancy, a simple Google form or Doodle

can do the trick.

A ADDITIONAL ACTIVITY PLOTS FOR ALL 2ND YEAR AVAILABLE LECTURES 29

Annex:

A Additional activity plots for all 2nd year available lec-

tures

These plot show the activity of all the available courses for 2nd year undergraduate (collège

universitaire) students labelled as "lectures" in the log-�le. Plots made using data with no

duplicated triplet (PIDM, CRN, TIME).

Important: These �gures are read the following way: 1st plot is on the top left (dark blue),

second is top right (red), third one is bottom left (green), last one is bottom right (cyan).

Figure 9: Activity of lecture 1 to 4

The lecture 1 shows signs of lurking.



This group of four lecture are a good example of the di�culty to interpret the activity.


Number of requests is surprisingly low for lecture 10.



Lecture 18 only has requests during the �rst minute. Keep in mind that there are other re-

quests for the same lecture but for other registration days (e.g the ones for dual degree students).

B GENERAL ACTIVITY FOR OTHER REGISTRATION DAYS 32

B General activity for other registration days

The following plots are constructed using the same method as in the main body of the disserta-

tion. The only di�erence is the use of a scatter plot instead of a bar plot.

Figure 13: General activity for Paris on Jan 6th

OLS Regression Results

==============================================================================

Dep. Variable: y R-squared: 0.660

Model: OLS Adj. R-squared: 0.659

Method: Least Squares F-statistic: 565.0

Date: Mon, 19 May 2014 Prob (F-statistic): 3.82e-70

Time: 18:01:23 Log-Likelihood: -225.97

No. Observations: 293 AIC: 455.9

Df Residuals: 291 BIC: 463.3

Df Model: 1

==============================================================================

coef std err t P>|t| [95.0% Conf. Int.]

------------------------------------------------------------------------------

const 6.4425 0.233 27.695 0.000 5.985 6.900

x1 -0.8265 0.035 -23.769 0.000 -0.895 -0.758

==============================================================================

Omnibus: 1.723 Durbin-Watson: 1.628

Prob(Omnibus): 0.422 Jarque-Bera (JB): 1.799

Skew: -0.178 Prob(JB): 0.407

Kurtosis: 2.856 Cond. No. 51.9

==============================================================================


Figure 14: General activity for Paris on Jan 7th


==============================================================================



Method: Least Squares F-statistic: 2743.





Df Model: 1

==============================================================================


------------------------------------------------------------------------------

const 12.2510 0.203 60.293 0.000 11.852 12.650

x1 -1.5341 0.029 -52.374 0.000 -1.592 -1.477

==============================================================================



Skew: -0.348 Prob(JB): 0.00948


==============================================================================


Figure 15: General activity for Reims region Campus on Jan 8th


==============================================================================



Method: Least Squares F-statistic: 343.0





Df Model: 1

==============================================================================


------------------------------------------------------------------------------

const 10.5568 0.472 22.360 0.000 9.619 11.495

x1 -1.5352 0.083 -18.519 0.000 -1.700 -1.371

==============================================================================



Skew: -0.495 Prob(JB): 0.130


==============================================================================

C REFERENCES 35

C References

1. Pathak and Sönmez (2013), "School Admissions Reform in Chicago and England: Com-

paring Mechanisms by Their Vulnerability to Manipulation", American Economic Review,

103(1): 80-106.

2. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," Interna-

tional Economic Review, Department of Economics, University of Pennsylvania and Osaka

University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123,

02.

3. Abdulkadiro§lu, Atila, and Tayfun Sönmez. 2003. "School Choice: A Mechanism Design

Approach ." American Economic Review, 93(3): 729-747

4. Anna Bogomolnaia and Hervé Moulin, "A Simple Random Assignment Problem with a

Unique Solution", Economic Theory, Vol. 19, No. 3 (Apr., 2002), pp. 623-635

5. Lars Ehlers, "Top Trading with Fixed Tie-Breaking in Markets with Indivisible Goods",

(2012), unpublished at the time of writing

6. Budish, Eric, and Estelle Cantillon. 2012. "The Multi-unit Assignment Problem: Theory

and Evidence from Course Allocation at Harvard." American Economic Review, 102(5):

2237-71

7. Pathak, Parag A., and Tayfun Sönmez. 2008. "Leveling the Playing Field: Sincere and

Sophisticated Players in the Boston Mechanism." American Economic Review, 98(4): 1636-

52

8. Gale, David, and Lloyd Shapley. 1962. �College Admissions and the Stability of Marriage.�

American Mathematical Monthly, 69(1): 9-15.

9. Mas-Colell A. 1984. "On a Theorem of Schmeidler." JME 13(1984): 201-206

10. L.S. Shapley and H. Scarf, 1974, On Cores and Indivisibility. Journal of Mathematical

Economics 1, 2337

11. Michel Balinski & Tayfun Sönmez. 1998. "A Tale of Two Mechanisms: Student Place-

ment." Journal of Economic Theory 84: 73-94

12. Che , Yeon-Koo and Koh, Youngwoo, Decentralized College Admissions (February 20,

2014)21

21Available at SSRN: http://ssrn.com/abstract=2399743 or http://dx.doi.org/10.2139/ssrn.2399743

LIST OF TABLES 36

List of Tables

1 Table of success rate for students who performed well . . . . . . . . . . . . . . . 17

2 Table of success rate for students who performed poorly . . . . . . . . . . . . . . 17

3 Table of success rate by types of courses . . . . . . . . . . . . . . . . . . . . . . . 18

List of Figures

1 The general activity of the server on January 8th 2014 . . . . . . . . . . . . . . . 19

2 The general activity of the server on January 8th (5sec interval) . . . . . . . . . 20

3 Activity for the tutorial number 55848 . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Activity for the tutorial number 55984 . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Activity for the lecture number 54137 . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Activity for tutorial 59408 with duplicates: . . . . . . . . . . . . . . . . . . . . . 23

7 Activity for the tutorial 59408 without duplicates : . . . . . . . . . . . . . . . . . 23

8 Frequency of time intervals between two requests of the same student: . . . . . . 24

9 Activity of lecture 1 to 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

10 Activity of lecture 5 to 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

11 Activity of lecture 9 to 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

12 Activity of lecture 14 to 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

13 General activity for Paris on Jan 6th . . . . . . . . . . . . . . . . . . . . . . . . . 32

14 General activity for Paris on Jan 7th . . . . . . . . . . . . . . . . . . . . . . . . . 33

15 General activity for Reims region Campus on Jan 8th . . . . . . . . . . . . . . . 34

Documents

The ght for courses: Documenting the Sciences-po's course registration ...econ.sciences-po.fr/...J_P-optimality_of_scpo_course_registration.pdf · The ght for courses: Documenting