BPS May112005presentation1

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Recommendation to ImplementA New BPS Assignment Algorithm

Boston School Committee

May 11, 2005

BPS Strategic Planning TeamContact: Carleton W. Jones, carljones!oston."12.ma.#s
mailto:[email protected]:[email protected]


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Contents

$. $m%et#s &or '(al#ating C#rrent BPS )ssignment

Mechanism * The +Boston Mechanism

$$. -e(ie o& /cto!er 200 +)lgorithm 101Presentation to School Committee

$$$. -e%ort on Preliminary inings o& BPS Choice

3ata St#y $4. -ecommenation to $m%lement e )lgorithm

4. e6t Ste%s


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I. Why Evaluate the Boston echanism!

This is one %art o& a larger re(ie to achie(e a higher

le(el o& %arental satis&actionan trans%arencyin the

o#tcomes o& the st#ent assignment %rocess.

$n res%onse to or" one !y a team o& 'conomic'ngineers on st#ent matching mechanisms:

* )tila )!#l"airo7l#, Ph.3., Pro&essor, Col#m!ia 8ni(ersity

* Parag ). Patha", Ph.3. Caniate, 9ar(ar 8ni(ersity

* )l(in '. -oth, Ph.3., Pro&essor, 9ar(ar 8ni(ersity* Tayn Snme;, Ph.3., Pro&essor,


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II. "cto#er $%%& 'Algorithm (%() Presentation to School Committee

What is an )lgorithm?


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What Is an Algorithm!

)n algorithm is +a set o& orere ste%s &or SOLVING APROBLEM, s#ch as a mathematical &orm#la

or the instr#ctions in a %rogram.

*Computer Desktop Encyclopedi! " #$%%&'(()! Computer Ln*u*e Compny! Inc.

$n o#r case, thepro+lemis to assign st#ents to schools,hile:

* -es%ecting each st#ent@s P-''-'C'S

* )hering to each school@s P-$/-$T$'S

* Ma"ing s#re that each school is &ille to its %ro%er ca%acity

/#r solution: The Boston )ssignment Mechanism AA thecom%#ter %rogram that act#ally im%lements assignment %olicy.


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Estella*s +rue Pre,erences

(stchoice- urphy

$nd

choice- Channing

rdchoice- Per/ins

Estella

0ere are the schools that Estella really wants-


8/408 Estella*s Priorities

C0"ICE SIB1IN2 WA13 RAN4"5

6RP07 ( N" N" 8

C0ANNIN2 $ 7ES N" 8

PER3INS N" 7ES 8

0ere are the PRI"RI+IES Estella has at each school-


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0ow the BPS Currently Assigns Students1stChoice 2nChoice >r Choice

Si!AWal"

Si!

Wal"

o Priority

)s

s%ace is

a(aila!le

)s

s%ace is

a(aila!le

Si!AWal"

Si!

Wal"

o Priority

Si!AWal"

Si!

Wal"

o Priority

Within each category, st#ents are orere !y their ranom n#m!ers


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Where Estella*s Priorities Position 0er,or the 6RP07 39: School1stChoice

Si!AWal"

Si!

Wal"

None

St#ents in >

%riority categories

are ahea o&

'stella

Seats ill !e &ille

!y st#ents in >

categories !e&ore

reaching 'stella

Estella

The

school

may !e

&ille !y

this %oint


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0ow it 1oo/s ,or Estella at Each School

1stChoice 2nChoice >r Choice

Si!AWal"

Si!

Wal"

one

Si!AWal"

Si!

Wal"

one

M8-P9 C9)$D P'-


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Estella*s Perceived Chances

9ere is hat 'stella@s &amily !elie(es are her

chances o& getting each school i& they ma"e it

their &irst choice:

Chance Beca#se?

Channing Best chance Si#ling priority.edium Popularity.

Per/ins Doo chance +hey live in thewal/ ;one.

Not


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Estella*s =amily Strategi;es

(stchoice- urphyChanning

$ndchoice- Channing

urphy

rdchoice- Per/ins

9ere is ho 'stella@s &amily reorders their choicesto

ens#re the !est o#tcome gi(en 'stella@s %re&erences an

%riorities:


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+he Pro#lems With the BPS System

The c#rrent %rocess &orces &amilies to ST-)T'D$F'.

Strategi;ing is im%er&ect !eca#se &amilies on@t "no:

* hat their ranom n#m!er ill !e.

* hat schools other &amilies are choosing.* ho many others they@re com%eting ith.

)ssignment !ecomes a highAsta"es gam!le&or &amilies.

8nermines &amilies@ tr#st in the BPS system.

amilies sho#l not ha(e to sacri&ice their tr#e %re&erences.

amilies sho#l !e a!le to !e &orthright a!o#t their choices.

The system, not &amilies, sho#l com%ensate &or mismatches !eteen%re&erences an %riorities.


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0ow It 1oo/s Now ,or Estella at Each School

1stChoice 2nChoice >r Choice

M8-P9C9)$D P'-


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Alternatives to Current echanism

To alternati(es that eliminate the nee &or strategi;ing are:

* The Gale -Shapley Deferred Acceptance Mechanism

* The Top-Trading Cycles Mechanism

The BPS has !een or"ing ith a team o& economists ho are e6%ertson these alternati(es

These economists are hel%ing the BPS e6%lore the %otential !ene&its o&sitching to one o& these alternati(es


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+he 2ale9Shapley ethod

Si#ling9Wal/ Si#ling Wal/

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

No Priority


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Estella With 2ale9Shapley ethod

Si#ling9Wal/ Si#ling Wal/

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

1stchoice

2nchoice

>rchoice

thchoice

No Priority

C0ANNIN2

PER3INS

6RP07


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2ale9Shapley ethod

/rers st#ents !y %riorities an !y choices, itho#t iscaring

) choices or %riorities

8ses $T'-)T$4' metho A searches !ac" an &orth to %#t eachst#ent into T/PAM/ST choice itho#t sacri&icing the %riorities o&

other st#ents

)llos st#ents to choose their Tr#e Pre&erencesitho#t

%otentially !eing %enali;e !y selecting a highly chosen school astheir &irst choice


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2ale9Shapley ethod Pros > Cons

Consiers all%riorities an

%re&erencesthro#gho#t thehole assignment%rocess

'liminates the nee&or &amilies tostrategi;e

Consiers %riorities more

strongly than 1st choices

$s not &oc#se on %ro(iing the highest %ercentage o& 1stchoices

P-/: C/:


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Estella With +op +rading Cycles ethod

M8-P9 G1st

H

C0ANNIN2

Estella =ran/

Priorities > Positions

Will Be +raded

'stella has a %riority to the C9)$D, hich ran"

ants, an ran" has a %riority to the M8-P9, hich

'stella ants, so the system lets them T-)3'. o

each gets a seat at their 1stchoice school

P'-


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+op +rading Cycles

Starts ith the highest %riority st#ents at the schools.St#ents either "ee% the seat i& it@s at their to% choiceschool, or trae it.

St#ents ho ant to trae %riorities are alloe to oso. This means that, hen to st#ents ant schoolsthat the other has the higher %riority &or, they can traetheir %riorities ith each other in e6change &or a seat in

each otherIs schools.

)llos st#ents to choose their Tr#e Pre&erencesitho#t %otentially !eing %enali;e !y selecting a highlychosen school as their &irst choice.


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+op +rading Cycles Pros > Cons

)llos st#ents to trae

%riorities &or to% choice

seats

'liminates the nee &or

&amilies to strategi;e

Can ha(e the e&&ect o& +il#ting %riorities@ im%acts, i& %riorities

are to !e +one !y the istrict, as o%%ose to !eing +one !y %arents

Co#l lea to &amilies !elie(ing they can strategi;e !y listing a schoolthey on@t ant in

ho%es o& a trae.

P-/: C/:


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Comparison Between BPS? 29S and ++C

RewardsStrate9gi;ing!

0olds@Place in1ine*!

Strongest4river-

Rewards+rue

Choices!

BPS 7ES N" =IRS+

C0"ICE

N"+

A1WA7S

2ale9Shapley

N" 7ES PRI"RI+IESAN7 C0"ICE

7ES

+op+radingCycles

N" 7ES +"PC0"ICES+RA4IN2

7ES


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III. Report on Preliminary =indings o, BPS Choice 4ata Study

$n )%ril 2005, o#r team o& economists

%resente a %reliminary re%ort o& &inings &rom

their st#y o& the %otential im%act o& changing

the BPS st#ent assignment algorithm &rom a

%riority matchingalgorithm to one o& the to

%ro%ose strategyA%roo&algorithms.

The economists ran the three algorithms,

!ase on the act#al school choices mae !y

BPS %arents &rom 1A200>


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Summary ", 3ey =indings

1. The analysis o& choice ata &rom S1A200> inicate that:

* Many &amilies tke t,e risko& choosing an o(erAemane school intoacco#nt hen ma"ing school selections.

* Many &amilies mitigate that ris" !y selecting a -s.ety/ sc,oolas theirsecon choice.

* Many &amilies ho o not aeK#ately ta"e this ris" into acco#nt recei(e0orse ssi*nmentsthan they otherise co#l ha(e.

2. The ao%tion o& a strategyA%roo&algorithm, hen holing c#rrent choice%atterns constant, oes not signi&icantly change the o#tcome o& the assignment%rocess hile remo(ing the ris"o& ran"ing schools in sim%le orer o&%re&erence.

>. )o%ting a strategyA%roo& algorithm o#l:

* 'liminate the nee &or %arents to +strategi;e in ran"ing school %re&erencesAA alloing %arents to ran" schools in orer o& tr#e %re&erences itho#tha(ing to consier the %o%#larity o& the esire school

* 3iminish the harm one to %arents ho o not strategi;e or o so ell.


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6nder Each Algorithm? Still & or 0igher o,

Students Receive +heir =irst Choice School

80%

79%

77% 77%

75%

74%

78%

75%75%

%

$

&

D

:

:%

2rade 3$ 2rade D 2rade

Current

2ale9Shapley

+op +rading

6sing Actual BPS Choices FS7%(9%$G


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So Why Change!

A Comparison o, the +hree Algorithms The %ercentage o& st#ents recei(ing their L&irst choice@ #sing the

Boston Mechanism is o(erstate, as com%are to the to

alternate mechanisms.

* $nitial e(ience an theory s#ggests !eca#se o& some le(el o&strategi;ing, c#rrently st#ents re only recei(ing a high

%ercentage o& their state&irst choices.

* St#ents re notrecei(ing a high %ercentage o& their tr#e &irst

choices. Gi.e. +here they rather go (s. +here they thin" they

can get in.H

This e&iciency ill !e com%letely remo(e #ner a strategyA%roo&

algorithm as it res%ons to a st#ent@s tr#e choices, an not their

strategi;e choices.


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A Smaller Percentage ", "ver9demanded SchoolsAre Ran/ed As Second And +hird Choices

&:.. $D

8$DB B&

%

(%

$%

.%

&%

8%

D%

B%

:%

E%

(%%

(st Choice $nd Choice .rd Choice

"therHH

"ver9demandedH

Base on %re(io#s year@s choice &ig#res. @/ther@ incl#es times hen no 2nor >rchoice is mae.

Drae


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Eample- 1yndon Receives =ar =ewer $ndand 0igherChoices +han (stChoices? Compared to +rotter

(8(

&8.%

(( :

.& .($&

(% B

%

$%

&%

D%

:%

(%%($%

(&%

(D%

(st

Choice

$nd

Choice

.rd

Choice

&th

Choice

8th

Choice

1yndon

+rotter

Seat Ca%acity: ynon N 50 Seats, Trotter N 51

Drae rChoices

more e(enly

istri!#te at

Trotter


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Current Situation- =irst Choice? =irst Served

The Boston Mechanism loo"s at e(eryone@s &irst choice

school &irst, an assigns !ase on %riorities an

ranom n#m!ers.

$& a st#ent is notassigne #ring the &irst %ass, they

&ace the li"elihoo o& ha(ing their 2n2, >r2an e(en th

choice schools &ille i& the &amily selects o(erAemane schools that other@s ha(e mae their &irst

choice.


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6nder +he Current Algorithm? Parents

Who Are 'Ris/ +a/ers) ",ten Su,,er -o#ghly 5O o& st#ents ho recei(e their thir choice or loero#l

ha(e !ene&ite &rom remo(ing an o(erAemane school as their to%choice.

'6am%le: ) %arent mae the &olloing choices:1. o#ng )chie(ers...G/(erAemane, ith limite n#m!er o& seatsH

2. Timilty

>. 9ar!or

. McCormac"

5. een!erg.G)ssigne SchoolH

Beca#se o& an a(erage lottery n#m!er, this st#ent as not assigne too#ng )chie(ers, !#t instea as assigne to the 5 thchoice school, theeen!erg.


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+his 'Ris/ +a/er) Could 0ave 4one Better

$n o#r e6am%le, i& the %arent ha remo(e o#ng )chie(ers as a

&irst choice an mo(e #% all other choices, the same lottery

n#m!er o#l ha(e sec#re a s%ot in the Timilty.

The %arent o#l ha(e gotten the Timilty:

1. Timilty.Goriginally, the n#m!er 2 choiceH

2. 9ar!or

>. McCormac"

. een!erg


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Anticipated "utcomes o, an Algorithm Change-

1. The ao%tion o& a strategyA%roo& algorithm GDaleASha%ley 3e&erre )cce%tance Mechanism or the To%Traing Cycles MechanismH ill ta"e the highAsta"es

gam!leo#t o& the assignment %rocess.2. Since a strategyA%roo& algorithm eliminates the nee

&or strategi;ing, %arents ill no longer !eisco#rage &rom %#tting a more %o%#lar school as

their &irst choice. Selection ha!its ill change, an&eer st#ents are e6%ecte recei(e their &irst choiceschool i& more %eo%le are (ying &or seats in o(erAemane schools.


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Anticipated "utcomes o, an Algorithm Change-

>. The n#m!er o& school choices mae !y &amilies is

li"ely to increase, as %arents ill !e more incline to

list llschools they are intereste in, not j#st those

to hich they are more li"ely to gain amittance.

. BPS ill ha(e to e&&ecti(ely in&orm &amilies o& the

algorithm change an acti(ely enco#rage them to

choose &rom eight to ten schools Gat the elementary

le(elH on their a%%lication &orms.

5. ) &amily s#!mitting a short list o& highly chosen

schools ill ramatically increase their chances o&

recei(ing an aministrati(e assignment.


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Conclusion

The c#rrent BPS assignment algorithm ma"es it ris"y &or %arentsto ran" an o(erAemane school &irst, #nless they ha(e a high%riority at that school.

) StrategyAProo& )lgorithm:* -emo(es the ris" &rom ran"ing schools in orer o& tr#e %re&erence.

* 'liminates the nee &or strategi;ing.

* )s +trans%arencyan clarity to the assignment %rocess, !yalloing &or clear an straight &orar a(ice to %arents regaringho to ran" schools.

* +e(els the %laying &iel!y iminishing the harm one to %arentsho o not strategi;e or o not strategi;e ell.


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I


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Why Not+op +rading Cycles!

The To% Traing Cycles )lgorithm allos st#ents to trae their

%riority&or a seat at a school ith another st#ent. This traing

shi&ts the em%hasis onto the %riorities an aay &rom the goals BPS

is trying to achie(e !y granting these %riorities in the &irst %lace.

This traing o& %riorities co#l lea &amilies to !elie(e they can still

!ene&it &rom strategi;ing, as they may !e enco#rage to ran"

schools to hich they ha(e %riority, e(en i& they o#l not ha(e %#t

it on the &orm i& the o%%ort#nity &or traing i not e6ist.

The !ehin the scenes mechani;e traing ma"es the st#ent

assignment %rocess less trans%arent.


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