DA SS19 Summary of Theory PDF

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01 01##Introduction Introduction## 1. Why#study#“Decision#Analysis”?# Why#study#“Decision#Analysis”?### • •

•

Intuitive#de Intuitive#decision#ma cision#ma cision#making#uses#p king#uses#p king#uses#past#expe ast#expe ast#experience#to#m rience#to#m rience#to#make#de ake#de ake#decisions#quic cisions#quic cisions#quickly# kly#(which#products#to# purchase#at#the#grocery#store,#what#movie#to#watch,#what#to#eat#for#lunch,#etc.)# Unfortun Unfortunately,# ately,# ately,#life# life# life#is#NOT# is#NOT# is#NOT#full# full# full#of#“no of#“no of#“no--bra brainer”#decisions! iner”#decisions! iner”#decisions!#We#often#face#tough# #We#often#face#tough# #We#often#face#tough#and#complex# and#complex# decisions#such# decisions#such#as# as## o changing#careers,#choosing#a#college#or#degree,#buying#a#car#or#house,#investing#for# retirement,#etc.## o hiring,#building#a#new#plant,#expanding#into#new#markets,#downsizing#the#organization,# building#a#new#product#pipeline,#etc.# We#o We#often ften ften#mak #mak #make#“ e#“ e#“bad” bad” bad”#dec #dec #decisi isi isions! ons! ons!###

2. Why#is#decision#making#difficult?# I. Cognitive#biases:#Our$brains$seek$coherence,$unity,$patterns,$sometimes$where$there$is$none;$ suppressing$ambiguity$in$favor$of$a$meaningful$picture.$That’s$what$gives$rise$to$our$cognitive$ biases.#-#Daniel#Kahneman# o Example:#Linda#is#31#years#old,#single,#outspoken,#and#very#bright.#She#majored#in# philosophy.#As#a#student,#she#was#deeply#concerned#with#issues#of#discrimination#and# social#justice,#and#participated#in#anti-nuclear#demonstrations.#Which#of#the#following#is# more#likely?# ¨ Linda#is#a#bank#teller.# ¨ Linda#is#a#bank#teller#and#is#active#in#the#feminist#movement.#

II. • •

III.

Complexity:## Complexity#can#cause#the#decision#maker#to#focus#on#the#wrong#problem#or#decision.## A#complex#decision#problem#is#easier#to#solve#if#the#problem#is#decomposed#into#its#four# decision#components:## I. Objectives#(and#preferences):#What$do$you$want?## II. Alternatives#(Actions):#What$can$you$do?$$ III. Uncertainties:#What$do$you$(not)$know?$# IV. Outcomes:#What$is$the$impact$of$choices$and$uncertain$events$on$objectives?$$ à Decision#Analysis#cannot#make#hard#decisions#easy,#BUT#it#can#help#you#to#manage#complex# decisions.##

Trade-offs#between#conflicting#objectives#

Available#alternatives#rarely#allow#for#improving#one#of#your#objectives#without#deteriorating# at#least#another#one#(e.g.#you#cannot#buy#a#better-quality#product#for#the#same#price)# à What#is#the#relative#importance#of#each#objective?# IV. Uncertain#Outcomes:#no#matter#how#much#time#and#thinking#you#put#into#it,#you#won’t# know#what#the#consequences#will#be#until#after#you#decide.# à Decision#Analysis#cannot#help#you#to#know#what#will#happen,#BUT#it#can#help#you#to# increase#the#odds#of#making#a#good#decision.# •

3. What#makes#a#good#decision?# requires#a#thorough#understanding#and#careful#thinking#of#the#decision#problem.# can#have#a#bad#outcome#and#vice#versa,#but#it#leads#to#better#outcomes#(on#average)#in#the# long#run.# • Two#criteria#for#a#good#decision#process:## I. 1.#Procedural#rationality# à the#procedure#that#leads#to#the#final#decision#can#be#more#or#less#rational# • •

I. tackle#the#right#problem# II. put#the#appropriate#level#of#effort#in#information#search# III. derive#proper#expectations#using#relevant#objective#data# IV. think#carefully#about#your#objectives#and#preferences# II. Rational#preferences# à refers#to#the#consistency#of#assumptions#in#the#decision#scenario# I. Prospective#orientation:#Decisions#should#be#forward#looking#(i.e.#depend#on#future# outcomes).#Therefore,#sunk#costs#should#be#ignored.# II. Transitivity:#If#a#is#better#than#b#and#b#is#better#than#c,#then#a#should#be#better#than#c.# III. Independence#of#irrelevant#alternatives:#Given#the#set#of#alternatives#{a,#b},#if#a#is# better#than#b,#then#for#the#set#{a,#b,#c},#a#should#still#be#preferred#over#b.# IV. Invariance:#Preferences#should#not#be#affected#when#the#same#problem#is#presented# in#a#different#way.# 4. Why#is#it#important#to#characterize#a#good#decision?# # Intuition#is#difficult#to#audit#for#completeness#and#quality#of#thought# à Long-term#decisions#with#important#consequences#should#be#based#on#a#systematic#and#indepth#evaluation.# 5. Solving#complex#decision#problem #

## • Objecti Objectives# ves#(and#preferences):#What$do$you$want?$$ à the#statement#of#a#desired#achievement# à Necessa Necessary ry#bc.# o find#and#generate#new#alternatives# o identify#the#relevant#environmental#influences#(e.g.#uncertainties)# o make#a#sensible#choice#between#alternatives# # à Wher Where#to e#to e#to#fi #fi #find# nd# nd#obje obje objecti cti ctives ves ves## I. Obvious#insufficiencies:#Look#for#things#that#you#are#currently#not#happy#with.## II. Comparison#of#alternatives:#Differences#between#alternatives#might#help#you#to#realize# what#is#important#to#you.## III. Strategic#goals:#Some#objectives#are#not#directly#linked#to#your#current#decision#but#are#of# overall#interest#(e.g.#company#reputation).## IV. External#guidelines:#Guidelines#and#constraints#(such#as#budget#constraints)#should# indicate#an#important#objective#(e.g.#minimizing#costs).## V. Impact#on#other#people:#Consider#the#objectives#of#other#people#(such#as#family,# shareholders,#employees,#etc.)#who#might#be#affected#by#the#consequences#of#your# decision.## à Fundamental#vs.#means#objectives Fundamental#vs.#means#objectives## Fundamental#objectives## Means Means#obj #obj #objecti ecti ectives# ves## #

To#move:##

Downward#in#hierarchy.##

Away#from#fundamental#objectives.##

Ask:##

What$do$we$mean$by$that?$#

How$can$we$achieve$this?$#

To#move:## Ask:##

Upward#in#hierarchy.## Of$what$more$general$objective$is$ this$an$aspect?$#

Towards#fundamental#objectives.## Why$is$this$important?$#

Fundamental#objectives:#considered#to#be#relevant#for#their#own#sake,#i.e.#without# requiring#any#further#justification.# à Example:#vehicle#injury:#Maximize#public#safety,#Minimize#loss#of#life,#Minimize#serious# injuries,#Minimize#minor#injuries## o means#objectives:#considered#to#be#relevant,#because#they#help#to#achieve#a#more# fundamental#objective.# à Example:#Educate#public,#More#traffic#lights,#Enforce#traffic#laws# Objectives# ives# ives#hierar hierar hierarchy chy:#diagram#of#relationships#between#objectives,#sub-objectives,#and# à Object attributes.# à REMARK:#All#objectives#in#a#hierarchy#should#be#fundamental!#The#system#should#not# contain#objectives#that#gain#relevance#only#by#having#an#assumed#impact#on#other# objectives#in#the#same#system#of#objectives# o most#general#objective#located#at#the#top#of#the#hierarchy# o higher#levels#=#more#general#objectives,#vaguely#stated# o Lower#levels#=#more#specific#statements#regarding#desirable#characteristics#of# alternatives# o lowest#levels#=#attributes#based#on#which#the#alternatives#will#be#compared#(therefore# they#are#measurable).# o Attributes/#measures#used#to#characterize#performance#in#relation#to#an#objective# à Criteri Criteria#for#dete a#for#dete a#for#determinin rminin rmining#the#appropriateness g#the#appropriateness g#the#appropriateness#of#objectives #of#objectives## I. Completeness:#All#fundamental#objectives#are#included# II. Simplicity:#A#small#set#of#fundamental#objectives#is#easier#to#communicate#and# requires#fewer#resources#to#estimate#the#performance#of#alternatives# III. No#redundancies:#Avoid#double#counting#or#overlapping#objectives# IV. Preference#independence:#Preferences#with#respect#to#the#attribute#levels#of#a#subset# of#objectives#should#be#independent#of#the#attribute#levels#of#the#remaining# objectives# V. Measurability:#The#achievement#of#objectives#should#be#accurately#measurable#(i.e.# there#is#an#attribute#for#each)$# 6. Attributes: #unambiguous#ratings#of#how#well#alternatives#do#with#respect#to#each#objective;#can# be#qualitative#or#quantitative# à Useful#for:# • describing#the#consequences#of#alternatives# • making#value#tradeoffs#between#objectives# à Good#attributes#(Keeney#and#Gregory#(2005))# I. Direct:#“number#of#fatalities”#versus#“number#of#accidents"# II. Operational:#low#cost#of#information#collection# III. Comprehensive:#attribute#levels#cover#the#full#range#of#possible#consequences#of#the# objective#(e.g.#attribute#“number#of#fatal#heart#attacks”#for#the#objective#“to#minimize# detrimental#health#effects#from#carbon#monoxide",#how#about#nonfatal#heart#attacks?)# IV. Understandable:#units#should#make#sense#to#the#decision#maker#(e.g.#miles#per#gallon#vs# liters#per#km)# V. Unambiguous:#we#should#all#have#the#same#interpretation#of#the#same#attribute#level#(e.g.# number#of#stars#on#Google)# o

à Types# I. Natural:#is#in#general#use#with#a#common#interpretation#by#everyone# o Cost,#Profit#or#NPV#(dollars)# o Weight#(grams,#tons#and#pounds)# o Time#(seconds,#minutes,#hours,#days# II. Zero#or#One#Measures:#describe#whether#the#alternatives#have#a#specific#attribute#or#not# o Vehicle#has#ABS#brakes#or#not# o High#school#diploma# o Technology#is#computer#controlled#or#not# III. Constructed#Measure:#is#developed#for#a#particular#decision#problem# o A#descriptive#phrase#is#attached#to#each#attribute#level#(e.g.#a#five-point#scale#to# measure#ease#of#use#in#the#case#of#a#personal#computer)# o Group#natural#attributes#to#obtain#discrete#attributes#when#the#natural#attribute#is#too# specific.#

7. Prescriptive#vs#Descriptive#decision#theory Prescriptive#vs#Descriptive#decision#theory## à Goal#of#both:#help#us#make#better,#more#“rational”#decisions.# • Prescriptive#decision#theory#aims#to#teach#you#the#methods#and#concepts#that#support#and# improve#rational#decision#making# à decompose#the#decision#problem## à reduction#of#complexity#for# à structured#analysis.# • Descript Descriptive ive#decision#theory#aims#to#raise#your#consciousness#about#decision-making#by# pointing#out#the#errors#and#biases#in#it# à description#of#a#real,#observed#decision#making#process# à decision#making#process#can#be#either#good#or#bad.

02#Making#Decisions# 02#Making#Decisions#with#Multiple#Object with#Multiple#Object with#Multiple#Objectives#under#Certaint ives#under#Certaint ives#under#Certaintyy(MAVT (MAVT))# 1. MAVT#considers#problems#that#fulfill#the#following#assumptions:# •

•

Rational#preferences# o Complete#(the#decision#maker#has#a#preference#for#any#pair#of#alternatives)# o Transitive#(If#a#is#better#than#b#and#b#is#better#than#c,#then#a#should#be#better#than#c)# No#uncertainty#about#the#outcome#of#each#alternative# Multiple#(conflicting)#objectives##

• 2. What#are#conflicting#objectives?#

No#dominance#relationship#between#alternatives# Trade-offs#between#objectives# Attributes#must#be#combined#into#single#index#to#compare#desirabilities#of#alternatives# 3. How How#to#solve#decision#problems#under#certainty? #to#solve#decision#problems#under#certainty? # I. Determine Determine## • the#fundamental#objectives# • how#to#measure#the#achievement#of#these#objectives#(attributes)# • the#set#of#alternatives#that#might#achieve#these#goals# à Example:#Car#choice# o Ultimate#objective:#Best#car# o Lower-level#fundamental#objectives:#Minimize#price#and#maximize#life#span#Attributes:# Price#(attribute#1)#and#Life#span#(attribute#2)# o Alternatives:#Model#a,#Model#b,#Model#c## Apply#the# Mult II. Multii-Attri Attribute bute bute##ValueThe ValueTheory ory ory##(MAVT) (MAVT)## • Assign#value#scores#to#each#attribute#level#for#all#alternatives# • Determine#the#weight#(the#relative#importance)#of#each#attribute# • Rank#all#alternatives#according#to#weighted-average#total#score# à Example:#Car#choice# o Ultimate#objective:#Best#car# o Lower-level#fundamental#objectives:#Minimize#price#and#maximize#life#span# o Attributes:#Price#(attribute#1)#and#Life#span#(attribute#2)# o Alternatives:#Model#a,#Model#b,#Model#c# ¨ Alternatives:#𝑎 = (𝑎$ , 𝑎& ),#𝑏 = (𝑏$ , 𝑏& ),#𝑐 = (𝑐$ , 𝑐& )# ¨ Attribute#value#functions:#𝜐$ #and#𝜐& #(subjective#value#scores)# ¨ Overall#value#of#alternative#a:#𝑉 𝑎 = 𝑓(𝜐- 𝑎- )# ¨ Aggregate#with#additive#value#function:## #𝑉 𝑎 = 0-1$ 𝜔- ∙ 𝜐- 𝑎- = 𝜔$ ∙ 𝜐$ 𝑎$ + ⋯ + 𝜔0 ∙ 𝜐0 𝑎0 # à :#𝑉 𝑎 :#value#of#alternative#𝑎# à 𝜔4 :#weight#for#attribute#𝑖# à 𝜐4 𝑎4 :#value#of#attribute#𝑖## 4. When#is#it#safe#to#assume#an#additive#multiWhen#is#it#safe#to#assume#an#additive#multi-attribute#value#functio attribute#value#functio attribute#value#function? n? # mutual#pr l#pr l#prefer efer eferenti enti ential# al# al#indep indep independen enden endence ce#of#attributes#𝑥$ ,#𝑥0 #(each#possible#subset#of#attributes#is# • If#mutua preferential#independent#of#the#complementary#set)#then# à preferences#can#be#represented#by#an#additive# ordina l#value#function.# • If#additive#diff additive#difference# erence# erence#indep indep independen enden endence ce#(preferences#over#transitions#between#attribute#levels#of#a# particular#attribute#should#not#depend#on#the#level#of#other#attributes) # is#satisfied,#then# à preferences#can#be#represented#by#an#additive #cardinal#value#function## • • •

Simple#preferential# Simple#preferential#independe independe independence nce:#preferences#over#attribute#levels#of#a#parti-#cular#attribute# should#not#depend#on#the#level#of#other#attributes## 8. Ordina Ordinal#vs. l#vs. l#vs.#Cardi #Cardi #Cardinal#V nal#V nal#Value#f alue#f alue#functi uncti unctions: ons:# • Ordinal:## BMW#≻#Audi#⇔#v(BMW)#>#v(Audi)# • Cardinal#(the#value#differences#reflect#preferences#over#transitions):# if#v(Audi)#=#0.5,#v(BM#W#)#=#0.7,#v(M#ercedes)#=#0.8,#then:##Audi#→#BMW#≻#BMW#→# Mercedes# 9. What#if#preferences#are#not#independent? # • Cannot#use#additive#value#functions!# • Try#to#redefine#attributes#in#order#to#eliminate#existing#dependencies# • If#not,#use#a#non-additive#value#function:# V#(a)#=#w1v1(a1)#+#w2v2(a2)#+#kw1w2v1(a1)v2(a2)## ###########quality#of#life#duration# o The#last#term#captures#the#interaction#between#the#attributes# o If#k#is#positive,#then#the#two#attributes#complement#each#other# o If#k#is#negative,#then#the#two#attributes#are#substitutes.# à Complex# à Permits#interactions#across#many#attributes# 10. Attribute#Value#functions# (convert#attribute#levels#into#levels#of#desirability,#worth,#utility)# • Methods#for#determining#attribute#value#functions# I. Direct#rating#method:#directly#assign#values#to#the#attribute#levels# II. Bi-section#method#(mid-value#splitting#technique):#find#the#attribute#level#whose#value#is# halfway#between#the#most#and#the#least#preferred#attribute#level# III. Difference#standard#sequence#technique#(DSST):#find#the#attribute#levels#x0#,#x1#,#...,#xn#,# such#that#the#increments#in#the#strength#of#preference#from#xi#to#xi+1#are#equal#for#all#i#=# 0,#...,#n#−#1# • Assumptions:# o Preferences#are#rational# o Value#functions#are#cardinal#(value#differences#reflect#preferences#over#transitions)# o (Attribute#values#are#continuous)# o (Monotonically#increasing#(or#decreasing)#value#functions# • What#if#the#“assumptions”#do#not#hold?# o What#if#attribute#values#are#discrete?# ¨ Bisection#method#and#DSST#cannot#be#used# ¨ Use#the#direct#method# o What#if#the#value#functions#are#non-monotonic?# ¨ Split#the#objective#into#monotonic#lower-level#objectives# ¨ Or#split#the#interval#into#subintervals#on#which#the#value#function#is# monotonically#increasing#or#decreasing.#Then,#apply#the#value#function# elicitation#methods#separately#on#both#intervals

•

03#Weights 03#Weights## 1. Weights # • •

Interpretation# withi within n #an#attribute:#reflect#the#additional#value#generated#by#increasing#the# attribute#from#its#least-preferred#to#the#most-preferred#level# Interpretation# between#attributes:#relate#the#valuations#of#different#attributes#to#each#other#

2. Methods#to#determine#weights# I.

Swing#method:# à does#not#require#the#knowledge#of#attribute#value#functions#(i.e.#involves#the#best#and#the# worst#attribute#levels#only)# o Generate#artificial#alternatives#𝑏4 #(𝑖 =#number#of#alternatives)#by#setting#each#of#the# attributes#to#its#highest#level#and#leaving#all#other#attributes#at#their#lowest#levels,# generate#worst#alternative#𝑎 7 #by#setting#each#attribute#to#its#lowest#level# o DM#assigns#values/#points#𝑡4 #to#each#artificial#alternative#(𝑏4 #and#𝑎 7 )#between#0#and#100# o

Then#𝑤: =

;< > ; =?@ =

#for#any#𝑗 = 1, … , 𝑖, . . 𝑚#

à Only#difference#between#weights#and#points#is#that#the#weights#are#normalized# Trade-off#method:# à requires#the#knowledge#of#attribute#value#functions# à problematic#if#the#attribute#levels#are#discrete# o The#DM#is#willing#to#trade#an#additional#levels#of#one#attribute#against#less#levels#of# another#attribute# o Pairwise#comparisons,#where#trade-offs#concern#only#2#attributes#at#a#time# o Number#of#indifference#statements#=#number#of#attributes#-#1# Direct-ratio#method:# à a#widely-used#method#but#unreliable#

II.

III.

3. Trade Trade-off#vs.#Swing#method# -off#vs.#Swing#method# •

•

Swing#method# o Point#assignments# o Simpler# o No#value#function#needed# o No#problems#with#discrete#attributes# o Does#not#allow#for#consistency#check#within#method# Trade-off#method# o Preference-based# o More#complicated# o Attribute#value#function#needed# o Discrete#attributes#are#problematic# o Consistency#check#within#method#possible#

4. Why#direct#ratio#method#is#unreliable# • DM#are#not#aware#that#weights#have#to#add#up#to#1 # •

•

tries#to#derive#weights#from#general#statements#about#the#importance#of#attributes#without# considering#their#range# à incredible#results# decision#makers#do#not#sufficiently#adjust#their#importance#statements#in#direct#ratio#method# even#if#the#assumed#intervals#were#made#transparent# à meaning#of#attribute#weights#is#unclear#to#the#decision#makers#

5. Fischer#Experiment#1995#

• • •

45#undergraduate#students#divided#into#two#groups#(Scenario#1#and#2)## Scenario#1#and#2#have#the#same#range#regarding#the#attribute#“Starting#salary”#but#differ#in#the# range#of#the#attribute#“Vacation#days”#(high#range#in#scenario#1#and#low#range#in#scenario#2)# Asked#to#weight#the#attributes#Vacation$days#and#Starting$Salary:#

## Subjects#were#clearly#asked#to#consider#attribute#ranges# Findings# à students#were#unaware#of#the#theoretical#connection#between#attribute#ranges#and#the# magnitudes#of#attribute#weights# à With#the#direct-ratio#method,#the#difference#between#the#high-range#weight#and#lowrange#weight#is#very#small# à The#trade-off#method#leads#to#a#much#larger#difference#between#the#high-range#weight# and#the#low#range#weight# à The#range#sensitivity#increases#a#lot#for#the#trade-off#method# • Range#effect:# o Dependence#of#decision#weights#on#attribute#range# o If#the#attribute#range#changes,#the#decision#weights#have#to#change# o The#greater#the#range#of#outcomes#for#attribute#X,#the#greater#the#weight#for#attribute#X# should#be.#(Otherwise,#we#might#get#inconsistent#preference#statements)# o Experiments#show#that#decision#makers#do#not#sufficiently#adjust#their#importance# statements#in#direct#ratio#method#even#if#the#assumed#intervals#were#made#transparent# →#this#indicates#that#the#meaning#of#attribute#weights#is#unclear#to#the#decision#maker# 6. The#Splitting#Bias# • Detail#of#attribute#specification#enhances#attribute#weights# • Overweighting#of#detailed#objectives#exists#independent#of#which#upper-level#objective#is# being#detailed# • Bias#exists#for#several#weighting#techniques,#but#less#pronounced#for#techniques#that#are# based#on#holistic#procedures#that#focus#attention#on#concrete#trade-offs# à Example#(Pöyhönen#and#Hämäläinen,#2000)# o The#students#were#first#asked#to#give#weights#for#all#the#individual#attributes#separately# and#then#weight#combinations#of#attributes#at#the#higher#level.# o The#weight#of#the#attribute#at#the#higher#level#is#compared#with#the#sum#of#the#weights# of#the#divided#attributes#below#it. • •

04#Incomplete#Informati 04#Incomplete#Information on on## 1. How#can#you#...