Second+third classes: Extension Irit Talmor (Ph.D) lritt@wgalil.ac.il Reminder... Operations the application of science Research W to decision-making WWII - the Battle of Britain One vs. many criteria i ft F* fx Possible solutions ti J * 2 Ideal vs. compromise decision Objective vs. subjective solution mu MCDA (or MCDM) criteria decision analysis (making) MCDA Concept Required decision alternatives ives t Model: - evaluate/weigh - ranking calculation Decision (chosen alternative) Please note: The preliminary stage is the most complicated part in this approach Structure of class MCDA - real-world case (using statistical data) AHP (technique) (using subjective preferences) Workshop Using MCDA for allocating budget of a political campaign Background (1) Israeli government system ■ A parliamentary democracy with a multi-party system. ■ Three branches: legislative, executive, judiciary ■ Designed to ensure a separation of powers, accountability, and representation of diverse political viewpoints, including minorities. ■ The legislative branch is vested in the unicameral parliament, the Knesset. Background (2) Israeli electoral system nationwide proportional representation A barrier: threshold requirement: i%-»i.5% -> 2% -> 3.25% State's funding: depends on achievements. Background (3) The pre-elections political campaign of a new party vs. marketing campaign for a new commercial product huge efforts 11 Background (4) large, established party small, new party Has a steady core of loyal voters who always vote for it X can present proof of tangible results to actual and potential constituents X has a steady federal budget to support its activities X It is critical for a new party's advertising campaign to be precise and targeted. Achieving this goal is not a simple task... Frame 40 parties competed in Israel's 2019 election 29 of them were new "Zehut" ("Z") was one of them Although "Z" was unknown and resource-poor at the beginning of the campaign, its strategic team was determined to maximize the party's achievements in the elections Decision required How can Z's physical advertising resources be allocated among localities? MCDA may help... Steps of the MCDA process Ncwparty Election cam pa fgn Ihlmk how to airetait rB-s ources for phytic a I •dvertitinp; among locality? Integrated MCDA Process Filtering localities (Pareto principle) Deciding on the criteria for comparing the localities Step 3 Assigning weights to each of the criteria I confidential Input data Step 4 Public input data Calculating the nominal and normalized scores of these criteria, for each locality. Step 5 14N Arriving at a single final score for each locality To get the ranking list Central Elections Committee Step 1 Filtering localities (Pareto principle) Total Number of voters In locality localities Total Number of voters (app.) r 250K Educated > Earn an average income. > Emigrated from the former Soviet Union Other attributes were not found to be meaningful in this context (-> Decisions about the slogans and campaign topics) Step 3 Assigning weights to each of the criteria To avoid biased judgment we set the weights in two stages: > Stage 1: ranking the criteria qualitatively > Stage 2: choosing 3 simple and easy to understand weighting techniques according to Barron & Barrett (1996): ❖ Equal weights (EW) 25%, 25%, 25%, 25% ❖ Arithmetic sequence weights (ASW) 40%, 30%, 20%, 10% ❖ Rank-order centroid (ROC) 52%, 27%, 14%, 6% Barron, R, & Barrett, B. (1996). Decision Quality Using Ranked Attribute Weights. Management Science, 42(11):1515-1523. Step 3 Assigning weights to each of the criteria To avoid biased judgment we set the weights in two stages: > Stage 1: ranking the criteria qualitatively > Stage 2: choosing 3 simple and easy to understand weighting techniques according to Barron & Barrett (1996): ❖ Equal weights (EW) 25%, 25%, 25%, 25% W; = — 3 N ❖ Arithmetic sequence weights (ASW) N-j + 1 _2(N-j + l) N(N + 1) 40%, 30%, 20%, 10% Wj = ❖ Rank-order centroid (ROC) N 1V1 52%, 27%, 14%, 6% k=j Barron, R, & Barrett, B. (1996). Decision Quality Using Ranked Attribute Weights. Management Science, 42(11):1515-1523. Step 3 Assigning weights to each of the criteria # Criterion Definition Equa welg (EW) S Arithmetic sequence weights (ASW) Rank order centtrold (ROC) 1 Age group Rate of people ages 20-34 in locality 25% 40% 52% 2 Country of origin Rate of people in locality who are immigrants from the former Soviet Union 25% 30% 27% 3 Educational level Rate of highly educated people in locality 25% 20% 15% 4 Income Gap, in absolute value, between the nationwide average income and locality's average income 25% 10% 6% Calculating the nominal and normalized scores of these criteria, for each locality Creating nominal score table: > CBS -> demographic and socioeconomic attributes np wood1? ji'TDinn now^n Central Bureau of Statistics ibjSjj,! *Las^JI Oyle* Normalizing SCOreS for each locality j in each criterion i normalized score of the i criterion in the j locality nominal score of locality j in criterion i maximal nominal score in criterion i Step 5 Arriving at a single final score for each locality To get the ranking list We used the classic and popular weighted sum (WS) model: final_score_of_locality_j =sumproduct(criteria weights, normalized scores) Example: Normalized scores locality Age group: 20-34 (%) Country of origin: Former Soviet Union (%) Higher education (%) Income EW ASW ROC Tel Aviv-Jaffa 1.00 0.38 0.76 0.81 73.8% 74.8% 77% EW 25% 25% 25% 25% 25% • 1 + 25%. 0.38+ 25%-0.76+ 25%- 0.81 = 73.8% ASW 40% 30% 20% 10% 40% • 1 + 30% • 0.38 + 20% • 0.76 + 10% ■ 0.81 = 74.8% ROC 52% 27% 15% 6% 52% • 1 + 27% •0.38+ 15%-0.76+ 6% ■ 0.81 = 77% The process flow Step 1 Filtering localities (Pareto principle) 70 localities (out of-1200) Step 4 Step 2 Deciding on the criteria for comparing the localities Step 3 confidential Input data Assigning weights to each of the criteria J Four criteria: age, origin, education, income EW, ASW, ROC Public input data Calculating the nominal and normalized scores of these criteria, for each locality. Step 5 I Calculations Arriving at a single final score for each locality To get the ranking list -► Results and Recommendation 23 Results and Recommendation 18 localities were ranked in the topl5 of at least one technique (12 localities were ranked in topl5 of all three techniques) Recommendation: focus party's efforts On these 18 localities ("focused list") Ariel Arad Ashdod Ashkelon Bat Yam Beer Sheva Carmiel Eilat Hadera Haifa Kiryat Gat Kiryat Yam Maa lot-Tars hi ha Nazareth Wit Nesher Netanya Sderot Tel Aviv-Jaffa 35» ISRAEL^N-IW _ t ; • V National capital tg District (meboZ) centre o City, town + Airport international boundary ----- Boundary ot iormei Palestine Mandate ----Armistice Demarcation Line ------- District (mehoz) boundary Main road - Secondary road ..... Raiifoad ■ ■ ■ ■ Oil pipeline LEBANON y umru. >j .'■ -CftVatL.Ti ;- ; !{<■ ^AI.QunayliR ÍGOLAN Acre Hai ort y^Cafniel J A \ NelanyaT í>TOI>iarm J ' WEST „ ' 0 Näbi HerzfivagS \V CR) .' >ffiriel Tel Aviv-Yarfti : 1 BANK BalYaflp-^',' ' Ram -Ö ti. Allah ,-Ramla^ ° y I JJarash 34" TabaS Al Aqabah yhul/j 36= Epilog ji The elections were held on April 9th, 2019. None of the 29 new parties that competed won Knesset seats. Zehut, that started its campaign with only 0.4% support, ended up with 2.74% of the votes. It was close, but not enough. (2nd place in the "losers list") Sub list (top 70) Focused 1 (top 18) ist votes percentage > 3.25% 17 (24%) 9 (50%) votes percentage > 2.74% 45 (64%) 16 (89%) The model provides a simple, valid tool for making data-driven decisions about allocating resources that can be easily updated for future election campaigns Analytical Hierarchy Process (AHP) AHP - background ■ Developed by Prof. Thomas Saaty ■ AHP is a structured and organized technique for making complex multidimensional decisions, based on mathematics and psychology ■ It is useful in various fields - government management, economy, industry... ■ Two main reasons for its strength: > Transparency and clarity > The integration of subjective assessments, including hu weaknesses, in the solution process AHP - technique steps ■ Evaluate preference for each pair of criteria (and/or pair of alternatives in each criteria), using a numeric scale ranging from 1 to 9 Degree of preference Equal Moderate Strong Very strong extreme Numeric value 1 3 5 7 9 Mid values may be chosen: 2, 4, 6, 8 ■ Create a pair-preference matrix as follows: if criterion i is preferred to criterion j by p, then write p in cell (i,y), and 1/p in cell (j, i) [ fill 1 in cells (i, i) ] ■ Normalize values to calculate weights ■ Check inconsistency ratio (CR) - the upper threshold is 10% 2v___/ Implementation Steps 1+2: evaluate preferences and create preference matrix Age group Country of origin Educational level Income Age group i 5 9 7 Country of origin 1/5 1 5 3 Educational level 1/9 1/5 1 1/3 in 1/7 1/3 3 1 Degree of preference Equal Moderate Strong Very strong extreme Numeric value 1 3 5 7 9 Mid values may be chosen: 2, 4, 6, 8 33N implementation Steps 3+4: normalize, calculate weights and check consistency ■ We can do it ourselves ■ Or we can use an AHP calculator... https://bpmsq.com/ahp/ahp-calc.php Age group Educational level Income Age group 1 5 9 7 Country of origin 1/5 1 5 3 Educational Level 1/9 1/5 1 1/3 Income 1/7 1/3 3 1 sum 1.454 6.533 | 18 11.333 Income 0.618 0.265 0.029 0.088 Weights! ► 65% 20.7% 4.8% 9.5% CR =6.3% Age group Country of origin Education a I level Age group 0.688 0.765 0.5 Country of origin 0.138 0.153 0.278 Educational level 0.076 0.031 0.055 Income 0.098 0.051 0.167 What's next? practicing: Applying MCDA and AHP for the problem of determining prisoners' eligibility fm pardon | ^Workshflp Workshop Suggestion of a scale Choose prisoners to pardon Age r--^ Behavior r--^ Severity Gender Health Portion served 1 - bad 2 - average 3 - good 0 - 0.1 and less or above 0.9 1 - between 0.11-0.40 2 - between 0.41-0.70 3 - between 0.71-0.9 1 - 31-40 2-21-30 or 41-50 3 - above 59 1 2 3 Severe Intermediate Minor offenses 1 - Healthy 2 - Minor health problems 3 - Major health problems Let's start by determining the weights of the criteria... ... continue with ranking the alternatives in each criterion. Be aware to normalize the values in each criterion before the final scoring Self-work Results Let's check who the lucky prisoners are... all groups results 38" summary We saw: > Applying MCDA approach using objective prioritization > An implementation of AHP technique You practiced MCDA and AHP for the problem of determining prisoners' eligibility for pardon 39N Ik of erations Research is useful and effect£„e '* be applied to a wide range of issues and dllem*^ 40N A short survey The purpose of this survey is to gather feedback on the short course you have just completed. Your input is valuable to me, as it will help me improve and better meet the needs of my students. Please take a few moments to complete this survey. Your feedback is greatly appreciated! https://forms.gle/odl5UcAHakvKSdYJ8 Irit Talmor (Ph.D) lritt@wgalil.ac.il Operations Research Understand -> Analyze Decide!