I.T.U. Institute of Science and Technology Industrial Engineering 2020-2021 Spring Semester Group Decision Making Under Multicriteria Project Presentation

I.T.U. INSTITUTE OF SCIENCE AND TECHNOLOGY INDUSTRIAL ENGINEERING 2020-2021 SPRING SEMESTER GROUP DECISION MAKING UNDER MULTICRITERIA PROJECT PRESENTATION

ASSOCIATE PROF. ÖZGÜR KABAK

GROUP – I Presentation

507202112 Mustafa BAL 507202114 Süleyman YAMAN 507202122 Sercan DİNÇ March, 2021 CONTENT

1st Paper Presentation A new monotonic, clone-independent, reversal symmetric, and condorcet- consistent single-winner election method, Social Choice and Welfare, 36, pp 267–303. 2nd Paper Presentation Müller, J., & Kosub, S. (2020). A note on the complexity of manipulating weighted Schulze voting. Information Processing Letters, 162, 105989. 3rd Paper Presentation Ruiz-Padillo, A., de Oliveira, T. B., Alves, M., Bazzan, A. L., & Ruiz, D. P. (2016). Social choice functions: A tool for ranking variables involved in action plans against road noise. Journal of environmental management, 178, 1-10. 4th Paper Presentation Metszosy, G. (2020). Evaluating Social Innovation Tools: Process-oriented Approach. Theory Methodology Practice: Club Of Economics In Miskolc, 16(01), 19-29. 5th Paper Presentation Subochev, A., Aleskerov, F., & Pislyakov, V. (2018). Ranking journals using social choice theory methods: A novel approach in bibliometrics. Journal of Informetrics, 12(2), 416-429. 1st Paper

Name: A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method

Introduction Aim and contributions of this paper

Preliminaries, basic definitions and Definition of the Schulze method implementation of method Example A basic example to demonstrate Schulze method Analysis of Schulze method Analysis with several criterion

Comparison with other methods Total 15 methods are compared

Discussion Preferences about Schulze method

Aim: To introduce a new method that satisfies transitivity, resolvability, pareto, reversal symmetry, monotonicity, independence of clones, Smith, minmax set and prudunce criterion. 1.Introduction

Simpson–Kramer method selects the monotonicity weakest alternative in comparisons

transitivity independence Top-set alternavites cannot be of clones selected. resolvability Smith It is vulnerable to similar propoerties alternatives, so-called clones. pareto minmax set

It is criticised according to its some Reversal symmetry cannot be reversal satisfied. symmetry prudunce Schulze methods provides following criterion following provides methods Schulze 2.Definition of Schulze method

Preliminaries Basic definitios Implementation A strict partial order is a transitive and Basic idea of the Schulze method is that asymmetric relation “x>y”. A strict the strength of the indirect comparison weak order is a strict partial order “alternative a vs. alternative b” is the with the additional property that also strength of the strongest path a ≡ c(1), . . It can be calculated with Floyd algorithm. the relation “not x> y” is transitive. A . , c(n) ≡ b from alternative a ∈ A to The runtime to calculate the strengths of profile is a finite list V of 0ballots of each type, not on their + 1), c(i)])|i = 1,...,(n − 1)}. absolute numbers. 3.Example 4.Analysis of Schulze method

monotonicity

Proof of the transitivity is an essential part of the proof that the Schulze transitivity method is well defined independence of clones Resolvability basically says that usually there is a unique winner S = {a}. There are two different versions of the resolvability criterion. resolvability Smith 1 An election method satisfies the first version of the resolvability criterion if the proportion of profiles without a unique winner tends to zero as the number of voters in the profile tends to infinity pareto 2 minmax set The second version of the resolvability criterion says that, when there is more than one winner, then, for every alternative a ∈ S, it is sufficient to add a single ballot w so that alternative a becomes the reversal unique winner. symmetry prudunce 4.Analysis of Schulze method

monotonicity 2 Second version addresses situations with “a ∼v b for all v ∈ V” (for some pair of alternatives a, b ∈ A). It says that, when no voter strictly prefers transitivity alternative b to alternative a (i.e., a ∼v b for all v ∈ V), then alternative b independence must not perform better than alternative a. of clones

1 The first version addresses situations with “a v b for all v ∈ V”. It says that, resolvability when every voter strictly prefers alternative a to alternative b (i.e., a v b for all Smith v ∈ V), then alternative a must perform better than alternative b.

The Pareto criterion says that the election method must respect pareto unanimous opinions. There are two different versions. minmax set

This criterion says that, when v is reversed for all v ∈ V, then also the reversal result of the elections must be reversed. symmetry prudunce 4.Analysis of Schulze method

When some voters rank alternative a ∈ A and without changing the order in which monotonicity they rank the other alternatives relatively to each other. Then this must not hurt alternative a.

transitivity This criterion says that running a large number of similar alternatives, so-called independence clones, must not have any impact on the result of the elections. Replacing an of clones alternative d ∈ A old by a set of clones K should not change the winner. resolvability The Smith criterion and Smith-IIA (where IIA means “independence of irrelevant Smith alternatives”) say that weak alternatives should have no impact on the result of the elections.

pareto In some sense, the MinMax set is a clone-proof generalization of the Simpson– minmax set Kramer winner.

reversal symmetry This criterion says that the strength λD of the strongest link ef, that is not supported prudunce by the binary relation O, should be as small as possible. So λD := max D(N[e, f ], N[ f, e])|ef ∈/ O } should be minimized. 5.Comparison with other methods

Final results of table;

Schulze(15) > Ranked pairs(14) > Kemeny-Young = Copeland(11) > Slater = Nanson(10) > Baldwin = Black (9) > Instant Runoff = Borda(8) > Simpson-Kramer = Bucklin(7) > Plurality(6) > Young(5) > Dodgson(4) 6.Discussion

ü In this article, a new single-winner election method (Schulze method) is introduced.

ü It is clone-proof and that always chooses from the MinMax set.

ü The Schulze method also satisfies many other criteria; some of them are also satisfied by the Simpson–Kramer method that is startting point, like the Pareto criterion, resolvability, monotonicity and prudence; some of them are violated by the Simpson–Kramer method, like the Smith criterion and reversal symmetry.

ü Due to this huge amount of satisfied criteria, Schulze method can be a strong alternative for the Simpson–Kramer method for actual implementations, indeedly when manipulation through clones or weak alternatives is a considerable issue. 2nd Paper

Name: Ruiz-Padillo, A., de Oliveira, T. B., Alves, M., Bazzan, A. L., & Ruiz, D. P. (2016). Social choice functions: A tool for ranking variables involved in action plans against road noise. Journal of environmental management,

Introduction

Road Stretch Results and Introduction Priority Methodology Discussion Variables Comparison with other methods

Discussion

Aim: to achieve a complete list of variables sorted by priority, such SCFs were adapted in order to be able to rank all candidates from the highest to lowest score 1.Introduction

Ø This paper seeks to estimate the order of importance for the variables influencing the decision problem of prioritizing road stretches in a Noise Action Plan and to introduce the results for hotspot sorting.

The main objective is to propose an easy and comprehensive method to rank the variables involved in an automated and consistent manner.

In this method, data is gathered from responses of a panel of experts, who selected and compared the relative importance of the variables involved in the problem of prioritizing actions against road traffic noise. For this, several social choice functions (SCF) were applied to the various orderings determined by each expert to establish an average consensus ranking. 2. Road Stretch Priority Variables

RSPV are variables used by the planners as criteria for prioritizing the road stretches included in a Noise Action Plan. They were determined and defined in Ruiz-Padillo et al. (2014), and are used in this paper with some refinements taking into account the previous experience. 3.Methodology

Because every SCF employs An expert panel was generated through various logic principles and surveys, where participants algorithms, were asked to sort the RSPV by the a set of SCF was used to reach criterion of the relative different ordered lists of importance of each variable in the the RSPV. Then, they were decision-making problem of compared to define a more sorting road stretches by priority for representative consensus action against road traffic ranking, supported by the noise. combination of both EPT and SCF techniques. 3.1 Expert Panel Technique

In the case of establishing priorities of actions on road stretches with noisy road traffic, decisions correspond The EPT is widely used as support for decision-making only to high levels of procedures, the public administrations responsible for allowing experts to participate in the collective decision road networks. Besides, making representatives of different administrative with their experience and knowledge. A group decision is levels and different generated, this normally being more accurate than the geographical areas should also be part of the decision expert panel. made by individual members. In this process, experts independently Finally, the information derived from the and anonymously express their judgments by filling out a expert panel was questionnaire statistically analyzed using a linear model for the analysis of variance (ANOVA), using Tukey's test, to compare and test the consistency of the results. 3.2 Social Choice Functions

Responses from an expert panel can be regarded as voting results. In this way, some scoring voting methods through SCF were implemented, which use the EPT's results in order to achieve a ranking that reflects the views of all the experts in an objective and plural manner. The SCFs used in this study were Plurality, Raynaud, Kemeny-Young, Copeland, Simpson, Schulze, and Borda, because they are either popular or adequate to the problem.

In short, SCFs take the candidates ordered by experts' preferences as input and then return the chosen candidates or a ranking of them. In the present research, the relationship of preference is strict, because the experts' questionnaire answers did not allow “ties” between the variables when sorting them by importance.

In applying voting methods in expert panel results, it is useful to construct a special ranking-schedule table (ranking matrix), with the following properties: The size of the matrix is m - n, where m is the number of voters (participants in the expert panel) and n is the number of candidates (the RSPV). 3.2 Social Choice Functions

SCF implemented Borda Count Kemeny- SCF Plurality Copeland Raynaud Schulze using a voting Young voting implemented voting method method method Python method method in R software method library 4. Results and Discussion

As a result, 24 experts were selected (almost the entire population involved in the decision-making process coming from all provinces in the region of Andalusia, southern Spain) and of these, 19 experts returned their filled-out questionnaires. This ratio means a very high degree of success (79%), which gave a great representativeness to the results. Also, the number of panel participants was adequate, according to the current literature, and all the provinces and administrative levels were fully represented in the data acquisition process.

An analysis of the findings gives the following results. The variables that take into account the exposure parameters of greater effect on the citizens (Pexp and SCexp) received the utmost importance of the RSPV as criteria for prioritizing the road stretches with noise problems due to the traffic. Following this ranking and with the ordering by the SCF, the next three variables indicated the importance given to the intensity of the problem, measured directly by DL, ADT and EC, respectively 4. Results and Discussion 5.Discussion

ü The relative importance of the main variables influencing the process of prioritizing road stretches for action against traffic noise (identified previously as nine Road Stretch Priority Variables, RSPV) was successfully evaluated by the expert panel technique (EPT).

ü The combination of EPT and SCF used in this study proved highly suitable for the data processing and for the variable selection and ranking to prioritize actions against road traffic noise. 4st Paper

Evaluating Social Innovation Tools: Process-Oriented Approach

1.Introduction

Innovator is a decision maker as a role in innovation process,

This study claims that innovator’s thinking approach or level of the innovation or the place of implementation can be the choice and prioritizing of these factors.

This study investigates determining the presence of linked variables to carry out identifying the forms and level of decisions in connection with success factors.

Aim: -To investigate the success factors of efficiency of social innovation, -To make a decision a number of success factors play an important part in adjusting to reach the optimal solution with the variables associated with the success factors in order to help. 2.Definitions

Social problems Environmental problems

Social innovation is described as innovation where the tools and goals are societal, new relationships or cooperation are New problems Social innovation includes the ideas, arise created and social needs are models, products, and services which being satisfied simultaneously.(1) satisfy social needs and create new social interactions. (2)

To improve people’s well-being To decrease the disadvantages of the peripheral areas

(1) Murray et al. (2010) (2) European Commission description (2014) 3.Literature Review Social Innovaion Criteria (The critical factors required different types of evaluation and consideration.)

To do good for society

Changing the social structure

Changing social practices

Contribution to regional or community development

Digital world, community presence in the innovation

Endowing different type of innovations with social importance

Process reengineering

Social work 4.Social Innovation Phases

Preparation

Systematic Specifying changes the directives

Adjustment, Conception measuring

Sustainment Prototyping

Cost Quality Satisfaction Acceptance Reduction 4. Success Factors Approach

Collaboration, integration: should include Culture Experience Sustainability Replicability individuals, organizations and communities involved in the action in any way. Lack of support and common thinking are Financial Non-financial Social learning Communication impediments during implementation, so an resources resources open-minded, innovative approach, empathy and patience are needed to conduct the Leader, Applied process Infrastructure Expectations innovator techniques

Novelty Networks 4.Analysis of Multi-Attribute Utility Theory and Outranking Relations

Multi-Attribute Utility Theory and Outranking relations are the two main lines of multi-criteria In Outranking relation an alternative comes forward decision techniques. Applying Multi-Attribute Utility in preference order if it is at least as good as the Theory means the aggregation of criteria into a follower while there is no essential reason to function, and the examination of mathematical disconfirm the statement (Bouyssou, 1996). conditions of aggregation by maximization of the function.

Based on the preference of the decision The compensation between maker, multi-criteria decision-making criteria is allowed by the theory of method can be selected to determine method, consequently the profit the importance of success factors and its of one criterion compensates for preference order. the loss of another (Pratt et al. 1976). 5. Choosing the Appropriate Method

Simple ranking method is used

The importance of success factors 6.Decision

Determining the relative importance of the factors by pairwise comparisons

Determining weight vectors

Determining the consistency 6.Decision The pairwise comparisons were done in individual structured interviews, categorizing the interviewees into four categories:

Local Organization Individual as Foundation as government as as innovator innovator (I) innovator (F), innovator (L), (O).

The participants had to indicate the preferred factor from pairs and determine its importance with a number from a scale, where the minimum (1) means equally important and maximum (9) means the most important factor. 6.Calculation

The relative importance of factors is represented by the elements of the matrix. Determining the consistency ratio (CR) is required to measure consistency. If the value of CR converges to zero, the consistency is presumable. 6. Calculation

The consistency ratio is equal to the quotient of the consistency index (CI) and the empirical average of consistency index (RI). Its value is considered satisfactory if it is not greater than 0.1.

Eliminating inconsistency does not have to be the goal of decisions as it is not The value 0.1 is an empirical limit and it a sufficient condition for can be varied depending on the decision making good decisions. situation. 7. Results • Four people participated in the study, one from each specified group • individual as innovator The consistency ratio is appropriate for the • local government as innovator external and functional factors, the values are • foundation as innovator less than 0.1 (CRE equal to 0.074 and CRF equal • to 0.092), but higher for the internal factors organization as innovator (CRI equal to 0.185).

The elements of weight vectors can be calculated with Experience (0.32 and 0.40) leader, innovator (0.11 and 0.23)

External factors financial resources Individual (0.51), Local government (0.67), Foundation (0.38) Most cited success factor Organization networks (0.47), Internal factors collaboration (weights (0.27 and 0.28) individual and foundation 7. Results 7. Results (Significant difference )

• Significant difference can be discovered between the priority rank of the individual, foundation, local government and organization. Kendall’s coefficient of concordance was calculated;

• Kendall’s coefficient of concordance is equal to the quotient of Δ quadratic variation and Δmax adjusted by maximum correction factor (it shows the 100% correlation). W is equal to 1 in the case of full agreement, and W is equal to zero if ranks show contrast. 7. Results (Significant difference )

• The W significance test is necessary to determine the correlation between the ranks. The fundamental assumption is the lack of agreement among the participants, therefore W greater than zero refers to a random effect, while the alternative hypothesis assumes agreement between participants. Significance test is possible to achieve with the value of χ2 distribution and its comparison to the threshold. 7. Results (Significant difference ) 5th Paper

Name: Ranking journals using social choice theory methods: A novel approach in bibliometrics

Introduction Aim and contributions of this paper

Data Explanation about data of paper

Correlation analysis of bibliometric- Basic ranking methods correlation indicator-based rankings Aggregation methods and their axiomatic Definitions of methods that are analysis implemented The correlation analysis of the Correlation results aggregate rankings Conclusions Method’s power explanations

Aim: To produce quantitative estimates of (in)consistency of the evaluations based on six popular bibliometric indicators (impact factor, 5-year impact factor, immediacy index, article influence score, SNIP and SJR) by using social choice theory. 1.Introduction

Ranking journals have a Interest for problem bibliometric measures is attractive Growing multiplicity Scopus database generates two questions and H-index

-How do the rankings based on different measures correlate with each other? -What can a decision-maker do if there are several rankings but he/she needs just one?

The multiplicity of Ordinal aggregation First for contradicting It uses methods based on the journal Has some problems evaluations majority rule ranking for decision makers 2.Data

Journal Citation Reports database Three academic disciplines’ (all for JCR-2011 edition), and the journal; two main rule Journal Metrics website powered Random selection for by the Scopus database are used. criteria? Economics, SNIP and SJR metrics for 2011 Management, Politics Impact factor (IF), 5-year IF, immediacy index (II) and -journal Citation Reports and the Scopus article influence score (AI) database classify the journal as either an economic, or management, or political The main selection criteria for science journal indicators were their popularity -values of all six bibliometric indicators and diversity of data sources and are known. methodologies. 3. Correlation analysis of bibliometric-indicator-based rankings

ü To evaluate the (in)consistency of any two rankings, their correlations are measured. For this purpose, the Kendall rank correlation coefficient Γb is used.

ü In all cases, the correlation is positive. 4. Aggregation methods and their axiomatic analysis

ü Since in all cases, the correlation is positive, it is not preferred to best alternative is selected.

ü Social choice theory is adopted.

ü Before starting aggregation methods implementation 1. Basic notations, 2. Axiomatic parameters 3. Used methods needs to be demonstrated. 4.1. Basic notations

ü X denotes the general set of alternatives. It is supposed that X is finite.

ü A denotes the feasible set of alternatives: A ⊆ X ∧ A =/ Ø. The feasible set is a variable.

ü N denotes a society (a group of people) making a collective decision. A voter i ∈ N (a member of the society N) has preferences for the alternatives from X.

ü It is supposed that individual preferences can be represented by a numerical function; �(x):X → R, such that �(x) > �(y) if and only if voter i strictly prefers x to y, and �(x) = �(y) if and only if i is indifferent regarding the choice between x and y.

ü The value of �(x) is interpreted as the utility of alternative x for voter i. The set U = {�(x) | i ∈ N} of utility functions is called the utility profile.

ü There exists a social choice correspondence S(U, A) with arguments A and U and values in the set of subsets of A, which determines a set �() of social optima in A: �() = S(U, A) ⊆ A.

ü There exists a social welfare functional R(U, A) with arguments A and U and values in the set of binary relations on A, R(U, A) ⊆ A × A. 4.2. Axiomatic properties

Under Ordinality, we do not presume that any quantities have any meaning, only Completeness Ordinality order of numbers is meaningful, each voter has an ordinal scale of measurement, and these scales are incomparable. Thus, (O) is also called the axiom of ordinal noncomparability

Independence of Transitivity Cardinal noncomparability is a weaker condition that implies that it is possible to irrelevant utilities meaningfully compare differences of values of a given indicator.

Neutrality Unrestricted domain Pareto dominance relation is a sub-relation of the majority relation, which is the outcome of the majority rule. In addition, when there are only two alternatives in the feasible choice set, the majority rule trivially satisfies transivity. There are more arguments in favor of the majority rule; Cardinal monotonicity, Ordinal Strong Pareto Anonymity monotonicity, Strict cardinal monotonicity, Computational simplicity principle Positive responsiveness is the requirement to use all the information available under Neutrality and Anonymity to resolve ties in the Pareto dominance relation 4.3. The Copeland Rule

ü The greater the number of alternatives which are worse than a given one, the better this alternative is (the 2nd version of the Copeland rule); Give 1 to any alternative for each win and 0 for each tie and each loss, add the numbers and rank alternatives by their respective score.

ü Alternatively, it could be put that an option is good if the number of alternatives which are better is small (the 3rd version of the rule). Give 1 to any alternative for each win and each tie and 0 for each loss. Finally, one can subtract the number of alternatives that are more preferable than a given one from the number of alternatives less preferable and then rank the alternatives by the values of these differences (the 1st version of the rule). ü All versions yield the same ranking when there are no ties.

ü The Copeland rule satisfies (T), (C), (N), (SP), (A), (UD), (O), (CM), (OM), (SCM), (CS) and (CC). This rule does not satisfy (IIU) and, consequently, the Arrowian axiom of Independence of Irrelevant Alternatives, which is a conjunction of (IIU) and (O).

If the values of indicators or the set of journals change so that this If the set of journals stays the same, and the values of indicators change does not affect the position of journals x and y relative to each other so that this does not affect the position of journals x and y relative to in any indicator-based ranking, then the position of x relative to y in each other and to any other journal in any indicator-based ranking then the aggregate ranking must not change. the position of x relative to y in the aggregate ranking will not change. Arrowian Independence of Irrelevant Alternatives Weak Arrowian Independence of Irrelevant Alternatives 4.4. A sorting procedure based on tournament solutions

ü In order to construct a ranking, it is also possible to use social choice correspondences.

S(U, A) determines a set �() of those alternatives that are considered to be social optima: �() = S(U, A) ⊆ A.

ü A tournament solution is a social choice correspondence S(P) that has the following properties: 1. Nonemptiness 2. Neutrality 3. Condorcet consistency

tournament solution

Uncovered set

minimal externally stable set 4.5. The Markovian method

ü Sorting the alternatives by the tournament solution called the weak top cycle WTC.

ü A subset WTC of the feasible set A is the weak top cycle of A if any alternative in WTC P-dominates any alternative outside WTC: ∀ x ∈ A\WTC, y ∈ WTC⇒yPx, and none of WTC’s proper subsets satisfies this property.

ü After the sorting, rank alternatives of the same sort in the following way.

ü In this paper difference is that if we are at node x at � another node y must be selected from the set {y | yRx}, consequently it is always to be obliged to move from x to y �.

ü The version of the Markovian procedure used in this paper satisfies (T), (C), (N), (SP), (A), (UD), (O), (CM), (OM), (SCM), (CS), (CC) and does not satisfy (IIU), (WAIIA), (IICA). (CM) and (OM) does not been satisfied other similar studies. 5. The correlation analysis of the aggregate rankings

Each ranking is characterized by the 6-tuple, its i-th component being the value of b for this ranking and a corresponding single-indicator-based ranking.

It is compared that these 6-tuples, compute the corresponding voting matrix and the tournament matrix representing the majority relation on the set of the eleven rankings compared.

It is applied to each of the three journal sets separately. 6*3 =18

When the Copeland rule (version 2) to the tournament matrices obtained, it will be get the five rankings of ranking methods. 6. Conclusions

ü This paper demonstrates the power of ordinal methods based on the majority rule. It brings a novelty for journal ranking. ü Though all majority-rule-based rules violate the independence of irrelevant alternatives/utilities, some of them do satisfy some weaker versions of this property: the Copeland rule satisfies the weak Arrowian independence of irrelevant alternatives, while the sorting based on MES satisfies the independence of irrelevant classes of alternatives. ü The Markovian method discriminates almost all journals. THANKS FOR LISTENING...