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

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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 0<N<∞ strict alternative b ∈ A\{a} and that the all strongest paths is O(Cˆ3), where C is weak orders each on the same finite strength of a path is the strength (N[c(i), the number of alternatives in A. set A of 1<C<∞ alternatives. c(i + 1)], N[c(i + 1), c(i)]) of its weakest link c(i), c(i + 1). There are three stage; Margin, ratio, vinning votes, losing 1. initialization votes are key terms. The most 1.x ≡ c(1). 2. calculation of the strengths of the strongest intuitive definitions for the strength of 2.y ≡ c(n). paths a link are its margin and its ratio. 3.2 ≤ n < ∞. 3. calculation of the binary relation O and the 4.For all i = 1,...,(n − 1) : c(i) ≡ c(i + 1). winners Homogeneity means that the result The strength of a path is the strength of depends only on the proportion of its weakest link. min{(N[c(i), c(i + 1)], N[c(i ballots 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 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. 3th 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.
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