Aleksandar Hatzivelkos | University of applied science Velika Gorica (original) (raw)
Papers by Aleksandar Hatzivelkos
Mathematical social sciences, Jun 1, 2024
The concept of compromise has been present in the theory of social choice from the very beginning... more The concept of compromise has been present in the theory of social choice from the very beginning. The result of social choice functions as such is often called a social compromise. In the last two decades, several functions of social choice dedicated to the concept of compromise, such as Fallback bargaining, Majoritarian compromise, Median voting rule or p-measure of compromise rules, have been considered in the literature. Furthermore, compromise axioms were formed in several attempts. However, we believe that the previous formalizations of compromise did not axiomatically describe this feature of the social choice functions. In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a Compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and established social choice functions. We will show that the division of SCFs in three classes with respect to these axioms fairly reflect relationship between those SCFs and colloquial expectations from notion of compromise. We then compare the defined axioms with the compromise axioms of Börgers and Cailloux. Finally, for SCFs that satisfy the strong compromise axiom, we define a compromise intensity function that numerically expresses the degree of tolerance of the SCF for choosing a compromise candidate.
Journal of information and organizational sciences, Dec 22, 2022
We investigate the notion of compromise in the strict preferential voting setting. We introduce d... more We investigate the notion of compromise in the strict preferential voting setting. We introduce divergence as an inverse measure of compromise in a collection of strict preferential votes. Classical functions of social choice theory are analyzed with respect to divergence. New social welfare functions and new social choice functions with the objective of compromise are defined directly from optimization of divergence and later analyzed with respect to the common desiderata of social choice theory. For a very natural function, a simple divergence minimizer, we prove it satisfies the properties of anonymity, neutrality, consistence, and continuity. Consequently, according to Young's theorem of characterization it follows that this function is a scoring point function. Its scoring point vector is also given. Finally, we discuss the parameter p in the divergence measure which was introduced to address vagueness and fuzziness of compromise and to control for a variety of intended levels of compromise.
Mathematical Social Sciences, 2024
The concept of compromise has been present in the theory of social choice from the very beginning... more The concept of compromise has been present in the theory of social choice from the very beginning. The result of social choice functions as such is often called a social compromise. In the last two decades, several functions of social choice dedicated to the concept of compromise, such as Fallback bargaining, Majoritarian compromise, Median voting rule or p-measure of compromise rules, have been considered in the literature. Furthermore, compromise axioms were formed in several attempts. However, we believe that the previous formalizations of compromise did not axiomatically describe this feature of the social choice functions. In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a Compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and established social choice functions. We will show that the division of SCFs in three classes with respect to these axioms fairly reflect relationship between those SCFs and colloquial expectations from notion of compromise. We then compare the defined axioms with the compromise axioms of Börgers and Cailloux. Finally, for SCFs that satisfy the strong compromise axiom, we define a compromise intensity function that numerically expresses the degree of tolerance of the SCF for choosing a compromise candidate.
Poučak, 2023
Na prvom Kongresu nastavnika matematike RH održanom 2000. godine, te potom odlukama Izvršnog odbo... more Na prvom Kongresu nastavnika matematike RH održanom 2000. godine, te potom odlukama Izvršnog odbora i Skupštine Hrvatskog matematičkog društva prihvaćena je odluka o standardnim oznakama u matematici koje su preporučene za upotrebu u Republici Hrvatskoj. Istaknimo kako je tom preporukom za označavanje decimalnog broja preporučeno korištenje točke (a ne zareza) kao decimalnog separatora. Decimalna točka bez problema se upotrebljava proteklih dvadeset godina u nastavi matematike, matematičkim udžbenicima, člancima i časopisima. No upotreba decimalne točke nije ograničena samo na matematiku, već se može naći i u raznim nastavnim, stručnim i znanstvenim sadržajima drugih prirodnih znanosti. S druge strane, hrvatski pravopis propisuje upotrebu zareza kao decimalnog separatora. Ta razlika između preporuka Hrvatskog matematičkog društva i Hrvatskog pravopisa rezultirala je polemikom u javnom prostoru koja traje do današnjih dana. Navedena polemika i opisana razlika pogotovo dolaze do izražaja u obrazovnom sustavu, u kojemu se paralelno koriste dvije vrste oznaka. Dok se u matematici i pripadnim nastavnim materijalima koristi decimalna točka, u drugim prirodnim znanostima prevladava upotreba decimalnog zareza. Također, treba istaknuti kako je navedena polemika u javnom prostoru pretežno jednostrana. Osim rijetkih izuzetaka, većina objavljenih tekstova pisana je s pozicije osude upotrebe točke kao decimalnog separatora. Cilj ovoga članka je argumentirano odgovoriti na navedene kritike.
Journal of information and organizational sciences, 2022
We investigate the notion of compromise in the strict preferential voting setting. We introduce d... more We investigate the notion of compromise in the strict preferential voting setting. We introduce divergence as an inverse measure of compromise in a collection of strict preferential votes. Classical functions of social choice theory are analyzed with respect to divergence. New social welfare functions and new social choice functions with the objective of compromise are defined directly from optimization of divergence and later analyzed with respect to the common desiderata of social choice theory. For a very natural function, a simple divergence minimizer, we prove it satisfies the properties of anonymity, neutrality, consistence, and continuity. Consequently, according to Young's theorem of characterization it follows that this function is a scoring point function. Its scoring point vector is also given. Finally, we discuss the parameter p in the divergence measure which was introduced to address vagueness and fuzziness of compromise and to control for a variety of intended levels of compromise.
Systems with partial distribution of heat allocators present a problem in terms of energy allocat... more Systems with partial distribution of heat allocators present a problem in terms of energy allocation. Since heat allocators provide pure numerical, and not the consumed energy value, energy consumed in the apartments without heat allocators is unknown. Furthermore, energy loss within the building is also unknown. Therefore, models for heat energy allocation are used. With those models, based upon partial (numerical) consumption readings, allocation to all apartments is formed. This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a n...
Logic and Applications 2021 Book of Abstracts, 2021
Poučak : časopis za metodiku i nastavu matematike, 2021
Poučak : časopis za metodiku i nastavu matematike, 2018
Poučak : časopis za metodiku i nastavu matematike, 2020
Proceedings of the 21st International Conference on Group Decision and Negotiation, 2021
In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and ... more In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and three major groups of social choice functions: position scoring functions, Condorcet functions and a group of social choice functions that aim to capture a notion of compromise (Sanver (2004) and Hatzivelkos (2019)). Finally, we will show that the division of social choice functions in three groups with respect to these axioms (ones that fail to satisfy weak compromise axiom, ones which meet weak, but not strong compromise axiom, and ones that satisfy strong compromise axiom) fairly reflect relationship between those social choice functions and colloquial expectations from notion of compromise.
This paper addresses the allocation methods used for allocation of the heat energy in systems wit... more This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a necessary allocation property, special attention is given to later two properties, monotonicity and local consistency. Those properties describe allocation methods from the perspective of a consumer. Finally, mathematical analysis of allocation methods behaviour in worst case scenario is given, i.e. scenario that produces the greatest error for observed allocation model. Key–Words: Heat energy allocation model
Interdisciplinary Description of Complex Systems, 2014
Proceedings of the 21st International Conference on Group Decision and Negotiation, 2021
In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and ... more In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and three major groups of social choice functions: position scoring functions, Condorcet functions and a group of social choice functions that aim to capture a notion of compromise (Sanver (2004) and Hatzivelkos (2019)). Finally, we will show that the division of social choice functions in three groups with respect to these axioms (ones that fail to satisfy weak compromise axiom, ones which meet weak, but not strong compromise axiom, and ones that satisfy strong compromise axiom) fairly reflect relationship between those social choice functions and colloquial expectations from notion of compromise.
Social choice decision aggregation is a form of complex system modelling which is based upon vote... more Social choice decision aggregation is a form of complex system modelling which is based upon voters' rankings over a set of candidates. Different social choice functions, such as Borda count, plurality count or Condorcet methods models different aspects of social choice decision criteria. One of such criteria which has not been fully described or modelled, is the notion of compromise. This article aims to define a measure which would capture the notion of compromise on a given profile of voter preferences, about certain candidate being appointed to a certain position by a certain social welfare function. The goal is to define what compromise should mean, and proposes the so-called " d-measure of divergence " as a measure of divergence for some candidate to be positioned to a certain position. This study compares the results of two well-established social welfare functions, Borda and plurality count d-measure of divergence.
Systems with partial distribution of heat allocators present a problem in terms of energy allocat... more Systems with partial distribution of heat allocators present a problem in terms of energy allocation. Since heat allocators provide pure numerical, and not the consumed energy value, energy consumed in the apartments without heat allocators is unknown. Furthermore, energy loss within the building is also unknown. Therefore, models for heat energy allocation are used. With those models, based upon partial (numerical) consumption readings , allocation to all apartments is formed. This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a necessary allocation property, special attention is given to later two properties, monotonicity and local consistency. Those properties describe allocation methods from the perspective of a consumer. Mathematical analysis of allocation methods behavior in worst case scenario is given, i.e. scenario that produces the greatest error for observed allocation model. Another high consumer visibility concept is analyzed: consumption reading point value. For a consumer, it is only natural to seek relation between consumption reading and energy allocation, which is described with concept of allocated energy value of consumption reading points. Criteria for consumption reading point value comparison is introduced and described by usage of simulations. Finally, notions of new areas of heat allocation model analysis are given.
Mathematical social sciences, Jun 1, 2024
The concept of compromise has been present in the theory of social choice from the very beginning... more The concept of compromise has been present in the theory of social choice from the very beginning. The result of social choice functions as such is often called a social compromise. In the last two decades, several functions of social choice dedicated to the concept of compromise, such as Fallback bargaining, Majoritarian compromise, Median voting rule or p-measure of compromise rules, have been considered in the literature. Furthermore, compromise axioms were formed in several attempts. However, we believe that the previous formalizations of compromise did not axiomatically describe this feature of the social choice functions. In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a Compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and established social choice functions. We will show that the division of SCFs in three classes with respect to these axioms fairly reflect relationship between those SCFs and colloquial expectations from notion of compromise. We then compare the defined axioms with the compromise axioms of Börgers and Cailloux. Finally, for SCFs that satisfy the strong compromise axiom, we define a compromise intensity function that numerically expresses the degree of tolerance of the SCF for choosing a compromise candidate.
Journal of information and organizational sciences, Dec 22, 2022
We investigate the notion of compromise in the strict preferential voting setting. We introduce d... more We investigate the notion of compromise in the strict preferential voting setting. We introduce divergence as an inverse measure of compromise in a collection of strict preferential votes. Classical functions of social choice theory are analyzed with respect to divergence. New social welfare functions and new social choice functions with the objective of compromise are defined directly from optimization of divergence and later analyzed with respect to the common desiderata of social choice theory. For a very natural function, a simple divergence minimizer, we prove it satisfies the properties of anonymity, neutrality, consistence, and continuity. Consequently, according to Young's theorem of characterization it follows that this function is a scoring point function. Its scoring point vector is also given. Finally, we discuss the parameter p in the divergence measure which was introduced to address vagueness and fuzziness of compromise and to control for a variety of intended levels of compromise.
Mathematical Social Sciences, 2024
The concept of compromise has been present in the theory of social choice from the very beginning... more The concept of compromise has been present in the theory of social choice from the very beginning. The result of social choice functions as such is often called a social compromise. In the last two decades, several functions of social choice dedicated to the concept of compromise, such as Fallback bargaining, Majoritarian compromise, Median voting rule or p-measure of compromise rules, have been considered in the literature. Furthermore, compromise axioms were formed in several attempts. However, we believe that the previous formalizations of compromise did not axiomatically describe this feature of the social choice functions. In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a Compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and established social choice functions. We will show that the division of SCFs in three classes with respect to these axioms fairly reflect relationship between those SCFs and colloquial expectations from notion of compromise. We then compare the defined axioms with the compromise axioms of Börgers and Cailloux. Finally, for SCFs that satisfy the strong compromise axiom, we define a compromise intensity function that numerically expresses the degree of tolerance of the SCF for choosing a compromise candidate.
Poučak, 2023
Na prvom Kongresu nastavnika matematike RH održanom 2000. godine, te potom odlukama Izvršnog odbo... more Na prvom Kongresu nastavnika matematike RH održanom 2000. godine, te potom odlukama Izvršnog odbora i Skupštine Hrvatskog matematičkog društva prihvaćena je odluka o standardnim oznakama u matematici koje su preporučene za upotrebu u Republici Hrvatskoj. Istaknimo kako je tom preporukom za označavanje decimalnog broja preporučeno korištenje točke (a ne zareza) kao decimalnog separatora. Decimalna točka bez problema se upotrebljava proteklih dvadeset godina u nastavi matematike, matematičkim udžbenicima, člancima i časopisima. No upotreba decimalne točke nije ograničena samo na matematiku, već se može naći i u raznim nastavnim, stručnim i znanstvenim sadržajima drugih prirodnih znanosti. S druge strane, hrvatski pravopis propisuje upotrebu zareza kao decimalnog separatora. Ta razlika između preporuka Hrvatskog matematičkog društva i Hrvatskog pravopisa rezultirala je polemikom u javnom prostoru koja traje do današnjih dana. Navedena polemika i opisana razlika pogotovo dolaze do izražaja u obrazovnom sustavu, u kojemu se paralelno koriste dvije vrste oznaka. Dok se u matematici i pripadnim nastavnim materijalima koristi decimalna točka, u drugim prirodnim znanostima prevladava upotreba decimalnog zareza. Također, treba istaknuti kako je navedena polemika u javnom prostoru pretežno jednostrana. Osim rijetkih izuzetaka, većina objavljenih tekstova pisana je s pozicije osude upotrebe točke kao decimalnog separatora. Cilj ovoga članka je argumentirano odgovoriti na navedene kritike.
Journal of information and organizational sciences, 2022
We investigate the notion of compromise in the strict preferential voting setting. We introduce d... more We investigate the notion of compromise in the strict preferential voting setting. We introduce divergence as an inverse measure of compromise in a collection of strict preferential votes. Classical functions of social choice theory are analyzed with respect to divergence. New social welfare functions and new social choice functions with the objective of compromise are defined directly from optimization of divergence and later analyzed with respect to the common desiderata of social choice theory. For a very natural function, a simple divergence minimizer, we prove it satisfies the properties of anonymity, neutrality, consistence, and continuity. Consequently, according to Young's theorem of characterization it follows that this function is a scoring point function. Its scoring point vector is also given. Finally, we discuss the parameter p in the divergence measure which was introduced to address vagueness and fuzziness of compromise and to control for a variety of intended levels of compromise.
Systems with partial distribution of heat allocators present a problem in terms of energy allocat... more Systems with partial distribution of heat allocators present a problem in terms of energy allocation. Since heat allocators provide pure numerical, and not the consumed energy value, energy consumed in the apartments without heat allocators is unknown. Furthermore, energy loss within the building is also unknown. Therefore, models for heat energy allocation are used. With those models, based upon partial (numerical) consumption readings, allocation to all apartments is formed. This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a n...
Logic and Applications 2021 Book of Abstracts, 2021
Poučak : časopis za metodiku i nastavu matematike, 2021
Poučak : časopis za metodiku i nastavu matematike, 2018
Poučak : časopis za metodiku i nastavu matematike, 2020
Proceedings of the 21st International Conference on Group Decision and Negotiation, 2021
In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and ... more In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and three major groups of social choice functions: position scoring functions, Condorcet functions and a group of social choice functions that aim to capture a notion of compromise (Sanver (2004) and Hatzivelkos (2019)). Finally, we will show that the division of social choice functions in three groups with respect to these axioms (ones that fail to satisfy weak compromise axiom, ones which meet weak, but not strong compromise axiom, and ones that satisfy strong compromise axiom) fairly reflect relationship between those social choice functions and colloquial expectations from notion of compromise.
This paper addresses the allocation methods used for allocation of the heat energy in systems wit... more This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a necessary allocation property, special attention is given to later two properties, monotonicity and local consistency. Those properties describe allocation methods from the perspective of a consumer. Finally, mathematical analysis of allocation methods behaviour in worst case scenario is given, i.e. scenario that produces the greatest error for observed allocation model. Key–Words: Heat energy allocation model
Interdisciplinary Description of Complex Systems, 2014
Proceedings of the 21st International Conference on Group Decision and Negotiation, 2021
In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and ... more In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and three major groups of social choice functions: position scoring functions, Condorcet functions and a group of social choice functions that aim to capture a notion of compromise (Sanver (2004) and Hatzivelkos (2019)). Finally, we will show that the division of social choice functions in three groups with respect to these axioms (ones that fail to satisfy weak compromise axiom, ones which meet weak, but not strong compromise axiom, and ones that satisfy strong compromise axiom) fairly reflect relationship between those social choice functions and colloquial expectations from notion of compromise.
Social choice decision aggregation is a form of complex system modelling which is based upon vote... more Social choice decision aggregation is a form of complex system modelling which is based upon voters' rankings over a set of candidates. Different social choice functions, such as Borda count, plurality count or Condorcet methods models different aspects of social choice decision criteria. One of such criteria which has not been fully described or modelled, is the notion of compromise. This article aims to define a measure which would capture the notion of compromise on a given profile of voter preferences, about certain candidate being appointed to a certain position by a certain social welfare function. The goal is to define what compromise should mean, and proposes the so-called " d-measure of divergence " as a measure of divergence for some candidate to be positioned to a certain position. This study compares the results of two well-established social welfare functions, Borda and plurality count d-measure of divergence.
Systems with partial distribution of heat allocators present a problem in terms of energy allocat... more Systems with partial distribution of heat allocators present a problem in terms of energy allocation. Since heat allocators provide pure numerical, and not the consumed energy value, energy consumed in the apartments without heat allocators is unknown. Furthermore, energy loss within the building is also unknown. Therefore, models for heat energy allocation are used. With those models, based upon partial (numerical) consumption readings , allocation to all apartments is formed. This paper addresses the allocation methods used for allocation of the heat energy in systems with partial distribution of the heat allocators. Mathematical definition and analysis of three heat energy allocation methods is given. Two of them were officially legislated in Croatia, and in use since year 2008. Third one is proposed in works of Hatzivelkos. Properties of allocation methods are introduced: consistency, monotonicity and local consistency. While consistency, as a global property can be viewed as a necessary allocation property, special attention is given to later two properties, monotonicity and local consistency. Those properties describe allocation methods from the perspective of a consumer. Mathematical analysis of allocation methods behavior in worst case scenario is given, i.e. scenario that produces the greatest error for observed allocation model. Another high consumer visibility concept is analyzed: consumption reading point value. For a consumer, it is only natural to seek relation between consumption reading and energy allocation, which is described with concept of allocated energy value of consumption reading points. Criteria for consumption reading point value comparison is introduced and described by usage of simulations. Finally, notions of new areas of heat allocation model analysis are given.
Central European Conference on Information and Intelligent Systems, 2017
This paper aims to define a measure which would capture notion of compromise on a given profile o... more This paper aims to define a measure which would capture notion of compromise on a given profile of voter preferences, about certain candidate being appointed to the certain position by some social welfare function. The goal is to define what compromise should mean, and proposes so called " d-measure of divergence " as a measure of divergence for some candidate to be positioned to certain position. Two well established social welfare functions, Borda and plurality count d-measure of divergence results are compared. Furthermore, d-measure of divergence enables us to define new social welfare functions, which would (in different ways) minimize d-measure of divergence (from the compromise): " Simple d-measure " , greedy minimization and " Total d-measure " social welfare functions. Characterization for the SdM function is given, and properties of later two functions are analyzed.