Strict Preference Research Articles

On random stable matchings: Cyclic ones with strict preferences and two-sided ones with partially ordered preferences

Consider a cyclically ordered collection of r equi-numerous “agent” sets with strict preferences of every agent over the agents from the next set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union of r-long cycles, one agent from each set per cycle, such that there are no destabilizing r-long cycles, i.e. cycles in which every agent strictly prefers its successor to its successor in the matching. Assuming that the preferences are uniformly random and independent, we show that the expected number of stable matchings grows with n (cardinality of each agent set) as (nlog⁡n)r−1. Next we consider a bipartite stable matching problem where preference list of each agent forms a partially ordered set. Each partial order is an intersection of several, ki for side i, independent, uniformly random, strict orders. For k1+k2>2, the expected number of stable matchings is analyzed for three, progressively stronger, notions of stability. The expected number of weakly stable matchings is shown to grow super-exponentially fast. In contrast, for min⁡(k1,k2)>1, the fraction of instances with at least one strongly stable (super-stable) matching is super-exponentially small.

Random mechanisms for house allocation with existing tenants

We study the house allocation problem with existing tenants: n houses (stand for “indivisible objects”) are to be allocated to n agents; each agent needs exactly one house and has strict preferences; k houses are initially unowned; k agents initially do not own houses; the remaining n−k agents (the so-called “existing tenants”) initially own the remaining n−k houses (each owns one). In this setting, we consider various randomized allocation rules under which voluntary participation of existing tenants is assured and the randomization procedure either treats agents equally or discriminates against some (or all) of the existing tenants. We obtain two equivalence results, which generalize the equivalence results in Abdulkadiroğlu and Sönmez (1999) and Sönmez and Ünver (2005).

Finding strongly popular [formula omitted]-matchings in bipartite graphs

The computational complexity of the bipartite popular matching problem depends on how indifference appears in the preference lists. If one side has strict preferences while nodes on the other side are all indifferent (but prefer to be matched), then a popular matching can be found in polynomial time (Cseh et al., 2015). However, as the same paper points out, the problem becomes NP-complete if nodes with strict preferences are allowed on both sides and indifferent nodes are allowed on one side. We show that the problem of finding a strongly popular matching is polynomial-time solvable even in the latter case. More generally, we give a polynomial-time algorithm for the many-to-many version, i.e. the strongly popular b-matching problem, in the setting where one side has strict preferences while agents on the other side may have one tie of arbitrary length at the end of their preference list.

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

ЗАРАХУВАННЯ вступників ДО ЗАКЛАДІВ ВИЩОЇ ОСВІТИ ЯК ЗАДАЧА БАГАТОКРИТЕРІАЛЬНОГО ПРИЙНЯТТЯ РІШЕНЬ за УМОВ НЕВИЗНАЧЕНОСТІ

Проблема аналізу виконання передумов застосування алгоритму Гейла – Шеплі до розподілу вступників є актуальною, оскільки цей алгоритм використовується при прийомі до закладів вищої освіти в Україні та багатьох інших країнах. В роботі визначено основні фактори невизначеності, що стосуються переваг вступників і закладів вищої освіти та впливають на результати розподілу. Перехід до фінансування закладів вищої освіти за результатами діяльності може зменшити вплив цих невизначеностей.

UL36 Encoded by Marek's Disease Virus Exhibits Linkage-Specific Deubiquitinase Activity.

(1) Background: Deubiquitinase (DUB) regulates various important cellular processes via reversing the protein ubiquitination. The N-terminal fragment of a giant tegument protein, UL36, encoded by the Marek’s disease (MD) virus (MDV), encompasses a putative DUB (UL36-DUB) and shares no homology with any known DUBs. The N-terminus 75 kDa fragment of UL36 exists in MD T lymphoma cells at a high level and participates in MDV pathogenicity. (2) Methods: To characterize deubiquitinating activity and substrate specificity of UL36-DUB, the UL36 N-terminal fragments, UL36(323), UL36(480), and mutants were prepared using the Bac-to-Bac system. The deubiquitinating activity and substrate specificity of these recombinant UL36-DUBs were analyzed using various ubiquitin (Ub) or ubiquitin-like (UbL) substrates and activity-based deubiquitinating enzyme probes. (3) Results: The results indicated that wild type UL36-DUBs show a different hydrolysis ability against varied types of ubiquitin chains. These wild type UL36-DUBs presented the highest activity to K11, K48, and K63 linkage Ub chains, weak activity to K6, K29, and K33 Ub chains, and no activity to K27 linkage Ub chain. UL36 has higher cleavage efficiency for K48 and K63 poly-ubiquitin than linear ubiquitin chain (M1-Ub4), but no activity on various ubiquitin-like modifiers. The mutation of C98 and H234 residues eliminated the deubiquitinating activity of UL36-DUB. D232A mutation impacted, but did not eliminated UL36(480) activity. The Ub-Br probe can bind to wild type UL36-DUB and mutants UL36(480)H234A and UL36(480)D232A, but not C98 mutants. These in vitro results suggested that the C98 and H234 are essential catalytic residues of UL36-DUB. UL36-DUB exhibited a strict substrate specificity. Inhibition assay revealed that UL36-DUB exhibits resistance to the Roche protease inhibitor cocktail and serine protease inhibitor, but not to the Solarbio protease inhibitor cocktail. (4) Conclusions: UL36-DUB exhibited a strict substrate preference, and the protocol developed in the current study for obtaining active UL36-DUB protein should promote the high-throughput screening of UL36 inhibitors and the study on the function of MDV-encoded UL36.

Gehrlein stability in committee selection: parameterized hardness and algorithms

In a multiwinner election based on the Condorcet criterion, we are given a set of candidates, and a set of voters with strict preference ranking over the candidates. A committee is \em weakly Gehrlein stable (WGS) if each committee member is preferred to each non-member by at least half of the voters. Recently, Aziz et al. [IJCAI 2017] studied the computational complexity of finding a WGS committee of size k. They show that this problem is \sf NP -hard in general and polynomial time solvable when the number of voters is odd. In this article, we initiate a systematic study of the problem in the realm of parameterized complexity. We first show that the problem is \sf W [1]-hard when parameterized by the size of the committee. To overcome this intractability result, we use a known reformulation of WGS as a problem on directed graphs and then use parameters that measure the "structure'' of these directed graphs. In particular, we consider the majority graph, defined as follows: there is a vertex corresponding to each candidate, and there is a directed arc from a candidate c to $c'$ if the number of voters that \em prefer c over $c'$ is more than those that prefer $c'$ over c. The problem of finding WGS committee of size k corresponds to finding a vertex subset X of size k in the majority graph with the following property: the set X contains no vertex outside the committee that has an in-neighbor in X. Observe that the polynomial time algorithm of Aziz et al. [IJCAI 2017] corresponds to solving the problem on a tournament (a complete graph with orientation on edges). Thus, natural parameters to study our problem are "closeness'' to being a tournament. We define closeness as the number of missing arcs in the given directed graph and the number of vertices we need to delete from the given directed graph such that the resulting graph is a tournament. We show that the problem is fixed parameter tractable (\sf FPT ) and admits linear kernels with respect to closeness parameters. Finally, we also design an exact exponential time algorithm running in time $OO(1.2207^nn^OO(1) )$. Here, n denotes the number of candidates.

Axiomatizing logics of fuzzy preferences using graded modalities

The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou et al.'s minimal modal logic over a finite and linearly ordered residuated lattice. We then define appropriate extensions on a multi-modal language with graded modalities, both for weak and strict preferences, and with truth-constants. Actually, the presence of truth-constants in the language allows us to show that the modal operators □ and ◇ of the minimal modal logic are inter-definable. Finally, we propose an axiomatic system for this logic in an extended language (where the preference modal operators are definable), and prove completeness with respect to the intended graded preference semantics.

From 'Rates of Innovation' to Measures for 'Innovation Quality and Culture'

This study provides formal theoretical evidence that the concept of 'rates of innovation' is not amenable to imposition of any preference structure, as such is misleading and non-robust. Dearth of robustness derives from the finding that a decreasing rate of innovation can be shown to be strictly preferred to either of an increasing or constant rate of innovation. This finding rules out either of patent counts, citation-weighted patent counts, or the term, 'innovation rates' as robust parameters for comparative studies of cross-sections of innovation activity. The formal theoretical model endogenously generates two parameters for comparative studies of cross-sections of innovation activity that, respectively are constructs for 'quality of innovation', and 'frequency', equivalently, 'culture of innovation'. Given the parameter for culture of innovation is derived, in entirety, from the quality of innovation parameter, it is obtained in context of a strict preference for higher quality innovations that is formally and theoretically established. A strict preference for higher quality innovations is shown, under regular conditions, to imply an intertemporal 'decreasing cascade' for each of quality of innovation, and frequency of innovation, a cascade that, simultaneously is susceptible to stochastic arrival of innovation events that induce upward 'jumps' to the intertemporal decreasing cascade process. Preliminary empirical tests show the quality of innovation parameter outperforms GDP Per Capita as measure of quality of innovation within cross-sections of countries. Given the terminology, 'studies of rates of innovation' embeds a misnomer, study findings recommend substitution of the terminology, 'studies of Innovation Quality and Culture (IQC)'.

Engineering high-robustness DNA molecular circuits by utilizing nucleases.

Toehold-mediated strand displacement (TMSD) as an important player in DNA nanotechnology has been widely utilized for engineering non-enzymatic molecular circuits. However, these circuits suffer from uncontrollable leakage and unsatisfactory response speed. We utilized site-specific and sequence-independent nucleases to engineer high- robustness DNA molecular circuits. First, we found that the kinetics of the APE1-catalyzed reaction is highly dependent on substrate stability, allowing for the elimination of asymptotic leakage of DNA split circuits. Second, we obtained strict substrate preference of λ exonuclease (λexo) by optimizing the reaction conditions. Robust single-layer and cascade gates with leak resistance were established by using λ exo. Owing to the remarkably fast kinetics of these nucleases, all the circuits yield a high speed of computation. Compared to TMSD-based approaches, nuclease-powered circuits render advanced features such as leakage resistance, hundreds of times higher speed, and simplified structures, representing a class of promising artificial molecule systems.

Finding the Largest Successful Coalition under the Strict Goal Preferences of Agents

Coalition formation has been a fundamental form of resource cooperation for achieving joint goals in multiagent systems. Most existing studies still focus on the traditional assumption that an agent has to contribute its resources to all the goals, even if the agent is not interested in the goal at all. In this article, a natural extension of the traditional coalitional resource games (CRGs) is studied from both theoretical and empirical perspectives, in which each agent has uncompromising, personalized preferences over goals. Specifically, a new CRGs model with agents’ strict preferences for goals is presented, in which an agent is willing to contribute its resources only to the goals that are in its own interest set. The computational complexity of the basic decision problems surrounding the successful coalition is reinvestigated. The results suggest that these problems in such a strict preference way are complex and intractable. To find the largest successful coalition for possible computation reduction or potential parallel processing, a flow-network–based exhaust algorithm, called FNetEA, is proposed to achieve the optimal solution. Then, to solve the problem more efficiently, a hybrid algorithm, named 2D-HA, is developed to find the approximately optimal solution on the basis of genetic algorithm, two-dimensional (2D) solution representation, and a heuristic for solution repairs. Through extensive experiments, the 2D-HA algorithm exhibits the prominent ability to provide reassurances that the optimal solution could be found within a reasonable period of time, even in a super-large-scale space.

Incompleteness, regularity, and collective preference

AbstractThis paper examines the incompleteness of collective preference. We provide a series of Arrovian impossibility theorems without completeness. First, we consider the notion of regularity introduced by Eliaz and Ok (2006, Games and Economic Behavior 56, 61–86); it is an appropriate richness property for strict preference when preference is allowed to be incomplete. We examine the implication of imposing regularity on collective preference. Second, we propose responsiveness, a variation of positive responsiveness. This axiom requires that some changes in individual preferences make an alternative weakly better than another. Third, we consider coherency conditions for collective preferences; this conditionally requires the existence of comparable pairs in a certain manner. We prove an impossibility result for each condition using Arrovian axioms.

Using the Choice Sequence in Time Trade-Off as Discrete Choices: Do the Two Stories Match?

ObjectivesThe EQ-5D-5L valuation protocol recommends combining time trade-off (TTO) and discrete choice experiments (DCEs). DCEs that include a duration attribute (DCETTO) allow modeling on the quality-adjusted life-year scale. Because the choice sequence in a TTO can be construed as a series of DCETTO, we used data from a single TTO study to investigate the extent to which DCE values match TTO values when based on identical preferences. MethodsIn a TTO design in which a fixed set of choices were administered without termination at preference indifference, 202 individuals each valued 10 EQ-5D health states. From identified indifference points, we estimated three sets of TTO values: (i) plotting means and (ii) applying censored regressions at −1 and 1. Using all strict preferences, we (iii) estimated DCETTO values with a logit model and a bootstrap procedure. ResultsEstimated DCETTO and TTO values agreed well at the severe end of the quality-adjusted life-year scale, but with decreasing severity, DCETTO values were higher than TTO-values, with the difference peaking at 0.37 for the mildest health state. Left-censoring TTO values at −1 worsen the agreement for the worst health states and did not affect health states. Right censoring at 1 improved the agreement for mild states. ConclusionsTTO and the DCETTO values estimated from the same preference data diverged, with increasing difference for milder health states. Although the values converged when applying censored regression at +1, we question the validity of this adjustment.

Three-sided matching problem with mixed preferences

In this paper, we study the three-sided matching problems with mixed preferences, where three agent sets are U, V and W. We discussed two matching problems with different types of preferences. The first is that each $$u\in U$$ has a strict preference over set V, each $$v\in V$$ has a strict preference over set W, each $$w\in W$$ has a strict preference over set V and each $$w\in W$$ has a strict preference over set U. The second is that each $$u\in U$$ has a strict preference over set V, each $$v\in V$$ has a strict preference over set W and each $$w\in W$$ has a strict preference over set $$U\times V=\{(u,v)|u\in U,v\in V \}$$. For these two kinds of matching problems, we give the concept of stable matching and the algorithm of solving stable matching respectively. Finally, we discuss the relationship between these two matching problems.

Problem of Indifference and Choice

The aim of this paper is to anchor the problem of indifference and choice in a time continuum. Every action is future-oriented. The choice that is being made here and now is the choice that should, from a subjective point of view, eliminate a feeling of uneasiness toward the future. As Shackle (1972) notes, it is too late for the past and even for the present. The goal of this paper will allow us to look critically at an interesting ongoing discussion about the problem of indifference and choice. Debate is conducted primarily in circles of the Austrian School. This is because Nozick (1977) addressed the problem implying the invalidity of the law of diminishing marginal utility in the absence of a presupposition of indifference to the representatives of the Austrian school. The whole genesis of the discussion on the topic can be seen at the beginning of Block (2012). This paper briefly introduces the discussion and its main problems. Stated reservations will be removed by suggested solution based on the modification of the theory of subjective value presented in greater detail in Posvanc (2019a, 2019d). It will be shown that proposed solution improves conclusions in Wysocki (2016) and Wysocki-Block (2018, 2019). It will allow to preserve elements of indifference analysis as interpreted by the neoclassical mainstream, however, it will also allow interpretation of the problem of indifference and choice based on strict preferences from the point of view of the Austrian School of Economics. This is a quite controversial conclusion, but it is a logical consequence of the proposed modification in the theory of subjective value.

Structure-Guided Tuning of a Selectivity Switch towards Ribonucleosides in Trypanosoma brucei Purine Nucleoside 2'-Deoxyribosyltransferase.

The use of nucleoside 2'-deoxyribosyltransferases (NDTs) as biocatalysts for the industrial synthesis of nucleoside analogues is often hindered by their strict preference for 2'-deoxyribonucleosides. It is shown herein that a highly versatile purine NDT from Trypanosoma brucei (TbPDT) can also accept ribonucleosides as substrates; this is most likely because of the distinct role played by Asn53 at a position that is usually occupied by Asp in other NDTs. Moreover, this unusual activity was improved about threefold by introducing a single amino acid replacement at position 5, following a structure-guided approach. Biophysical and biochemical characterization revealed that the TbPDTY5F variant is a homodimer that displays maximum activity at 50 °C and pH 6.5 and shows a remarkably high melting temperature of 69 °C. Substrate specificity studies demonstrate that 6-oxopurine ribonucleosides are the best donors (inosine>guanosine≫adenosine), whereas no significant preferences exist between 6-aminopurines and 6-oxopurines as base acceptors. In contrast, no transferase activity could be detected on xanthine and 7-deazapurines. TbPDTY5F was successfully employed in the synthesis of a wide range of modified ribonucleosides containing different purine analogues.

Construction of models of students’ behavior based on matrixes of fuzzy relations considering their motivations to improve success in learning

Problem. In this article, the student behavior models are formalized, considering their motivation to improve the performance. The relevance of this topic is due to the need to introduce new information technologies into the education system of Ukraine, which are aimed at reforming the educational process in order to overcome the crisis in education and increase the level of professional education of university graduates. Goal. In the process of developing models, a large number of works were considered in which the problems of mathematical modeling and management of the learning process were discussed, with the aim of increasing student performance. The purpose of this article is to describe the behavior patterns of students for the development of information technologies aimed at improving academic performance. Methodology. To achieve this goal, the methods of cluster analysis, fuzzy sets and production modeling were used. Clustering parameters were determined as a result of processing statistical data obtained experimentally. According to the results of the experiments, the students were divided into typological groups depending on their performance, for this purpose a modified cluster analysis method was used. Considering poorly formalized factors, this task was presented as a decision-making task under conditions of uncertainty. The result of clustering was presented with the help of a fuzzy function, and production models of students' behavior during the test (exam) were built. Results. As a result, 5 models of students' behavior during the test (exam) were identified and described, and these models were formalized in the language of predicates. Matrices of fuzzy relations of students' preferences for evaluating their knowledge are built and formalized. The relations of strict preference for each model of student behavior are defined and a number of clearly non-dominant alternatives of student behavior that want to improve their academic performance are identified. Graphic representations of fuzzy possibilities of redistributing students to another typological group by academic performance, depending on their behavioral patterns, are constructed. Originality. This article proposes the production models of building up student behavior during the test (exam). Practical value. Formalization of student distribution models by typological groups depending on academic performance can be used in the development of an automated tool for creating information technology to form individual methods of teaching studentsProblem. In this article, the student behavior models are formalized, considering their motivation to improve the performance. The relevance of this topic is due to the need to introduce new information technologies into the education system of Ukraine, which are aimed at reforming the educational process in order to overcome the crisis in education and increase the level of professional education of university graduates. Goal. In the process of developing models, a large number of works were considered in which the problems of mathematical modeling and management of the learning process were discussed, with the aim of increasing student performance. The purpose of this article is to describe the behavior patterns of students for the development of information technologies aimed at improving academic performance. Methodology. To achieve this goal, the methods of cluster analysis, fuzzy sets and production modeling were used. Clustering parameters were determined as a result of processing statistical data obtained experimentally. According to the results of the experiments, the students were divided into typological groups depending on their performance, for this purpose a modified cluster analysis method was used. Considering poorly formalized factors, this task was presented as a decision-making task under conditions of uncertainty. The result of clustering was presented with the help of a fuzzy function, and production models of students' behavior during the test (exam) were built. Results. As a result, 5 models of students' behavior during the test (exam) were identified and described, and these models were formalized in the language of predicates. Matrices of fuzzy relations of students' preferences for evaluating their knowledge are built and formalized. The relations of strict preference for each model of student behavior are defined and a number of clearly non-dominant alternatives of student behavior that want to improve their academic performance are identified. Graphic representations of fuzzy possibilities of redistributing students to another typological group by academic performance, depending on their behavioral patterns, are constructed. Originality. This article proposes the production models of building up student behavior during the test (exam). Practical value. Formalization of student distribution models by typological groups depending on academic performance can be used in the development of an automated tool for creating information technology to form individual methods of teaching students

Short trading cycles: Paired kidney exchange with strict ordinal preferences

I study kidney exchange with strict ordinal preferences and with constraints on the lengths of the exchange cycles. Efficient deterministic mechanisms have poor fairness properties in this environment. Instead, I propose an individually rational, ordinally efficient and anonymous random mechanism for two-way kidney exchange based on Bogomolnaia and Moulin’s (2001) Probabilistic Serial mechanism. Individual rationality incentivizes patient–donor pairs who are compatible with each other to participate in the exchange, thus increasing the overall transplantation rate. Finally, individual rationality, ex-post efficiency and weak strategyproofness are incompatible for any mechanism.

(Il)legal Assignments in School Choice

Abstract In public school choice, students with strict preferences are assigned to schools. Schools are endowed with priorities over students. Incorporating constraints from different applications, priorities are often modelled as choice functions over sets of students. It has been argued that the most desirable criterion for an assignment is stability; there should not exist any blocking pair: no student shall prefer some school to her assigned school and have higher priority than some student who got into that school or the school has an empty seat. We propose a blocking notion where in addition it must be possible to assign the student to her preferred school. We then define the following stability criterion for a set of assignments: a set of assignments is legal if and only if any assignment outside the set is blocked with some assignment in the set and no two assignments inside the set block each other. We show that under very basic conditions on priorities, there always exists a unique legal set of assignments, and that this set has a structure common to the set of stable assignments: (i) it is a lattice and (ii) it satisfies the rural hospitals theorem. The student-optimal legal assignment is efficient and provides a solution for the conflict between stability and efficiency.

Robust continuous in vitro culture of the Plasmodium cynomolgi erythrocytic stages

The ability to culture pathogenic organisms substantially enhances the quest for fundamental knowledge and the development of vaccines and drugs. Thus, the elaboration of a protocol for the in vitro cultivation of the erythrocytic stages of Plasmodium falciparum revolutionized research on this important parasite. However, for P. vivax, the most widely distributed and difficult to treat malaria parasite, a strict preference for reticulocytes thwarts efforts to maintain it in vitro. Cultivation of P. cynomolgi, a macaque-infecting species phylogenetically close to P. vivax, was briefly reported in the early 1980s, but not pursued further. Here, we define the conditions under which P. cynomolgi can be adapted to long term in vitro culture to yield parasites that share many of the morphological and phenotypic features of P. vivax. We further validate the potential of this culture system for high-throughput screening to prime and accelerate anti-P. vivax drug discovery efforts.