On the logic of preference and judgment aggregation

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The recently emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation of such rules. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox - which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation - including classical preference aggregation.

Computational social choice is a new interdisciplinary research area at the intersection of social choice theory and computer science that studies computational aspects of social choice mechanisms as well as applications of social choice ideas in the design and analysis of computing systems. Research on computational social choice now encompasses a variety of topics, including the algorithmic aspects of voting rules, computational barriers to strategic behaviour, collective decision-making in multi-agent systems, preference elicitation and communication issues in voting, fair division, computational aspects of weighted voting games, collective decision-making in combinatorial domains, logic-based formalisms for social choice problems, belief and judgement aggregation, and social software. The aim of this special issue is to build on the spectacular success of two workshops on computational social choice (COMSOC’06, Amsterdam and COMSOC’08, Liverpool), and provide a forum for reseachers in the area to present their ideas on a variety of topics. This special issue is composed of nine research articles and a short note that span a fairly wide range of issues, including voting, mechanism design, judgment aggregation, and fairness, and a similarly wide range of techniques, such as logic, experiments, and computational complexity. The paper by Agotnes, van der Hoek and Wooldridge defines a new modal logic for representing and reasoning about preference and judgment aggregation. The authors show that their logic can be used to express a variety of concepts and results from the social choice domain, including majority voting, the discursive paradox, Arrow’s theorem and Condorcet’s paradox. Baharad, Goldberger, Koppel and Nitzan propose a maximum likelihood estimation-based approach for aggregating voters’ opinions over several issues. They argue that their method is vastly superior to simple majority voting, and use both analytical and empirical evaluation to support their argument. Balan, Richards and Luke deal with the problem of selecting a sequence of actions when the actions have multiple beneficiaries. Their goal is to select the actions according to a lexicographic fairness criterion. The explore the complexity of this problem for both finite and infinite sequences of actions and present both algorithms and intractability results for this problem. The paper by Caminada and Pigozzi applies argumentation theory to judgment aggregation, and proposes aggregation operators satisfying not only the usual property of collective rationality, but another highly desirable property,

Preference aggregation and judgment aggregation are two basic research models of group decision making. And preference aggregation has been deeply studied in social choice theory. However, researches of social choice theory gradually focus on judgment aggregation which appears recently. Judgment aggregation focuses on how to aggregate many consistent logical formulas into one, from the perspective of logic. We try to start with judgment aggregation model based on logic and then explore different solutions to problem of judgment aggregation.

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p263.pdf **Abstract:** We simulate voting rules for multiwinner elections in a model of judgment aggregation that distinguishes between rationality and feasibility constraints. These constraints restrict the structure of the individual judgments and of the collective outcome computed by the rule, respectively. We extend known results regarding the simulation of single-winner voting rules to the multiwinner setting, both for elections with ordinal preferences and for elections with approval-based preferences. This not only provides us with a new tool to analyse multiwinner elections, but it also suggests the definition of new judgment aggregation rules, by generalising some of the principles at the core of well-known multiwinner voting rules to this richer setting. We explore this opportunity with regards to the principle of proportionality. Finally, in view of the computational difficulty associated with many judgment aggregation rules, we investigate the computational complexity of our embeddings and of the new judgment aggregation rules we put forward.

Judgment aggregation is a recent theory that combines aggregation problems previously studied by social choice theory with logic. Social choice theory is a vast subject, including not only the study of preference aggregation and voting theory but also topics like social welfare and justice. Given the tight links between judgment aggregation and preference aggregation, in this first chapter we give a concise survey on some historical aspects of preference aggregation and then introduce and motivate the more recent field of judgment aggregation. The chapter builds on [Sen99, Sen86, Bla58] for the historical overview on social choice theory, and on [KS93, Kor92] for the informal introduction to judgment aggregation.

Comparative evaluation of moisture susceptibility of modified/foamed asphalt binders combined with different types of aggregates using surface free energy approach

This paper presents the results of research focused on the modification of composition of the polymer-cement mortars. The use of these materials is quite wide. The greatest use can be found in the production of reinforced concrete repair materials. Specifically, the article analyzes problems of lightweight aggregate effect on the resistance of polymer-cement mortars to extremely high temperatures. The link is particularly evident with the risk of fire. Attention was given to the two different types of aggregates - from primary raw materials (Liapor) and alternative sources of raw materials (fly ash aggloporite). The study was carried out by the laboratory analyzing the basic material characteristics of prepared samples which were exposed to temperatures up to 1200 ° C.

To investigate the mechanical properties of recycled aggregate concrete filled square steel tubular column under bias voltage, and to analyze the effects of three influencing factors (steel ratio, eccentricity and different types of aggregates) on mechanical properties of test specimens. The experimental results indicated that recycled aggregate concrete filled square steel tubular column had high bearing capacity and excellent deformation performance, and its final fracture morphology was similar to that of common concrete-filled steel tube, which was bending failure. Steel ratio, eccentricity and different types of aggregates had significantly effects on the mechanical properties of bias column. Mid-span longitudinal strain distribution of the test specimens could basically satisfy the plane cross-section assumption, the calculated value according to standard GB 50936-2014 was close to the measured value, which was more suitable for calculating the bearing capacity of bias column.

Perhaps the most influential result in social choice theory is Arrow’s impossibility theorem, which states that a seemingly modest set of desiderata cannot be satisfied when aggregating preferences [1]. While Arrow’s theorem might appear rather negative, it can also be interpreted in a positive way by identifying what can be achieved in preference aggregation.In this talk, I present a number of variations of Arrow’s theorem–such as those due to Mas-Colell and Sonnenschein [8] and Blau and Deb [2]–in their choice-theoretic version. The critical condition in all these theorems is the assumption of a rationalizing binary relation or equivalent notions of choice-consistency. The bulk of my presentation contains three escape routes from these results. The first one is to ignore consistency with respect to a variable set of alternatives altogether and require consistency with respect to a variable electorate instead. As Smith [12] and Young [14] have famously shown, this essentially characterizes the class of scoring rules, which contains plurality and Borda’s rule. For the second escape route, we factorize choice-consistency into two parts, contraction-consistency and expansions-consistency [11]. While even the mildest dose of the former has severe consequences on the possibility of choice, varying degrees of the latter characterize a number of appealing social choice functions, namely the top cycle, the uncovered set, and the Banks set [3,9,4]. Finally, I suggest to redefine choice-consistency by making reference to the set of chosen alternatives rather than individual chosen alternatives [6]. It turns out that the resulting condition is a weakening of transitive rationalizability and can be used to characterize the minimal covering set and the bipartisan set. Based on a two decades-old conjecture due to Schwartz [10], the tournament equilibrium set can be characterized by the same condition or, alternatively, by a weak expansion-consistency condition from the second escape route. Whether Schwartz’s conjecture actually holds remains a challenging combinatorial problem as well as one of the enigmatic open problems of social choice theory.Throughout the presentation I will discuss the algorithmic aspects of all considered social choice functions. While some of the mentioned functions can be easily computed, other ones do not admit an efficient algorithm unless P equals NP [13,5,7].

This paper aims at evaluating the compressive strength of structural sand lightweight aggregate concrete (LWC) by the non-destructive ultrasonic pulse velocity method. To this end, a comprehensive experimental study was carried out involving more than 70 different compositions tested between 3 and 180 days with mean compressive strengths ranging from about 30 to 80 MPa and density classes from D1.6 to D2.0. The influence of several factors on the relation between the ultrasonic pulse velocity (UPV) and compressive strength was examined, including the type and binder content, type and volume of aggregates. It is found that lightweight and normal weight concretes (NWC) are affected differently by mix design parameters. NWC is more affected by the volume of aggregate and the dispersion effect caused by concrete heterogeneity tends to be lower in LWC. The prediction of the concrete's compressive strength by means of the non-destructive UPV test is analysed. Based on the dependence of the UPV on the density and elasticity of concrete, a simplified expression is proposed to estimate the compressive strength, regardless of the type of concrete and its composition. High correlation coefficients were obtained taking into account several results for different types of aggregates and concrete compositions.

Supramolecular structure of ultrathin films of hemicyanine dye bearing a crown ether group (CrHCR) was tuned by lateral pressure and investigated by means of compression isotherms, UV-vis and fluorescence spectroscopies, and X-ray reflectivity. Two different types of aggregation were revealed, depending on the absence or the presence of metal cations in the water subphase. While CrHCR forms at high surface pressures head-to-tail stacking aggregates on pure water, changing the subphase to a metal-cation-containing one leads to the appearance of well-defined excimers with head-to-head orientation. The structure of monolayers transferred onto solid supports by the Langmuir-Blodgett (LB) technique was examined by use of X-ray reflectivity measurements and molecular modeling. A model of cation-induced excimer formation in hemicyanine Langmuir monolayers is proposed. Finally, fluorescence emission properties of LB films of CrHCR can be managed by appropriate changes in the subphase composition, this last one determining the type of chromophore aggregation.

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of individual inputs in two aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth.

The problem of disposal of concrete scrap of dismantled building structures is relevant for most countries of the world. For Ukraine, this problem is even more acute due to the significant amount of destruction caused by hostilities and rocket attacks. In current research the properties of concrete and fibre-reinforced concrete for the bases of road clothes based on natural and secondary aggregates were compared: granite river gravel, secondary crushed stone with a heterogeneous composition, quartz sand and secondary sand from recycled reinforced concrete structures. CEM III/A slag Portland cement with a blast furnace slag content of 65% and a polycarboxylate type superplasticizer were used. Three series of samples were studied: without fibre; with glass fibre ANTI-CRAK HP 12 (length 12 mm, diameter 0.017 mm, equivalent thread diameter 0.3 mm) in the amount of 1 kg/m3; with polypropylene fibre BeneSteel 55 (length 55 mm, equivalent thread diameter 0.48 mm) in the amount of 4 kg/m3. In each series, concrete on granite gravel and quartz sand, concrete on secondary crushed stone and quartz sand, concrete on secondary crushed stone and secondary sand were studied. The workability of all mixtures was equal to S1. Due to the use of different types of aggregates and fibres, the W/C of concrete mixtures differed significantly. Concretes on secondary aggregates had a higher W/C than on natural aggregates. When using the Anti-Crak HP 12 fibre, the mobility of mixtures with equal W/C increased by 5.5 – 6.9 %. When using BeneSteel 55 fibre, W/C increased by 10.6 – 15.5 %. The type of aggregate had a significant effect on the average density of concrete. When using secondary crushed stone and quartz sand, the average density decreased by 3.8 – 4.6 %. When using secondary crushed stone simultaneously with secondary sand, the average density of concrete decreased by 5.2 – 8.5 %. When using Anti-Crak HP 12 fiber, the average density of concrete decreases by 2 %, when using BeneSteel 55 fibre – up to 4.1 %. Concretes on secondary crushed stone with heterogeneous composition and quartz sand had 4 % higher compressive strength and 2 % higher tensile strength in bending than concretes on granite gravel and similar sand (29.8 MPa and 3.18 MPa, respectively). When secondary crushed stone is used simultaneously with secondary sand, the compressive strength of concrete is only 1.1 % lower than the strength of concrete on natural aggregates, and the tensile strength in bending is 10 % lower. This confirms the possibility of effective use of these concretes for arranging of bases of road clothes. The high-quality performance of secondary aggregates in concrete explains due to their better adhesion to the cement-sand matrix. Dispersed fibre reinforcement with Anti-Crak HP 12 has a positive effect on the compressive strength of concrete on all types of aggregate and increases the tensile strength of concrete on natural aggregates. The use of BeneSteel 55 fibre was not effective due to a significant increase in the W/C of the mixture when it was introduced. In general, taking into account the economic factor, dispersion reinforcement of concrete on secondary aggregates with the types of fibres used in the research is not advisable.

Analysis of the effect of aggregate type on the dynamic behaviour of concrete