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Sequence Semantics for Modelling Reason-based Preferences

Calardo E., Governatori G., Rotolo A.

Fundamenta Informaticae

2018

Vol. 158, nr 1/3

217--238

We study how the non-classical n-ary operator ⊗, originally intended to capture the concept of reparative obligation, can be used in the context of social choice theory to model preferences. A novel possible-world model-theoretic semantics, called sequence semantics, was proposed for the operator. In this paper, we propose a sound and complete axiomatisation of a minimal modal logic for the operator, and we extend it with axioms suitable to model social choice consistency principles such as extension consistency and contraction consistency. We provide completeness results for such extensions.

Logics for Modelling Collective Attitudes

Porello D.

Fundamenta Informaticae

2018

Vol. 158, nr 1/3

239--275

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained.

Selection of subcontractors using ordinal ranking methods based on Condorcet approach

Biruk S., Jaśkowski P.

Budownictwo i Architektura

2016

Vol. 15, nr 4

33--40

A choice of a subcontractor may have critical impact on realization of the project, it has influence on the cost, duration, and quality. Selection of the best sucontractor can be defined as multiple criteria decision making problem (MCDM) of choosing a proper offer from set of alternatives evaluated by using set of criteria. Decision maker should determine the criteria as objective and measurable. Significance of decision making problem is presented by large amount of theories and methods developed for solving MCDM problems and number of criteria considered in these problems. A Condorcet method (formulated over two centuries ago) is commonly accepted for democratic (majority of criteria determines the winner) and fair election – a Condorcet winner is the alternative which is preferred in all pair-wise comparisons. According to social choice theory where a Condorcet winner cannot be obtained from a set of alternatives, the best solution is close to being a Condorcet winner. The paper presents four selection methods of the best alternative that is as close as possible to being a Condorcet winner and contains examples of a subcontractor selection using only ordinal scales of evaluation of alternatives.