A Characterization of Lexicographic Preferences

This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: a weaker notion of continuity called “mild continuity” (strict preference order between any two alternatives that are different with respect to every attribute is preserved around their small neighborhoods) and an “unhappy set” (any alternative outside such a set is preferred to all alternatives inside). Three key aspects of our characterization are as follows: (i) we use continuity arguments; (ii) we use the stepwise approach of looking at two attributes at a time; and (iii) in contrast with the previous literature, we do not impose noncompensation on the preference and consider an alternative weaker condition.

Roberts’ weak welfarism theorem: a minor correction

Roberts’ “weak neutrality” or “weak welfarism” theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts (Rev Econ Stud 47(2):421–439, 1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors—that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated.

Structural Determinants of Substrate Specificity of SplF Protease from Staphylococcus aureus

Accumulating evidence suggests that six proteases encoded in the spl operon of a dangerous human pathogen, Staphylococcus aureus, may play a role in virulence. Interestingly, SplA, B, D, and E have complementary substrate specificities while SplF remains to be characterized in this regard. Here, we describe the prerequisites of a heterologous expression system for active SplF protease and characterize the enzyme in terms of substrate specificity and its structural determinants. Substrate specificity of SplF is comprehensively profiled using combinatorial libraries of peptide substrates demonstrating strict preference for long aliphatic sidechains at the P1 subsite and significant selectivity for aromatic residues at P3. The crystal structure of SplF was provided at 1.7 Å resolution to define the structural basis of substrate specificity of SplF. The obtained results were compared and contrasted with the characteristics of other Spl proteases determined to date to conclude that the spl operon encodes a unique extracellular proteolytic system.

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.

An intuitionistic logic for preference relations

We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely axiomatizable in first-order logic.

N-Reciprocity Property for Interval-Valued Fuzzy Relations with an Application to Group Decision Making Problems in Social Networks

In this paper we study interval-valued fuzzy relations. We consider preference relations, i.e. a triplet consisting of strict preference, indifference and incomparability which are defined with the use of a fuzzy negation. We analyze the preservation of the fuzzy negation based reciprocity property of interval-valued fuzzy relations by aggregation functions and by some basic interval-valued fuzzy relations. We use diverse representa-tions of aggregation functions. We also consider the connection between N-reciprocal relations and transitivity properties. We provide a numerical example where the final alternative is chosen with the use of generalized voting method, where admissible linear orders for intervals are applied.

THE FITTING-ATTITUDE ANALYSIS OF VALUE RELATIONS AND THE PREFERENCES VS. VALUE JUDGEMENTS OBJECTION

According to Wlodek Rabinowicz's (2008) fitting-attitude analysis of value relations, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. Rabinowicz's account is subject, however, to one important objection: if strict preferences involve betterness judgements, then his analysis contrasts with the intuitive understanding of parity. In this paper, I examine Rabinowicz's three responses to this objection and argue that they do not succeed. I then propose an alternative solution. I argue that the objection can be avoided if we ‘relativize’ Rabinowicz's account and define parity in terms of opposite strict preferences between two items that are only relatively permissible, rather than permissible simpliciter. I argue that this account of parity can be defended if we take seriously the distinction between sufficient and decisive reason for a preference relation. I also show that, on the basis of this distinction, we can arrive at a more extensive taxonomy of value relations than the one proposed by Rabinowicz.

The strong and the weak: evaluation in modal desideratives

<p>Modal auxiliaries can generate two desiderative readings: strong (1) and weak (2) desiderativity. These differ notably in whether they express strict preference and whether they are felicitous out of the blue.</p><p>(1) (A: Cookie anyone?) B: I would like/enjoy a cookie.</p><p>(2) #(A: Cookie anyone?) B: I would/might have/take/eat a cookie.</p><p>We provide an analysis that accounts for the contrast by introducing 1) a comparison operator ≥ as part of the subjective morphology that can be pragmatically strengthened to &gt; and 2) a criterion determining how alternative situations are introduced for comparison which allows introduction by evaluatives (<em>like</em>, <em>enjoy</em>).</p>