We explore the implications of consistency in sequencing problems. We first identify all rules satisfying Pareto indifference, individual rationality, and consistency. Next, we ask whether there is a rule satisfying the three axioms together with either one of two additional own-time monotonicity requirements: an agent should lose (or gain) as a result of changes in his service time. As it turn...

Let −∞ ≤ a < b ≤ ∞, let f and g be continuously differentiable functions defined on the interval (a, b), and let r = f/g and ρ = f /g. In [13], general “rules” for monotonicity patterns, resembling the usual l’Hospital rules for limits, were given. For example, according to Proposition 1.9 in [13], one has the following: if ρ is increasing and gg > 0 on (a, b), then r ցր, which means that there...

In many real problem domains, the main variable of interest behaves monotonically in the observable variables, in the sense that higher values for the variable of interest become more likely with higher-ordered observations. This type of knowledge appears to arise naturally during knowledge elicitation, without explicit prompting. The monotonicity properties declared by experts, however, may no...

We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as monotonic functions of the hyperparameters. Our proposed algorithm adapts Bayesia...

We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the axiom of self-consistent monotonicity. The class of win-loss combining scoring procedures is introduced which contains a majority of known scoring procedures. Tw...

Noise in multi-criteria data sets can manifest itself as non-monotonicity. Work on the remediation of such non-monotonicity is rather scarce. Nevertheless, errors are often present in real-life data sets, and several monotone classification algorithms are unable to use such partially non-monotone data sets. Fortunately, as we will show here, it is possible to restore monotonicity in an optimal ...

Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while ...

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity known to be necessary for Bayesian...