The instrumental variables (IV) method provides a way to estimate the causal effect of a treatment when there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment. An additional assumption often mad...

In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way — giving each agent a piece with a value of at least 1/n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are connected. We propose two additional requirements: ...

We study the monotonicity properties of solutions in the classic problem of fair cake-cutting — dividing a heterogeneous resource among agents with different preferences. Resourceand population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all o...

Complex economic models often lack the structure for the application of standard techniques in monotone comparative statics. Generalized monotonicity analysis (GMA) extends the available methods in several directions. First, it provides a way of finding parameter moves that yield monotonicity of model solutions. Second, it allows studying the monotonicity of functions or subsets of variables. T...

Heterogeneous Treatment Effects: Instrumental Variables without Monotonicity? A fundamental identification problem in program evaluation arises when idiosyncratic gains from participation and the treatment decision depend on each other. Imbens and Angrist (1994) were the first to exploit a monotonicity condition in order to identify an average treatment effect parameter using instrumental varia...

For positive integers n,d, the hypergrid [n]d is equipped with the coordinatewise product partial ordering denoted by ≺. A function f : [n]d → N is monotone if ∀x ≺ y, f (x)≤ f (y). A function f is ε-far from monotone if at least an ε fraction of values must be changed to make f monotone. Given a parameter ε , a monotonicity tester must distinguish with high probability a monotone function from...

The effect of non-monotonicity of similarity measures is addressed which can be observed when measuring the similarity between patterns with increasing displacement. This effect becomes the more apparent the less smooth the pattern is. It is proven that commonly used similarity measures like f -divergence measures or kernel functions show this non-monotonicity effect which results from neglecti...

We know that the same set of selected extrema can be represented by a large number of different monotonicity graphs. We are interested in understanding how different, or how similar, the converged reconstruction results can be with respect to different monotonicity graphs. To do so, we made the following experiment. We constructed 100 random monotonicity graphs for the 2D vorticity data set (Fi...

Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over (abstract) variables. Size-change graphs are a subclass where only constraints of the form x > y and x ≥ y are allowed. Both theory and practice are now more evolv...

Termination analysis is often performed over the abstract domains of monotonicity constraints or of size change graphs. First, the transition relation for a given program is approximated by a set of descriptions. Then, this set is closed under a composition operation. Finally, termination is determined if all of the idempotent loop descriptions in this closure have (possibly different) ranking ...