scholarly journals Impossibility Results for Nondifferentiable Functionals

Econometrica ◽  
2012 ◽  
Vol 80 (4) ◽  
pp. 1769-1790 ◽  
Keyword(s):  
Impossibility Results ◽  
Nondifferentiable Functionals

Impossibility Results for Rational Belief

Noûs ◽  
2017 ◽  
Vol 53 (1) ◽  
pp. 134-159 ◽  
Author(s):  
Gerhard Schurz
Keyword(s):  
Rational Belief ◽  
Impossibility Results

scholarly journals Preferences Single-Peaked on a Circle

2020 ◽  
Vol 68 ◽  
pp. 463-502 ◽  
Author(s):  
Dominik Peters ◽  
Martin Lackner
Keyword(s):  
Polynomial Time ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Recognition Algorithm ◽  
Approval Voting ◽  
Voting Rules ◽  
One Dimensional ◽  
Facility Location Problems ◽  
Impossibility Results ◽  
Fast Recognition

We introduce the domain of preferences that are single-peaked on a circle, which is a generalization of the well-studied single-peaked domain. This preference restriction is useful, e.g., for scheduling decisions, certain facility location problems, and for one-dimensional decisions in the presence of extremist preferences. We give a fast recognition algorithm of this domain, provide a characterisation by finitely many forbidden subprofiles, and show that many popular single- and multi-winner voting rules are polynomial-time computable on this domain. In particular, we prove that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle. In contrast, Kemeny's rule remains hard to evaluate, and several impossibility results from social choice theory can be proved using only profiles in this domain.

The computational power of the W and GHZ states

2006 ◽  
Vol 6 (2) ◽  
pp. 173-183
Author(s):  
E. D'Hondt ◽  
P. Panangaden
Keyword(s):  
Pure State ◽  
Lie Symmetry ◽  
Leader Election ◽  
Ghz State ◽  
W State ◽  
Computational Power ◽  
Post Processing ◽  
Distributed Consensus ◽  
Quantum Networks ◽  
Impossibility Results

It is well understood that the use of quantum entanglement significantly enhances the computational power of systems. Much of the attention has focused on Bell states and their multipartite generalizations. However, in the multipartite case it is known that there are several inequivalent classes of states, such as those represented by the W-state and the GHZ-state. Our main contribution is a demonstration of the special computational power of these states in the context of paradigmatic problems from classical distributed computing. Concretely, we show that the W-state is the only pure state that can be used to exactly solve the problem of leader election in anonymous quantum networks. Similarly we show that the GHZ-state is the only one that can be used to solve the problem of distributed consensus when no classical post-processing is considered. These results generalize to a family of W- and GHZ-like states. At the heart of the proofs of these impossibility results lie symmetry arguments.

Does Climate Change Policy Depend Importantly on Population Ethics?

2021 ◽  
pp. 111-136
Author(s):  
Gustaf Arrhenius ◽  
Mark Budolfson ◽  
Dean Spears
Keyword(s):  
Climate Change ◽  
Policy Evaluation ◽  
Climate Change Policy ◽  
Policy Response ◽  
Population Ethics ◽  
Impossibility Results ◽  
Climate Policies ◽  
Change Policy ◽  
Population Axiology

Choosing a policy response to climate change seems to demand a population axiology. A formal literature involving impossibility theorems has demonstrated that all possible approaches to population axiology have one or more seemingly counterintuitive implications. This leads to the worry that because axiological theory is radically unresolved, this theoretical ignorance implies serious practical ignorance about what climate policies to pursue. This chapter offers two deflationary responses to this worry. First, it may be that given the actual facts of climate change, all axiologies agree on a particular policy response. In this case, there would be a clear dominance conclusion, and the puzzles of axiology would be practically irrelevant (albeit still theoretically challenging). Second, despite the impossibility results, the authors prove the possibility of axiologies that satisfy bounded versions of all of the desiderata from the population axiology literature, which may be all that is needed for policy evaluation.

Unrestricted and controlled identification of loss functions: Possibility and impossibility results

2019 ◽  
Vol 35 (3) ◽  
pp. 878-890
Author(s):  
Robert P. Lieli ◽  
Maxwell B. Stinchcombe ◽  
Viola M. Grolmusz
Keyword(s):  
Loss Functions ◽  
Impossibility Results
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