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A coupled cell system is a network of dynamical systems, or 'cells', coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells that preserves all internal dynamics and all couplings. Symmetry can… (More)

Let A Z D be the Cantor space of Z D-indexed configurations in a finite alphabet A, and let σ be the Z D-action of shifts on A Z D. A cellular automaton is a continuous, σ-commuting self-map Φ of A Z D , and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset A ⊂ A Z D. Suppose a ∈ A Z D is A-admissible everywhere except for some small region we… (More)

Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations ('views') on a family of logically interconnected propositions, or yes/no issues. However, simply complying with the majority opinion in each issue often yields a logically inconsistent collective view. Thus, we consider the… (More)

Let A Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let σ be the shift map on A Z. A cellular automaton is a continuous, σ-commuting self-map Φ of A Z , and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset S ⊂ A Z. Suppose a ∈ A Z is S-admissible everywhere except for some small region we call a defect. It has been… (More)

Sequential majority voting over interconnected binary propositions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, under what circumstances this happens for some sequence of the voting process. It turns out that the class of aggregation spaces for which this difficulty arises is very… (More)

Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent truth-valuations ('judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. We show that, for a variety of spaces, proposi-tionwise… (More)