Competitive intransitivity occurs when species' competitive abilities cannot be listed in a strict hierarchy, but rather form competitive loops, as in the game 'Rock-Paper-Scissors'. Indices are useful for summarizing intransitivity in communities; however, as with most indices, a great deal of information is compressed into single number. So while recent ecological theory, experiments, and nat...

Using a spatially explicit cellular automaton model with local competition, we investigate the potential for varied levels of competitive intransitivity (i.e., nonhierarchical competition) to promote species coexistence. As predicted, on average, increased levels of intransitivity result in more sustained coexistence within simulated communities, although the outcome of competition also becomes...

This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This w...

Competitive intransitivity, a situation in which species' competitive ranks cannot be listed in a strict hierarchy, promotes species coexistence through "enemy's enemy indirect facilitation." Theory suggests that intransitivity-mediated coexistence is enhanced when competitive interactions occur at local spatial scales, although this hypothesis has not been thoroughly tested. Here, we use a lat...

Philosophers have spent a great deal of time debating whether intransitive preferences can be rational. I present risky decision that poses challenge for the defender intransitivity. The intransitivity faces trilemma and must either: (i) reject rationality preferences, (ii) deny State-wise Dominance, or (iii) accept bizarre verdict you required to pay relabel tickets fair lottery. If we take fi...

Left and right commutativity and the Church-Rosser and reverse Church-Rosser properties are necessary conditions for a graph (frame) to be a (non-trivial) product of two other graphs, but their conjunction is not a sufficient condition. This work presents a fifth property, called H-V intransitivity, that, when added to the four previous properties, results in a necessary and sufficient conditio...

This paper addresses the issue of Split Intransitivity (si) and Unaccusative Mismatches (uMs), proposing a constraint-based approach to si and ums within a recent framework of Head-driven Phrase Structure Grammar. I argue against the widely accepted dichotomous distinction of intransitive verbs, which has been advanced by the Unaccusative Hypothesis [Perlmutter (1978)]. I then propose a quadrip...