Intransitivity

Counting Tournaments with a Specified Number of Circular Triads

We investigate the counting of tournaments with a specified number of circular triads (3-cycles). We derive the generating functions for the sequences of the counts, and give explicit expressions for the sequences for when the number of circular …

triad (on private)

Supports Circular Triad-Related Calculations

Number of n-node tournaments that have exactly d circular triads

Scissors beats Rock (and other failures of Transitive Models using Paired Comparisons)

If the Utah Jazz beat the Portland Trailblazers and the Trailblazers beat the Denver Nuggets, does that mean that the Jazz are better than the Nuggets, or could the Nuggets actually be better than the Jazz? To answer this question, we investigate the …

Modeling Stochastically Intransitive Relationships in Paired Comparison Data

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a …

CRSP: Modeling Stochastically Intransitive Relationships between NBA Teams

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could diehard Spurs fans make a …

CRSP: Modeling Stochastically Intransitive Relationships between NBA Teams

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could diehard Spurs fans make a …