Minimal extending sets in tournaments

In 2011, Brandt proposed a new tournament solution called the minimal extending set (ME). It was conjectured that ME satisfies a large number of desirable properties. In this paper, we non-constructively show that ME fails to satisfy most of these properties. However, no concrete examples of these violations are known and it appears that ME satisfies these properties for all practical purposes. This casts doubt on the axiomatic method.

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