The Finagle Point and the Epsilon-Core: A Comment on Bräuninger’s Proof
نویسنده
چکیده
The Finagle point (Wuffle et al., 1989), the yolk (McKelvey, 1986; Ferejohn et al., 1984) and the epsilon-core (Wooders, 1983; Salant and Goodstein, 1990; Tovey, 2010; Feld and Grofman, 1991) are three solution concepts that have been proposed to predict the outcome of majority voting in the Euclidean spatial model. Relationships among these three concepts are investigated in (Bra̋uninger, 2007). In particular, it is claimed there that the Finagle point is within the epsilon-core. The main purpose of this note is to point out that the proof of this claim has a significant logical gap. I do not know whether or not the claimed result is true, but I will show that the argument given there is not sufficient to prove it. Definitions: We are given a odd cardinality set of voter ideal points in <. A line is median if at least half the voter ideal points lie in each closed halfplane defined by the line. For two points x and y we say x y (x is majority preferred to y) if at least half the voter ideal points are not farther from x than they are from y. Similarly, for two points x and y we say x y (x is epsilon-preferred to y) if at least half the voter ideal points are not more than farther from y than from x. For x ∈ <, the ball of radius δ around x is denoted D(x, δ) ≡ {y : ||x− y|| ≤ δ}.
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