Finagle's Law and the Finagle Point, a New Solution Concept for Two-Candidate Competition in Spatial Voting Games Without a Core

We investigate the geometry underlying Finagle's Law, which states, "No matter what happens, you can come out ahead if you just know how to finagle," and we introduce a new solution concept for two-candidate sequential spatial voting games, the "finagle point." The finagle radius is the radius of a circle such that if a candidate locates at its center, some alternative in the circle can beat any alternative in the space. The finagle point is the point with minimum finagle radius-from it a candidate can, with only minuscule changes in his initial policy location, find a response to any challenger that will defeat that challenger. For each possible candidate location, we provide a geometric construction which gives an outer bound for its "finagle radius," a measure of the attractiveness of that location to a finagling politician. For three-voter games without a core, we provide an analytic solution for the point with minimal finagle radius that guarantees that the maximum finagle needed to defeat an opponent will, in general, be quite small relative to the Pareto set. We also show how the construction used to generate the finagle point in the three-voter case can be extended to the n-voter case. The basic idea underlying the finagle point is that it is unnecessary (and indeed usually impossible) to find a position that will defeat all challengers, but it is possible to find a position that is virtually invulnerable to challenge, since any position that beats it can be countered by shifting to a position very close to the original location that will defeat the challenger. Moreover, even if not at the point with minimal finagle radius, in searching for positions to respond optimally to the location of the other candidate, a candidate will in general not find it necessary to move far from an initial point located near the finagle point, since points located near the finagle point will also have a small finagle radius.

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