Stability in Spatial Voting Games with Restricted Preference Maximizing

Spatial models of simple majority rule voting suggest that stable decisions are not likely to exist under normal circumstances. Yet this instability result stands in contrast to the stability observed in experiments. This article examines the effect of relaxing the assumption that voting is costless by requiring a proposal to be a finite distance closer to a member’s ideal point than the pending proposal before it is regarded as attractive. Using the concept of the epsilon-core the article estimates the minimal decision costs that guarantee stable outcomes. It shows that the minimal costs are equal to the minimal finagle radius (Wuffle et al., 1989) and that the epsilon-core contains the finagle point which is close to the center of the yolk. While the analytical model establishes that the minimal costs are smaller than the yolk radius, computational simulations of majority voting by committees of size 3 to 101 suggest that this is a weak upper bound, only, as the ratio of minimal costs to the yolk radius usually is small and decreases as committee size approaches infinity.