Towards a General Methodology of Bridging Ideological Spaces

Abstract

Bridging ideological spaces is an important, but relatively troubled branch of the scaling literature. The most common bridging procedure, joint-scaling, ignores structural differences between groups resulting in uninformative results. Alternatively, dimensional-mapping addresses this issue by using transformation rather than merging. However, current implementations cannot bridge multi-dimensional spaces nor estimate ideal points non-parametrically. Furthermore, these methods require shared individuals between the two groups. To address these major issues, we introduce a generalized methodology for dimensional-mapping that enables both non-parametric and multi-dimensional ideal point estimation using either real or ''synthetic anchors.'' Synthetic anchors remove the stringent anchor assumption and are generated by transferring a small number of individuals from one group to the other and, when used appropriately, do not distort the ideological space. We demonstrate the utility of our methodology on two sets of voter-politician data from the United States and Japan by comparing its performance with existing approaches. Our results suggest that not only does our method make less stringent assumptions and is more widely applicable than existing techniques, but our approach also generates bridged ideal point estimates comparable to those generated by other methods.

Keywords: Ideal-Point Estimation, Bridging, Procrustes Transformation, Non- Parametric