Abstract
Perceiving differences by means of spatial analogies is intrinsic to human cognition. Multi-dimensional scaling (MDS) analysis based on Minkowski geometry has been used primarily on data on sensory similarity judgments, leaving judgments on abstractive differences unanalyzed. Indeed, analysts have failed to find appropriate experimental or real-life data in this regard. Our MDS analysis used survey data on political scientists' judgments of the similarities and differences between political positions expressed in terms of distance. Both distance smoothing and majorization techniques were applied to a three-way dataset of similarity judgments provided by at least seven experts on at least five parties' positions on at least seven policies (i.e., originally yielding 245 dimensions) to substantially reduce the risk of local minima. The analysis found two dimensions, which were sufficient for mapping differences, and fit the city-block dimensions better than the Euclidean metric in all datasets obtained from 13 countries. Most city-block dimensions were highly correlated with the simplified criterion (i.e., the left–right ideology) for differences that are actually used in real politics. The isometry of the city-block and dominance metrics in two-dimensional space carries further implications. More specifically, individuals may pay attention to two dimensions (if represented in the city-block metric) or focus on a single dimension (if represented in the dominance metric) when judging differences between the same objects. Switching between metrics may be expected to occur during cognitive processing as frequently as the apparent discontinuities and shifts in human attention that may underlie changing judgments in real situations occur. Consequently, the result has extended strong support for the validity of the geometric models to represent an important social cognition, i.e., the one of political differences, which is deeply rooted in human nature.
Highlights
The expression of differences in terms of spatial analogies appears to be intrinsic to human cognition
A common criterion for interpreting stress is that stress below 0.1 indicates a good fit. Given that this criterion was met for all countries, we can say that the multidimensional scaling (MDS) yielded a good fit in an only two-dimensional solution for our data
The analysis provides two implications immediately drawn from the results and one inferred from the geometric property of the Minkowski metric
Summary
The expression of differences in terms of spatial analogies appears to be intrinsic to human cognition. Based on Minkowski geometric modeling, multidimensional scaling (MDS) has primarily analyzed the similarity judgment data related to visual and auditory sensations [2,3,4,5]. The judgment of abstract differences in semantics lies close to the core of human intelligence but is hard to analyze with geometric modeling. Modeling the analysis of semantic differences requires assignment of a real number, known as a distance, to represent the (dis)similarity between the objects in terms of meanings that are more subtle than sensations. Reasoning and/or taxonomy when obtaining semantic similarity judgment data tend to depend exclusively on experimental controls that differ among studies [6,7,8,9] and may not have immediate relevance to real social contexts
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