Is the left-right alignment of parties outdated?

The advocates of modern western democracy promote the viewpoint that the class division of the society is becoming outdated. We attempt to disprove this statement with an example of 28 German parties who participated in the 2013 federal election. The official party positions on 38 policy issues are considered and the parties are identified with vectors of this 38-dimensional policy space. The statement in question, that there is no predominant political axis, would imply that the party vectors are scattered homogeneously, making a ball-shaped cloud of `observations'. However, the Prime Component Analysis (PCA) shows that the party vectors constitute a thin ellipsoid whose two longest diameters cover 83.4% of the total variance. The consequent party ordering is the left-right axis rolled in a circumference, making the far-left and far-right ends meet. Basing on this empirical evidence, we conclude that neither the left-right characterization of parties nor the class opposition is outdated.

Next, it is shown that the electoral success is highly correlated with the number of party members, but not with the party's capacity to represent public opinion. For this purpose, a representativeness index is defined which measures how well the party policy profiles match with the results of 36 public opinion polls on 36 out of the 38 policy issues mentioned. To reveal representativeness trends, the parties are ordered contiguously, with neighboring parties having close policy profiles. This contiguous ordering is found with four optimization methods: (1) dimensionality reduction by means of PCA, (2) traveling salesman problem to construct the shortest chain of proximate parties, (3) least squares to minimize the distances between parties with close profiles, and (4) largest squares to maximize the distances between parties with opposite profiles. The most salient trend is observed for the circular left-right party ordering found with the PCA. The best representatives of public opinion are the moderate left, next come the far-left and the far-right, and the least representative are moderate right (conservative) parties.