>>Can you show me a specific problem with the definitions?
I don't just disagree with the definitions, I disagree with the entire idea that one may map ideologies on two arbitrary dimensions.
Why not: map all ideologies on the dimensions "loyalty" and "frivolity"? Or "Pascal" and "Descartes"?
It's a meaningless parlor game.
A mapping of people's political views onto two dimensions will be oversimplified, but not nearly as eggregiously so as the even more common mapping onto a single dimension. A method of quantifying the usefulness of the two-dimensional mapping would be to rate various people on a third dimension and then produce a 3d scatterplot using that new dimension along with the existing two. If the 2d mapping does well to determine people's positions on the third issue, the resulting points will be concentrated along a 2d contour (analagous to the way nice data will be concentrated along a 1d curve on a 2d scatterplot). If the third issue is orthagonal to the first two dimensions, then no such concentration will exist.
Personally, I would think it interesting to plot "abortion" as a third axis, where positive maximum allows abortion on demand for any reason at any time, while negative maximum forbids any and all abortions, period. I would expect a loose clustering of the abortion result along a contour, but with a lot of scatter.