The Vote Compass FAQ links through to a methodology paper: http://voxpoplabs.com/votecompass/methodology.pdf

It talks about using factor analysis to uncover underlying latent dimensions.

However, I think this means the definition of those dimensions then depends on the questions asked; e.g. the dimension they call “social” appears to be “degree of care for refugees”. i.e. If I ask 10 questions about football, and then 10 questions about random topics, factor analysis — without knowing the questions — could detect there is a latent dimension highly correlated with those 10 questions (and them with each other), and can further give a weighting for how much each of those 10 question correlates.

Because there are multiple questions on asylum seekers, that is the latent dimension that would be detected.

I am not sure if this is the best approach, unless you have a broad selection of questions.