By asking the people voting how well they feel they are able to express their interests and how well they think the result expresses the group interest.

In this case it sounds like they’ve got a group who are used to voting together and having outcomes that don’t make it very clear exactly what the group wants, and then after implementing this the group found the results much more expressive.

Specifically, how does one measure democracy? I hadn't thought about this before, but I'm intrigued and no good answers are springing to mind.

there is a democracy index: https://en.wikipedia.org/wiki/Democracy_Index

there is something similar for voting systems but it isn't as elegant: https://en.wikipedia.org/wiki/Comparison_of_electoral_system...