Fair rating countries based on border quality with neighbours

On an imaginary map we have countries which can have between 1 and 20 neighbours with discrete boundaries.

We want to rate each country based on the quality of its boundaries with each of its neigbours

So that we can come up with a comparison scheme to rank countries based on the quality of their boundaries.

So for example:

Country A has 8 boundaries (8 neighbours) 4 of which are good boundaries +/- some uncertainty

Country B has 3 boundaries (3 neighbours) 2 of which are good boundaries +/- some uncertainty

So Country B rank > Country A rank ?

The problem requires comparison on features (boundaries) that vary in number for each country.

A comparison scheme suggests that there is some function which is proportionate to the number of good boundaries and inversely proportionate to the total number of boundaries that each country has.

Unmoderated this simple proportionality would be a decaying saw tooth pattern with decreasing frequency with number of boundaries, which impedes simple ranking between countries with disparate number of boundaries.

What would be a fair* and valid way of rating the countries based on boundary quality in such a way that they can be compared?

*Note 'fair' here relates to appropriate weighting scheme to compensate for number of neighbors.

https://stackoverflow.com/questions/65760644/fair-rating-countries-based-on-border-quality-with-neighbours January 17, 2021 at 08:36PM