one in $9

That prompted me to wonder what the population split between islands is.

Over three-quarters of the population (76.4%) live in the North Island...

From the Wikipedia page, but I can't find a citation for that particular figure.

So 1/9 of the roading spend is disproportionate to the population: $2.5/9 would be fairer.

With a similar geographic area and only a third of the relative population, SI would need more than their population based share to have equivalent quality roading.