Slitherine

To quote (my interest is in the italicized part):

5.2.3. Advantages of Provinces
A province allows you to pool resources and production across the regions of the province, as well as allowing the option of automating population and building management. In addition to items that are fully pooled across the region (such as military equipment), resources such as food are partially pooled and moved between regions if one is short of food. If a region has a surplus of food or infrastructure points, it will share up to 50% of current production and 15% of anything that is stockpiled. Finally, regions that are part of a province, only contribute 50% of the per-turn decadence score of a region on its own (8.1.4).

So, Food and Infrastructure points are shared, but how does that sharing work? Does it only compensate for those regions which have a negative production rate, to avoid the food and infrastructure count in a region from suffering the effects of having less Food or Infrastructure points than those that are needed (in other words, to avoid essentially going negative)? Or will it actually contribute to building up the stockpile of Food and Infrastructure in those regions which are below some certain value?

The fact that I am drilling down to learn enough to ask these questions shows that I'm really enjoying the game

Food is shifted to compensate for shortages, so in effect a region with -ve production gets protected, but I think there is a more general balancing as well so that surpluses are shared around.

Infra is more deliberate. You must have at least one region in the province actively building (I think that shuffling counts for this), then all those not building will send their surplus infra to the regions that are building. So be careful, if you have -ve infra production and nothing is being built there is no protection (can often happen by mid-game if all the building slots are used up).

Remember if you have -ve infra production in a region there is a risk of a building falling down.