Intersecting 2 layers without creating duplication using QGIS?

Question

I have 2 polygons that i wish to combine into one layer, in QGIS.

on the first layer (neighborhoods) i have bigger areas (that divide a city to 7 major areas, or smaller neighborhoods). that i wish to intersect with a second layer (statistical areas) that is built of smaller polygons- this layer holds population numbers and other data. when I perform intersect, from the second layer i get duplication of the areas, so that each smaller area can show in one or two of the larger areas. i want to perform this combination, while either:

1) setting a rule that each of the smaller area will be associated only with one of the bigger areas, the one that the majority of the polygon is in

or

2) create the same intersection with the duplication but that an attribute of my choice (population number) will be divided relatively to the size of the area that is relevant to the bigger area (under the assumption that the population is equally distributed)

Answer 1

This method should let you achieve your first option, "each of the smaller area will be associated only with one of the bigger areas"

1. Select the sliver polygons using the "select features by expression" tool, with the expression $area < threshold. Substitute a minimal area value where the expression says "threshold".

2. Use the tool "eliminate selected polygons" to dissolve the slivers into nearby adjacent polygons.

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Your second option is more complicated, but doable. Have a look at the several questions on GIS SE about calculating values proportional to area, eg Calculate proportional area of polygon within another layer's polygon

Basically you'll use the Field Calculator to add an "old_area" field before you run the intersection, and add a "new_area" field after the intersection. Then calculate "new_area"/"old_area" and multiply by the field you want to scale.