Assigning points which are very close to the boundary when polygons share boundaries?

Based on my literature review, it's a common practice to divide the crash by number of polygons it intersect with.

Urban Bicyclists: Spatial Analysis of Adult and Youth Traffic Hazard Intensity

“In this case study, 42% of crashes happen to fall on tract boundaries, which renders the issue all the more critical. Several options exist in this situation. The first is to use the address assigned to the crash by the reporting officer as recorded on the police report……A significant drawback of this method stems from the accuracy of the recorded address…… Another option is recording boundary crashes twice—once in each of the tracts it shares or up to five times for crashes occurring at the convergence of five different census tracts. This method also introduces error by creating a false number of total crashes and also gives more weight to the boundary crashes over others as they are counted more frequently. A third alternative is to apportion the crash, giving a count of one half to each tract if it is on the border between two census units, one third if it is at an intersection of three units, and so forth. Although this is a more time-consuming process, it should produce the most accurate representation of the number of crashes per tract of the three options presented and is the approach taken in this analysis.”

Macrolevel Model Development for Safety Assessment of Road Network Structures (it refers to the article above)

“For the quantitative features of the road network, the GIS spatial join function was used to extract signals, intersections, roads, and average annual daily traffic data at the TAZ level. In this study, a method proposed by Lovegrove and Sun was applied to treat roads on the TAZ boundary (6). Polyline or point features on the TAZ boundaries were shared by corresponding TAZs by use of a prerating with a weight equal to the reciprocal of the related TAZs. By this method, an intersection on the boundaries of three TAZs, for example, was assigned a weight of 0.333. The roads on the TAZ boundary were assigned by the number of adjacent TAZs.” “However, studies that focused on the spatial distributions of crashes at intersections found that crashes at intersections were not equally distributed among the four approaches (32). In this study, the vehicle traveling directions recorded in the crash data were used.”

Investigation of road network features and safety performance

“In this study, a method proposed by Sun and Lovegrove (2010) was applied to assign roads on the TAZ boundary. Polyline or point features on the TAZ boundaries were shared by corresponding TAZs by pre-rating them with a weight equal to the reciprocal of related TAZs. Using this method, an intersection on the boundaries of three TAZs (for example) would be assigned a weight of 0.333. The roads on the TAZ boundary were assigned by the number of adjacent TAZs.”