I find J.B. Harley's Maps, Knowledge, and Power, to be a particularly relevant analysis when attempting to understand the issues around flood plain mapping in NYC. Harley exclaims that "It is true that in political geography and the history of geographical thought the link is increasingly being made between maps and power... but the particular role of maps, as images with historically specific codes, remains largely undifferentiated from the wider geographical discourse in which they are often embedded."
I believe this is an especially relevant observation. First of all, the issue of flood plain maps involves drawing lines that necessarily create areas of spatial exclusion or inclusion. The presence of a building inside or outside of a flood zone has major implications for its owner in the form of its perceived risk. This can then trigger a host of upgrades and additional insurance obligations requiring potentially destabilizing capital expenditures while simultaneously reducing property value. So the power of these maps is significant.
The maps cannot be viewed in isolation however, as some academics (such as Sarah Praille at Syracuse) make connections between lines drawn on a flood plain map and the so-called redlining (red lines on maps) defining poor and minority areas as "high risk" for investment. These historical scars are not absent from the current debate, but are rather present as a form of historical knowledge.
At the same time, these maps have an obligation to accurately express risk to both current and future residents. The question then becomes, what obligation does the flood plain mapping process have to rectify both historical and current gaps in equity, if that compromises an accurate depiction of risk? Is it acceptable to modify maps designed to accurately express risk in order to appease various factions through a politicized process?