I don't think I need to track the IDs. As long as the variables for each ID enter into the corresponding columes for each observation in the final dataset, It is OK to not have IDs. So the first three colums in the final dataset are the housing price, school quality, and share of greenspace for ID 92, because that is the first choice for observation 1, The 3-6 columns are housing price, school quality, and share of green space for ID 72 (the second choice for observation 1). The last three columns will be housing price, school quality, and share of green space for ID 54 for observation 1.
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