We_PNP argue_VVB that_CJT the_AT0 database_NN1 reconstruction_NN1 experiment_NN1 is_VBZ flawed_AJ0 because_CJS the_AT0 Census_NN1 Bureau_NN1 never_AV0 compared_VVN their_DPS results_NN2 with_PRP a_AT0 null_AJ0 model_NN1 to_TO0 evaluate_VVI how_AVQ effectively_AV0 it_PNP worked_VVD ._SENT As_CJS it_PNP stands_VVZ ,_PUN the_AT0 Census_NN1 Bureau_NN1 experiment_NN1 is_VBZ like_PRP a_AT0 clinical_AJ0 trial_NN1 with_PRP no_AT0 control_NN1 group_NN1 ;_PUN just_AV0 because_CJS some_DT0 patients_NN2 recover_VVB ,_PUN that_DT0 does_VDZ not_XX0 provide_VVI evidence_NN1 that_CJT the_AT0 treatment_NN1 was_VBD effective_AJ0 ._SENT To_TO0 evaluate_VVI the_AT0 database_NN1 reconstruction_NN1 experiment_NN1 ,_PUN it_PNP is_VBZ not_XX0 sufficient_AJ0 to_TO0 count_VVI the_AT0 matches_NN2 between_PRP the_AT0 reconstructed_AJ0 population_NN1 and_CJC the_AT0 real_AJ0 population_NN1 ._SENT Rather_AV0 ,_PUN we_PNP must_VM0 assess_VVI how_AVQ much_DT0 the_AT0 reconstruction_NN1 experiment_NN1 outperforms_VVZ a_AT0 null_AJ0 model_NN1 of_PRF random_AJ0 guessing_NN1 ._SENT 
It_PNP is_VBZ reasonable_AJ0 to_TO0 expect_VVI one_PNI would_VM0 get_VVI a_AT0 lot_NN1 of_PRF matches_NN2 between_PRP the_AT0 reconstructed_AJ0 data_NN0 and_CJC the_AT0 real_AJ0 data_NN0 purely_AV0 by_PRP chance_NN1 ._SENT The_AT0 Census_NN1 Bureau_NN1 's_POS new_AJ0 documentation_NN1 of_PRF the_AT0 experiment_NN1 shows_VVZ that_CJT the_AT0 "_PUQ exact_AJ0 match_NN1 rate_NN1 "_PUQ was_VBD positively_AV0 associated_VVN with_PRP the_AT0 number_NN1 of_PRF people_NN0 on_PRP the_AT0 block_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 ,_PUN p._NN0 4_CRD )_PUR :_PUN The_AT0 larger_AJC the_AT0 block_NN1 ,_PUN the_AT0 more_AV0 exact_AJ0 matches_NN2 ;_PUN in_PRP fact_NN1 ,_PUN large_AJ0 blocks_NN2 had_VHD three_CRD times_NN2 the_AT0 match_NN1 rate_NN1 of_PRF small_AJ0 blocks_NN2 ._SENT Database_NN1 reconstruction_NN1 ought_VM0 to_TO0 work_VVI best_AV0 with_PRP small_AJ0 blocks_NN2 where_AVQ the_AT0 published_AJ0 tables_NN2 directly_AV0 reveal_VVB unique_AJ0 combinations_NN2 of_PRF respondent_NN1 characteristics_NN2 ._SENT The_AT0 obvious_AJ0 explanation_NN1 is_VBZ that_CJT larger_AJC blocks_NN2 have_VHB higher_AJC odds_NN2 of_PRF including_VVG by_PRP chance_NN1 any_DT0 specific_AJ0 combination_NN1 of_PRF age_NN1 ,_PUN sex_NN1 ,_PUN race_NN1 ,_PUN and_CJC ethnicity_NN1 ._SENT 
In_PRP the_AT0 real_AJ0 2010_CRD population_NN1 ,_PUN 57_CRD %_NN0 of_PRF persons_NN2 are_VBB unique_AJ0 at_PRP the_AT0 census_NN1 block-level_NN1 with_PRP respect_NN1 to_PRP the_AT0 combination_NN1 of_PRF age_NN1 ,_PUN sex_NN1 ,_PUN race_NN1 ,_PUN and_CJC ethnicity_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 )_PUR ._SENT This_DT0 means_VVZ that_CJT 43_CRD %_NN0 of_PRF persons_NN2 reside_VVB on_PRP a_AT0 block_NN1 with_PRP one_CRD or_CJC more_DT0 other_AJ0 people_NN0 who_PNQ share_VVB their_DPS exact_AJ0 characteristics_NN2 ._SENT This_DT0 also_AV0 suggests_VVZ that_CJT a_AT0 person_NN1 with_PRP randomly_AV0 selected_AJ0 characteristics_NN2 would_VM0 have_VHI a_AT0 reasonably_AV0 high_AJ0 chance_NN1 of_PRF exactly_AV0 matching_VVG someone_PNI on_PRP any_DT0 given_AJ0 block_NN1 ._SENT 
The_AT0 Census_NN1 Bureau_NN1 did_VDD not_XX0 calculate_VVI the_AT0 odds_NN2 that_CJT they_PNP could_VM0 get_VVI matches_NN2 between_PRP their_DPS hypothetical_AJ0 reconstructed_AJ0 population_NN1 and_CJC the_AT0 actual_AJ0 population_NN1 purely_AV0 by_PRP chance_NN1 ._SENT Our_DPS analysis_NN1 suggests_VVZ ,_PUN however_AV0 ,_PUN that_DT0 among_PRP the_AT0 minority_NN1 of_PRF cases_NN2 where_AVQ the_AT0 Census_NN1 Bureau_NN1 did_VDD find_VVI a_AT0 match_NN1 between_PRP their_DPS hypothetical_AJ0 population_NN1 and_CJC a_AT0 real_AJ0 person_NN1 ,_PUN most_DT0 of_PRF the_AT0 matches_NN2 would_VM0 be_VBI expected_VVN to_TO0 occur_VVI by_PRP chance_NN1 ._SENT 
To_TO0 investigate_VVI the_AT0 issue_NN1 ,_PUN we_PNP conducted_VVD a_AT0 simple_AJ0 Monte_NP0 Carlo_NP0 simulation_NN1 ._SENT We_PNP estimate_VVB that_CJT randomly_AV0 chosen_AJ0 age_NN1 –_PUN sex_NN1 combinations_NN2 would_VM0 match_VVI someone_PNI on_PRP any_DT0 given_AJ0 block_NN1 52.6_CRD %_NN0 of_PRF the_AT0 time_NN1 ,_PUN assuming_VVG the_AT0 age_NN1 ,_PUN sex_NN1 ,_PUN and_CJC block_NN1 size_NN1 distributions_NN2 from_PRP the_AT0 2010_CRD census_NN1 ._SENT To_TO0 estimate_VVI the_AT0 percentage_NN1 of_PRF random_AJ0 age_NN1 –_PUN sex_NN1 combinations_NN2 that_CJT would_VM0 match_VVI someone_PNI on_PRP a_AT0 block_NN1 by_PRP chance_NN1 ,_PUN we_PNP generated_VVD 10_CRD ,_PUN 000_CRD simulated_AJ0 blocks_NN2 and_CJC populated_VVD them_PNP with_PRP random_AJ0 draws_NN2 from_PRP the_AT0 2010_CRD single-year-of-age_NN1 and_CJC sex_NN1 distribution_NN1 ._SENT The_AT0 simulated_AJ0 blocks_NN2 conformed_VVN to_PRP the_AT0 population-weighted_AJ0 size_NN1 distribution_NN1 of_PRF blocks_NN2 observed_VVN in_PRP the_AT0 2010_CRD census_NN1 ._SENT We_PNP then_AV0 randomly_AV0 drew_VVD 10_CRD ,_PUN 000_CRD new_AJ0 age_NN1 –_PUN sex_NN1 combinations_NN2 and_CJC searched_VVD for_PRP them_PNP in_PRP each_DT0 of_PRF the_AT0 10_CRD ,_PUN 000_CRD simulated_AJ0 blocks_NN2 ._SENT Footnote_NN1 1_CRD In_PRP 52.6_CRD %_NN0 of_PRF cases_NN2 we_PNP found_VVD someone_PNI in_PRP the_AT0 simulated_AJ0 block_NN1 who_PNQ exactly_AV0 matched_VVD the_AT0 random_AJ0 age_NN1 –_PUN sex_NN1 combination_NN1 ._SENT The_AT0 relationship_NN1 between_PRP block_NN1 size_NN1 and_CJC the_AT0 percent_NN0 of_PRF random_AJ0 age_NN1 –_PUN sex_NN1 combinations_NN2 present_NN1 appears_VVZ in_PRP Fig._NN1 1._CRD 
We_PNP would_VM0 therefore_AV0 expect_VVI the_AT0 Census_NN1 Bureau_NN1 to_TO0 be_VBI "_PUQ correct_AJ0 "_PUQ on_PRP age_NN1 and_CJC sex_NN1 most_AV0 of_PRF the_AT0 time_NN1 even_AV0 if_CJS they_PNP had_VHD never_AV0 looked_VVN at_PRP the_AT0 tabular_AJ0 data_NN0 from_PRP 2010_CRD and_CJC had_VHD instead_AV0 just_AV0 assigned_VVN ages_NN2 and_CJC sexes_NN2 to_PRP their_DPS hypothetical_AJ0 population_NN1 at_PRP random_AJ0 ._SENT The_AT0 randomly_AV0 simulated_AJ0 population_NN1 was_VBD similar_AJ0 to_PRP the_AT0 real_AJ0 census_NN1 population_NN1 with_PRP respect_NN1 to_PRP the_AT0 frequency_NN1 of_PRF unique_AJ0 respondents_NN2 :_PUN we_PNP found_VVD that_CJT 47.7_CRD %_NN0 of_PRF the_AT0 simulated_AJ0 population_NN1 was_VBD unique_AJ0 within_PRP the_AT0 block_NN1 with_PRP respect_NN1 to_PRP age_NN1 and_CJC sex_NN1 ,_PUN compared_VVN with_PRP 44_CRD %_NN0 in_PRP the_AT0 real_AJ0 population_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 )_PUR ._SENT 
Our_DPS calculation_NN1 does_VDZ not_XX0 factor_NN1 in_PRP race_NN1 or_CJC ethnicity_NN1 ,_PUN but_CJC because_CJS of_PRF high_AJ0 residential_AJ0 segregation_NN1 most_DT0 blocks_NN2 are_VBB highly_AV0 homogenous_AJ0 with_PRP respect_NN1 to_PRP race_NN1 and_CJC ethnicity_NN1 ._SENT If_CJS we_PNP assign_VVB everyone_PNI on_PRP each_DT0 block_NN1 the_AT0 most_AV0 frequent_AJ0 race_NN1 and_CJC ethnicity_NN1 of_PRF the_AT0 block_NN1 using_VVG data_NN0 from_PRP the_AT0 census_NN1 (_PUL U.S._NP0 Census_NN1 Bureau_NN1 ,_PUN 2012_CRD )_PUR ,_PUN then_AV0 race_NN1 and_CJC ethnicity_NN1 assignment_NN1 will_VM0 be_VBI correct_AJ0 in_PRP 77.8_CRD %_NN0 of_PRF cases_NN2 ._SENT Using_VVG that_DT0 method_NN1 to_TO0 adjust_VVI the_AT0 random_AJ0 age_NN1 –_PUN sex_NN1 combinations_NN2 described_VVN above_AV0 ,_PUN 40.9_CRD %_NN0 of_PRF cases_NN2 would_VM0 be_VBI expected_VVN to_TO0 match_VVI on_PRP all_DT0 four_CRD characteristics_NN2 to_PRP a_AT0 respondent_NN1 on_PRP the_AT0 same_DT0 block_NN1 ._SENT That_DT0 does_VDZ not_XX0 differ_VVI greatly_AV0 from_PRP the_AT0 Census_NN1 Bureau_NN1 's_VHZ reported_VVN 46.48_CRD %_NN0 match_NN1 rate_NN1 for_PRP their_DPS reconstructed_AJ0 data_NN0 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 ,_PUN 2021b_NP0 ,_PUN p._NN0 3_CRD )_PUR ._SENT 
Despite_PRP the_AT0 Census_NN1 Bureau_NN1 's_POS massive_AJ0 investment_NN1 of_PRF resources_NN2 and_CJC computing_AJ0 power_NN1 ,_PUN the_AT0 database_NN1 reconstruction_NN1 technique_NN1 does_VDZ not_XX0 perform_VVI much_AV0 better_AJC than_CJS a_AT0 random_AJ0 number_NN1 generator_NN1 combined_VVN with_PRP a_AT0 simple_AJ0 assignment_NN1 rule_NN1 for_PRP race_NN1 and_CJC ethnicity_NN1 ._SENT This_DT0 is_VBZ analogous_AJ0 to_PRP a_AT0 clinical_AJ0 trial_NN1 in_PRP which_DTQ the_AT0 treatment_NN1 and_CJC the_AT0 placebo_NN1 produce_VVI virtually_AV0 the_AT0 same_DT0 outcome_NN1 ._SENT 
Re-identification_NN1 Experiment_NN1 
The_AT0 Census_NN1 Bureau_NN1 took_VVD the_AT0 experiment_NN1 one_CRD step_NN1 further_AV0 by_PRP assessing_VVG whether_CJS their_DPS hypothetical_AJ0 population_NN1 shared_VVD characteristics_NN2 with_PRP people_NN0 who_PNQ appeared_VVD in_PRP non-census_AJ0 sources_NN2 ._SENT Within_PRP each_DT0 block_NN1 they_PNP matched_VVD the_AT0 age_NN1 and_CJC sex_NN1 of_PRF persons_NN2 in_PRP the_AT0 hypothetical_AJ0 population_NN1 to_PRP the_AT0 age_NN1 and_CJC sex_NN1 of_PRF persons_NN2 in_PRP financial_AJ0 and_CJC marketing_NN1 data_NN0 purchased_VVN from_PRP commercial_AJ0 vendors_NN2 after_PRP the_AT0 2010_CRD census_NN1 (_PUL Rastogi_NP0 &_NP0 O'Hara_NP0 ,_PUN 2012_CRD )_PUR ._SENT A_AT0 match_NN1 on_PRP race_NN1 or_CJC ethnicity_NN1 was_VBD not_XX0 required_VVN for_PRP this_DT0 experiment_NN1 ._SENT In_PRP most_DT0 cases_NN2 ,_PUN the_AT0 hypothetical_AJ0 individuals_NN2 constructed_VVN by_PRP the_AT0 Census_NN1 Bureau_NN1 did_VDD not_XX0 share_VVI the_AT0 same_DT0 age_NN1 ,_PUN sex_NN1 ,_PUN and_CJC block_NN1 as_PRP anyone_PNI in_PRP the_AT0 commercial_AJ0 data_NN0 ;_PUN in_PRP just_AV0 45_CRD %_NN0 of_PRF cases_NN2 was_VBD there_AV0 at_PRP least_AV0 one_CRD person_NN1 in_PRP the_AT0 commercial_AJ0 data_NN0 who_PNQ matched_VVD the_AT0 age_NN1 ,_PUN sex_NN1 and_CJC block_NN1 number_NN1 of_PRF at_PRP least_AV0 one_CRD row_NN1 of_PRF the_AT0 hypothetical_AJ0 database_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 )_PUR ._SENT This_DT0 45_CRD %_NN0 match_NN1 rate_NN1 between_PRP the_AT0 reconstructed_AJ0 data_NN0 and_CJC the_AT0 commercial_AJ0 data_NN0 is_VBZ substantially_AV0 lower_AJC than_CJS one_PNI would_VM0 expect_VVI by_PRP chance_NN1 ._SENT Our_DPS simulation_NN1 exercise_NN1 —_PUN also_AV0 based_VVN only_AV0 on_PRP age_NN1 and_CJC sex_NN1 —_PUN suggests_VVZ that_CJT one_PNI would_VM0 expect_VVI a_AT0 52.6_CRD %_NN0 match_NN1 rate_NN1 for_PRP a_AT0 random_AJ0 population_NN1 ._SENT 
Among_PRP the_AT0 cases_NN2 where_AVQ there_EX0 was_VBD at_PRP least_AV0 one_CRD person_NN1 in_PRP the_AT0 commercial_AJ0 database_NN1 who_PNQ matched_VVD the_AT0 age_NN1 ,_PUN sex_NN1 ,_PUN and_CJC block_NN1 of_PRF a_AT0 row_NN1 in_PRP the_AT0 hypothetical_AJ0 population_NN1 ,_PUN the_AT0 Census_NN1 Bureau_NN1 then_AV0 harvested_VVN the_AT0 names_NN2 from_PRP the_AT0 commercial_AJ0 database_NN1 and_CJC attempted_VVD to_TO0 match_VVI them_PNP with_PRP names_NN2 on_PRP the_AT0 same_DT0 block_NN1 as_CJS enumerated_VVN in_PRP the_AT0 2010_CRD census_NN1 ._SENT They_PNP found_VVD that_CJT 38_CRD %_NN0 of_PRF the_AT0 names_NN2 from_PRP the_AT0 commercial_AJ0 database_NN1 were_VBD actually_AV0 present_AJ0 on_PRP the_AT0 block_NN1 ._SENT Based_VVN on_PRP this_DT0 exercise_NN1 ,_PUN the_AT0 Census_NN1 Bureau_NN1 claimed_VVD to_TO0 have_VHI successfully_AV0 "_PUQ re-identified_VVN "_PUQ 16.85_CRD %_NN0 (_PUL 38_CRD %_NN0 of_PRF 45_CRD %_NN0 )_PUR of_PRF the_AT0 population_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 )_PUR ._SENT 
Once_AV0 again_AV0 ,_PUN there_EX0 is_VBZ no_AT0 null_AJ0 model_NN1 for_PRP comparison_NN1 purposes_NN2 ._SENT One_PNI would_VM0 expect_VVI that_CJT people_NN0 recorded_VVN as_PRP residing_VVG on_PRP any_DT0 given_AJ0 block_NN1 in_PRP a_AT0 2010_CRD commercial_AJ0 database_NN1 would_VM0 have_VHI a_AT0 high_AJ0 chance_NN1 of_PRF also_AV0 appearing_VVG on_PRP the_AT0 same_DT0 block_NN1 in_PRP the_AT0 2010_CRD Census_NN1 ._SENT Is_VBZ the_AT0 38_CRD %_NN0 match_NN1 rate_NN1 on_PRP names_NN2 between_PRP the_AT0 commercial_AJ0 database_NN1 high_AJ0 or_CJC low_AJ0 ?_SENT Without_PRP access_NN1 to_PRP internal_AJ0 Census_NN1 data_NN0 ,_PUN it_PNP is_VBZ impossible_AJ0 for_PRP us_PNP to_TO0 construct_VVI a_AT0 usable_AJ0 control_NN1 group_NN1 ,_PUN but_CJC it_PNP would_VM0 have_VHI been_VBN simple_AJ0 for_PRP the_AT0 Census_NN1 Bureau_NN1 to_TO0 do_VDI so_AV0 ._SENT In_PRP particular_AJ0 ,_PUN the_AT0 Census_NN1 Bureau_NN1 could_VM0 have_VHI attempted_VVN to_TO0 match_VVI the_AT0 names_NN2 of_PRF people_NN0 randomly_AV0 selected_VVN from_PRP the_AT0 commercial_AJ0 database_NN1 to_PRP persons_NN2 in_PRP the_AT0 2010_CRD census_NN1 living_VVG on_PRP the_AT0 same_DT0 census_NN1 block_NN1 ,_PUN without_PRP any_DT0 reference_NN1 to_PRP the_AT0 Census_NN1 Bureau_NN1 's_POS database_NN1 reconstruction_NN1 ._SENT If_CJS the_AT0 38_CRD %_NN0 match_NN1 rate_NN1 on_PRP names_NN2 for_PRP the_AT0 reconstructed_AJ0 population_NN1 is_VBZ no_AV0 higher_AJC than_CJS the_AT0 match_NN1 rate_NN1 for_PRP a_AT0 randomly_AV0 selected_AJ0 subset_NN1 of_PRF the_AT0 commercial_AJ0 data_NN0 ,_PUN it_PNP would_VM0 mean_VVI the_AT0 database_NN1 reconstruction_NN1 has_VHZ no_AT0 effect_NN1 on_PRP re-identification_NN1 risk_NN1 ._SENT Without_PRP any_DT0 comparison_NN1 to_PRP a_AT0 null_AJ0 model_NN1 ,_PUN the_AT0 match_NN1 rates_NN2 quoted_VVN by_PRP the_AT0 Census_NN1 Bureau_NN1 between_PRP the_AT0 commercial_AJ0 database_NN1 and_CJC the_AT0 census_NN1 enumeration_NN1 are_VBB not_XX0 meaningful_AJ0 ._SENT 
Small_AJ0 Blocks_NN2 and_CJC Swapping_VVG 
In_PRP a_AT0 recent_AJ0 supplemental_AJ0 court_NN1 filing_NN1 ,_PUN the_AT0 Census_NN1 Bureau_NN1 argues_VVZ that_CJT even_AV0 if_CJS most_DT0 of_PRF the_AT0 matches_NN2 would_VM0 be_VBI expected_VVN by_PRP chance_NN1 ,_PUN people_NN0 in_PRP very_AV0 small_AJ0 blocks_NN2 are_VBB at_PRP high_AJ0 risk_NN1 of_PRF database_NN1 reconstruction_NN1 (_PUL Abowd_NP0 ,_PUN 2021b_CRD )_PUR ._SENT On_PRP blocks_NN2 with_PRP fewer_DT0 than_CJS ten_CRD people_NN0 ,_PUN the_AT0 Census_NN1 Bureau_NN1 's_POS database_NN1 reconstruction_NN1 match_NN1 rate_NN1 for_PRP age_NN1 ,_PUN sex_NN1 ,_PUN race_NN1 ,_PUN and_CJC ethnicity_NN1 was_VBD just_AV0 over_PRP 20_CRD %_NN0 ,_PUN meaning_VVG that_CJT the_AT0 error_NN1 rate_NN1 was_VBD just_AV0 under_PRP 80_CRD %_NN0 ._SENT Although_CJS this_DT0 success_NN1 rate_NN1 seems_VVZ low_AJ0 ,_PUN random_AJ0 assignment_NN1 is_VBZ even_AV0 worse_AJC for_PRP very_AV0 small_AJ0 blocks_NN2 ;_PUN our_DPS random_AJ0 simulation_NN1 guessed_VVD age_NN1 and_CJC sex_NN1 correctly_AV0 in_PRP just_AV0 2.6_CRD %_NN0 of_PRF cases_NN2 for_PRP blocks_NN2 with_PRP fewer_DT0 than_CJS ten_CRD people_NN0 ._SENT 
The_AT0 key_AJ0 table_NN1 powering_VVG the_AT0 database_NN1 reconstruction_NN1 experiment_NN1 —_PUN Summary_NN1 File_NN1 1_CRD P012A-I_NP0 —_PUN provides_VVZ information_NN1 on_PRP age_NN1 by_PRP sex_NN1 by_PRP race_NN1 by_PRP ethnicity_NN1 ._SENT This_DT0 table_NN1 can_VM0 easily_AV0 be_VBI rearranged_VVN into_PRP individual-level_AJ0 format_NN1 ,_PUN providing_VVG the_AT0 age_NN1 ,_PUN sex_NN1 ,_PUN and_CJC race_NN1 /_PUN ethnicity_NN1 of_PRF the_AT0 population_NN1 of_PRF each_DT0 block_NN1 with_PRP near-perfect_AJ0 accuracy_NN1 (_PUL Ruggles_NP0 et_NP0 al._NP0 ,_PUN 2018a_NP0 ,_PUN 2018b_CRD )_PUR ._SENT How_AVQ is_VBZ it_PNP possible_AJ0 ,_PUN then_AV0 ,_PUN that_CJT the_AT0 Census_NN1 Bureau_NN1 's_POS database_NN1 reconstruction_NN1 incorrect_AJ0 in_PRP almost_AV0 80_CRD %_NN0 of_PRF cases_NN2 ?_SENT The_AT0 main_AJ0 challenge_NN1 is_VBZ that_CJT the_AT0 ages_NN2 in_PRP Table_NN1 P012A-I_NN2 are_VBB given_VVN in_PRP 5-year_AJ0 groups_NN2 instead_AV0 of_PRF exact_AJ0 years_NN2 ._SENT A_AT0 random_AJ0 number_NN1 generator_NN1 would_VM0 guess_VVI the_AT0 correct_AJ0 exact_AJ0 age_NN1 within_PRP the_AT0 5-year_AJ0 age_NN1 group_NN1 approximately_AV0 20_CRD %_NN0 of_PRF the_AT0 time_NN1 ,_PUN which_DTQ is_VBZ very_AV0 close_AJ0 to_PRP the_AT0 accuracy_NN1 level_NN1 achieved_VVN by_PRP the_AT0 database_NN1 reconstruction_NN1 experiment_NN1 ._SENT 
Another_DT0 possible_AJ0 explanation_NN1 for_PRP the_AT0 nearly_AV0 80_CRD %_NN0 error_NN1 rate_NN1 in_PRP the_AT0 reconstruction_NN1 of_PRF small_AJ0 blocks_NN2 ,_PUN as_CJS suggested_VVN in_PRP Census_NN1 Bureau_NN1 testimony_NN1 (_PUL Abowd_NP0 ,_PUN 2021a_NP0 )_PUR ,_PUN is_VBZ that_CJT traditional_AJ0 methods_NN2 of_PRF disclosure_NN1 control_NN1 may_VM0 actually_AV0 be_VBI effective_AJ0 at_PRP protecting_VVG persons_NN2 in_PRP the_AT0 smallest_AJS blocks_NN2 ._SENT The_AT0 most_AV0 important_AJ0 of_PRF these_DT0 methods_NN2 is_VBZ swapping_VVG ,_PUN in_PRP which_DTQ a_AT0 small_AJ0 fraction_NN1 of_PRF households_NN2 are_VBB exchanged_VVN with_PRP nearby_AJ0 paired_AJ0 households_NN2 that_CJT share_VVB key_AJ0 characteristics_NN2 (_PUL McKenna_NP0 ,_PUN 2018_CRD )_PUR ._SENT 
The_AT0 Census_NN1 Bureau_NN1 recently_AV0 reported_VVN on_PRP a_AT0 new_AJ0 experiment_NN1 to_TO0 assess_VVI the_AT0 impact_NN1 of_PRF swapping_VVG on_PRP their_DPS database_NN1 reconstruction_NN1 experiment_NN1 (_PUL Hawes_NP0 &_NP0 Rodriguez_NP0 ,_PUN 2021_CRD )_PUR ._SENT To_TO0 simulate_VVI an_AT0 extreme_AJ0 level_NN1 of_PRF swapping_NN1 ,_PUN the_AT0 Bureau_NN1 designed_VVD an_AT0 algorithm_NN1 with_PRP far_AV0 higher_AJC high_AJ0 levels_NN2 of_PRF swapping_NN1 and_CJC perturbation_NN1 than_CJS are_VBB ever_AV0 used_VVN for_PRP disclosure_NN1 control_NN1 ._SENT In_PRP particular_AJ0 ,_PUN the_AT0 experiment_NN1 "_PUQ perturbed_VVN "_PUQ household_NN1 size_NN1 for_PRP 50_CRD %_NN0 of_PRF cases_NN2 and_CJC tract_NN1 location_NN1 in_PRP 70_CRD %_NN0 of_PRF cases_NN2 ,_PUN and_CJC then_AV0 swapped_VVD 50_CRD %_NN0 of_PRF the_AT0 households_NN2 with_PRP someone_PNI in_PRP a_AT0 different_AJ0 census_NN1 block_NN1 ._SENT In_PRP other_AJ0 words_NN2 ,_PUN they_PNP eliminated_VVD the_AT0 real_AJ0 characteristics_NN2 of_PRF the_AT0 population_NN1 for_PRP half_DT0 the_AT0 cases_NN2 on_PRP each_DT0 block_NN1 ._SENT Then_AV0 they_PNP ran_VVD the_AT0 database_NN1 reconstruction_NN1 attack_NN1 on_PRP the_AT0 altered_AJ0 data_NN0 and_CJC found_VVD that_CJT eliminating_VVG half_DT0 the_AT0 real_AJ0 population_NN1 has_VHZ little_DT0 impact_NN1 on_PRP the_AT0 rate_NN1 of_PRF re-identification_NN1 ._SENT In_PRP this_DT0 experiment_NN1 ,_PUN they_PNP found_VVD a_AT0 match_NN1 rate_NN1 of_PRF age_NN1 ,_PUN sex_NN1 ,_PUN race_NN1 ,_PUN and_CJC ethnicity_NN1 of_PRF 44.6_CRD %_NN0 using_VVG unswapped_AJ0 data_NN0 ,_PUN and_CJC 42.7_CRD %_NN0 on_PRP the_AT0 extremely_AV0 swapped_VVN data_NN0 ._SENT 
The_AT0 Census_NN1 Bureau_NN1 interpreted_VVD these_DT0 results_NN2 to_TO0 mean_VVI that_DT0 even_AV0 extreme_AJ0 swapping_NN1 does_VDZ not_XX0 protect_VVI from_PRP database_NN1 reconstruction_NN1 ,_PUN so_AV0 differential_AJ0 privacy_NN1 is_VBZ essential_AJ0 ._SENT A_AT0 much_AV0 more_AV0 plausible_AJ0 explanation_NN1 is_VBZ that_CJT the_AT0 great_AJ0 majority_NN1 of_PRF matches_NN2 occurred_VVN entirely_AV0 by_PRP chance_NN1 ,_PUN so_AV0 the_AT0 match_NN1 rate_NN1 is_VBZ unaffected_AJ0 by_PRP substituting_VVG the_AT0 data_NN0 ._SENT It_PNP is_VBZ likely_AJ0 they_PNP would_VM0 get_VVI virtually_AV0 the_AT0 same_DT0 result_NN1 if_CJS instead_AV0 of_PRF 50_CRD %_NN0 they_PNP used_VVD a_AT0 100_CRD %_NN0 swapping_VVG rate_NN1 ,_PUN which_DTQ would_VM0 mean_VVI that_CJT zero_CRD of_PRF the_AT0 re-identifications_NN2 would_VM0 be_VBI true_AJ0 ._SENT Without_PRP a_AT0 null_AJ0 model_NN1 for_PRP comparison_NN1 ,_PUN this_DT0 kind_NN1 of_PRF experiment_NN1 cannot_NN1 be_VBI interpreted_VVN ._SENT 
Discussion_NN1 
According_VVG to_PRP the_AT0 Census_NN1 Bureau_NN1 's_POS chief_AJ0 scientist_NN1 Abowd_NN1 (_PUL 2021a_NP0 ,_PUN p._NN0 18_CRD )_PUR "_PUQ the_AT0 results_NN2 from_PRP the_AT0 Census_NN1 Bureau_NN1 's_VBZ 2016_CRD –_PUN 2019_CRD research_NN1 program_NN1 on_PRP simulated_AJ0 reconstruction-abetted_AJ0 re-identification_NN1 attack_NN1 were_VBD conclusive_AJ0 ,_PUN indisputable_AJ0 ,_PUN and_CJC alarming_AJ0 ._SENT "_PUQ Abowd_NP0 contends_VVZ that_CJT the_AT0 published_AJ0 tabulations_NN2 of_PRF the_AT0 2010_CRD Census_NN1 "_PUQ would_VM0 allow_VVI an_AT0 attacker_NN1 to_TO0 accurately_AV0 re-identify_VVI at_PRP least_AV0 52_CRD million_CRD 2010_CRD Census_NN1 respondents_NN2 (_PUL 17_CRD %_NN0 of_PRF the_AT0 population_NN1 )_PUR and_CJC the_AT0 attacker_NN1 would_VM0 have_VHI a_AT0 high_AJ0 degree_NN1 of_PRF confidence_NN1 in_PRP their_DPS results_NN2 ,_PUN "_PUQ and_CJC with_PRP access_NN1 to_PRP better_AJC commercial_AJ0 data_NN0 an_AT0 attacker_NN1 "_PUQ could_VM0 accurately_AV0 re-identify_VVI around_PRP 179_CRD million_CRD Americans_NN2 or_CJC around_PRP 58_CRD %_NN0 of_PRF the_AT0 population_NN1 ._SENT "_PUQ (_PUL Abowd_NP0 ,_PUN 2021a_NP0 ,_PUN p._NN0 18_CRD )_PUR ._SENT 
Without_PRP a_AT0 control_NN1 group_NN1 for_PRP comparison_NN1 ,_PUN the_AT0 alarmist_NN1 results_NN2 reported_VVN by_PRP the_AT0 Census_NN1 Bureau_NN1 from_PRP the_AT0 database_NN1 reconstruction_NN1 experiment_NN1 are_VBB not_XX0 meaningful_AJ0 ._SENT Our_DPS analysis_NN1 shows_VVZ that_CJT the_AT0 threat_NN1 posed_VVN by_PRP the_AT0 reconstruction_NN1 to_PRP respondents_NN2 '_POS confidentiality_NN1 is_VBZ similar_AJ0 to_PRP the_AT0 threat_NN1 posed_VVN by_PRP randomly_AV0 guessing_VVG their_DPS characteristics_NN2 ._SENT If_CJS a_AT0 clinical_AJ0 trial_NN1 showed_VVD that_CJT 17_CRD %_NN0 of_PRF a_AT0 treated_AJ0 population_NN1 recovers_VVZ ,_PUN that_DT0 would_VM0 not_XX0 prove_VVI the_AT0 treatment_NN1 is_VBZ effective_AJ0 ;_PUN we_PNP would_VM0 also_AV0 need_VVI to_TO0 compare_VVI the_AT0 recovery_NN1 rate_NN1 of_PRF a_AT0 control_NN1 group_NN1 ._SENT Without_PRP a_AT0 null_AJ0 model_NN1 ,_PUN the_AT0 Census_NN1 Bureau_NN1 experiment_NN1 fails_VVZ to_TO0 demonstrate_VVI that_DT0 reconstruction_NN1 of_PRF the_AT0 tabular_AJ0 data_NN0 poses_VVZ a_AT0 significant_AJ0 disclosure_NN1 risk_NN1 ._SENT 
The_AT0 Census_NN1 Bureau_NN1 has_VHZ severely_AV0 exaggerated_VVN the_AT0 risk_NN1 of_PRF exposure_NN1 of_PRF personal_AJ0 census_NN1 responses_NN2 to_PRP the_AT0 decennial_AJ0 census_NN1 ._SENT As_CJS the_AT0 Acting_AJ0 Director_NN1 of_PRF the_AT0 Census_NN1 Bureau_NN1 reluctantly_AV0 acknowledged_VVN ,_PUN the_AT0 database_NN1 reconstruction_NN1 is_VBZ incorrect_AJ0 in_PRP most_DT0 instances_NN2 and_CJC an_AT0 outside_AJ0 intruder_NN1 would_VM0 have_VHI no_AT0 means_NN0 of_PRF determining_VVG if_CJS any_DT0 particular_AJ0 inference_NN1 was_VBD true_AJ0 (_PUL Jarmin_NP0 ,_PUN 2019_CRD )_PUR ._SENT 
