Document ID: ./input/supremecourt_opinions/opinions/22pdf/21-1086_1co6.pdf
Page Number: 68

Cite as:  599 U. S. ____ (2023) 

23 

THOMAS, J., dissenting 

would not yield a race-neutral case for treating the plain-
tiffs’ approach as a suitable benchmark: Absent core reten-
tion, there is no apparent race-neutral reason to insist that 
District 7 remain a majority-black district uniting Birming-
ham’s  majority-black  neighborhoods  with  majority-black 
rural areas in the Black Belt. 
  Finally,  it  is  surely  probative  that  over  2  million  race-
neutral  simulations  did  not  yield  a  single  plan  with  two 
majority-black districts, and even 20,000 simulations with 
a one-majority-black-district floor did not yield a second dis-
trict with  a  black  voting-age  population  over  40%.   If  any 
plan with two majority-black districts would be an “out-out-
out-outlier” within  the likely  universe  of  race-neutral dis-
tricting plans, Rucho, 588 U. S., at ___ (KAGAN, J., dissent-
ing) (slip op., at 19), it is hard to see how the mere possibil-
ity of drawing two majority-black districts could show that 
a one-district map diluted black Alabamians’ votes relative 
to any appropriate benchmark.14 

—————— 

14 The majority points to limitations of Dr. Duchin’s and Dr. Imai’s al-
gorithms that do not undermine the strong inference from their results 
to the conclusion that no two-majority-black-district plan could be an ap-
propriate proxy for the undiluted benchmark.  Ante, at 26, 28–29.  I have 
already explained why the fact that Dr. Duchin’s study used 2010 census 
data  is irrelevant.    See  n. 9,  supra.    As  for  the algorithms’  inability  to 
incorporate  all  possible  districting  considerations,  the  absence  of addi-
tional constraints cannot explain their failure to produce any maps hit-
ting the plaintiffs’ preferred racial target.  Next, while it is true that the 
number  of  possible  districting  plans  is  extremely  large,  that  does  not 
mean it is impossible to generate a statistically significant sample.  Here, 
for instance, Dr. Imai explained that “10,000 simulated plans” was suffi-
cient to “yield statistically precise conclusions” and that any higher num-
ber would “not materially affect” the results.  Supp. App. 60.  Finally, the 
majority notes Dr. Duchin’s testimony that her “exploratory algorithms” 
found “thousands” of possible two-majority-black-district maps.  2 App. 
622; see ante, at 27, n. 7.  Setting aside that Dr. Duchin never provided 
the denominator of which those “thousands” were the numerator, it is no 
wonder  that  the  algorithms  in  question  generated  such  maps;  as  Dr.