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#1: Initial revision by user avatar Chgg Clou‭ · 2021-06-04T07:51:58Z (almost 3 years ago)
What was Justice Scalia's mathematical mistake in Penry v. Lynaugh (1989)?
Please see the bolden phrase below. Please don't hesitate to reduce the amount of quotation, which I know is lengthy, whilst preserving enough context. 

>&nbsp; &nbsp; &nbsp; But even granting this point, Scalia writes, state legislatures have not
demonstrated a national consensus against execution of the mentally retarded,
as the precedent of _Penry_ requires:

>>The Court pays lip service to these precedents as it
miraculously extracts a “national consensus” forbidding
execution of the mentally retarded . . . from the fact that 18 States—less than half (47%) of the 38 States that permit
capital punishment (for whom the issue exists)—have very
recently enacted legislation barring execution of the mentally
retarded. . . . That bare number of States alone—18—should
be enough to convince any reasonable person that no “national
consensus” exists. How is it possible that agreement among
47% of the death penalty jurisdictions amounts to
“consensus”?   

>&nbsp; &nbsp; &nbsp;  The majority’s ruling does the math differently. By their reckoning, there
are thirty states that prohibit execution of the mentally retarded: the eighteen
mentioned by Scalia and the twelve that prohibit capital punishment entirely.
That makes thirty out of fifty, a substantial majority.    
>&nbsp; &nbsp; &nbsp; Which fraction is correct? Akhil and Vikram Amar, brothers and
constitutional law professors, explain why the majority has the better of it on
mathematical grounds. Imagine, they ask, a scenario in which forty-seven state
legislatures have outlawed capital punishment, but two of the three
nonconforming states allow execution of mentally retarded convicts. In this
case, it’s hard to deny that the national standard of decency excludes the death
penalty in general, and the death penalty for the mentally retarded even more
so. To conclude otherwise concedes an awful lot of moral authority to the
three states out of step with the national mood. The right fraction to consider
here is 48 out of 50, not 1 out of 3.       
&nbsp; &nbsp; &nbsp;  In real life, though, there is plainly no national consensus against the death
penalty itself. This confers a certain appeal to Scalia’s argument. It’s the
twelve states that forbid the death penalty* that are out of step with general
national opinion in favor of capital punishment; if they don’t think executions
should be allowed at all, how can they be said to have an opinion about which
executions are permissible?        
&nbsp; &nbsp; &nbsp; **Scalia’s mistake is the same one that constantly trips up attempts to make
sense of public opinion; the inconsistency of aggregate judgments. [Emphasis mine]** Break it
down like this. How many states believed in 2002 that capital punishment was
morally unacceptable? On the evidence of legislation, only twelve. In other
words, the majority of states, thirty-eight out of fifty, hold capital punishment
to be morally acceptable.      
&nbsp; &nbsp; &nbsp; Now, how many states think that executing a mentally retarded criminal is
worse, legally speaking, than executing anyone else? Certainly the twenty
states that are okay with both practices can’t be counted among this number.
Neither can the twelve states where capital punishment is categorically
forbidden. There are only eighteen states that draw the relevant legal  distinction; more than when Penry was decided, but still a small minority.  
>&nbsp; &nbsp; &nbsp; The majority of states, thirty-two out of fifty, hold capital punishment for
mentally retarded criminals in the same legal standing as capital punishment
generally.†   
>&nbsp; &nbsp; &nbsp; Putting those statements together seems like a matter of simple logic: if
the majority thinks capital punishment in general is fine, and if the majority
thinks capital punishment for mentally retarded criminals is no worse than
capital punishment in general, then the majority must approve of capital
punishment for mentally retarded criminals.     
&nbsp; &nbsp; &nbsp; But this is wrong. As we’ve seen, “the majority” isn’t a unified entity that
follows logical rules. Remember, the majority of voters didn’t want George
H. W. Bush to be re-elected in 1992, and the majority of voters didn’t want
Bill Clinton to take over Bush’s job; but, much as H. Ross Perot might have
wished it, it doesn’t follow that the majority wanted neither Bush nor Clinton
in the Oval Office.

>* Since 2002, the number has risen to seventeen.    
>† This is not precisely Scalia's computation; Scalia didn't go so far as to assert that the no-death-penalty states thought execution of mentally retarded criminals no worse than execution in general. Rather, his argument amounts to the claim that we have no information about their opinions in this matter, so we shouldn't count these states in our tally. 


Ellenberg, *How Not to Be Wrong* (2014), pages 373-374.