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CREATE TABLE respondent (
    id unsigned int not null auto_increment primary key
...
   ,response   unsigned int
   ,PRIMARY KEY (respondent, response)
);

SELECT A.respondent AS respondent
  FROM responses A JOIN responses B on (A.respondent = B.respondent)
 WHERE A.response = ?
   AND B.response = ?

my $sth = $dbh->prepare_cached( $sql );
$sth->execute( $response_x, $response_y );
...
}

$sth->finish;