(D+ + R-) - (R+ + D-)
PI = 100 * --------------------------- (1)
D+ + D- + D= + R+ + R- + R=
where D+, D- and D= are the number of positive, negative and neutral
Democratic references, and R+, R- and R= are positive, negative and
neutral Republican
references. The numerator is the difference
between Democratic- and Republican-leaning references, and the
denominator is the total number of all kinds of references, including
neutral ones.
When presenting the numbers, the absolute value of the PI is usually
shown in color, with blue indicating a Democratic-leaning PI (positive PI,
first term in the numerator larger than the second) and red indicating
Republican. The absolute value of PI ranges from 0 to 100, with 0
meaning that the
references are exactly balanced between the parties, and 100 meaning that all
the references favor only one party. When there are no references to
either party, the PI is numerically undefined, but is assigned a
value of zero.
PI = 100 * ( DF*DI - RF*RI ) (2)
where the Democratic and Republican Fractions are:
D+ + D- + D=
DF = -----------------------------
(D+ + D- + D= + R+ + R- + R=)
R+ + R- + R=
RF = -----------------------------
(D+ + D- + D= + R+ + R- + R=)
and the Democratic and Republican Indices are:
D+ - D-
DI = 100 * -------------- (3)
(D+ + D- + D=)
R+ - R-
RI = 100 * -------------- (4)
(R+ + R- + R=)
From equation (2), it can be seen that a pundit who treats both
parties exactly the same (DI equal to RI) would nevertheless have a
nonzero PI if they refer to one party more than the other (DF not
equal to RF), even if the disparity is fully explained by the fact
that one party is dominating the political news. To remedy this,
normalization factors are calculated based on the frequency of party
occurrence for the entire set of pundits over the entire current
year. If there are more total Democratic references (DTOT) than total
Republican references (RTOT) for the year, then the Democratic and
Republican normalization factors are:
RTOT
DN = ---- , RN = 1 (5)
DTOT
or if the reverse is true:
DTOT
DN = 1, RN = ---- (6)
RTOT
The normalization doesn't affect the Democratic and Republican
Indices, but the Democratic and Republican Fractions are replaced by
Normalized Democratic and Republican Fractions:
DN*(D+ + D- + D=)
NDF = -------------------------------------
DN*(D+ + D- + D=) + RN*(R+ + R- + R=)
RN*(R+ + R- + R=)
NRF = -------------------------------------
DN*(D+ + D- + D=) + RN*(R+ + R- + R=)
Then the Normalized Partisanship Index (NPI) becomes:
NPI = 100 * ( NDF*DI - NRF*RI ) (7)
The effect is to "devalue" references to the dominant party in all
calculations. With this modification, a columnist would properly
receive a zero value of NPI
if they treat both parties equally and have the same ratio of party
references as the Lying in Ponds roster of pundits.
D+ + R+
POS = 100 * --------------------------- (6)
D+ + D- + D= + R+ + R- + R=
The Negative Index is:
D- + R-
NEG = 100 * --------------------------- (7)
D+ + D- + D= + R+ + R- + R=
The Neutral Index is:
D= + R=
NEU = 100 * --------------------------- (8)
D+ + D- + D= + R+ + R- + R=