
X
M
q
M
p
A
g
M
, k
M
, σ
ðÞ
¼
1
2
:
Let the power index be defined as
π ¼ min 2
σ 1,1ðÞ:
The minimal value, zero, occurs when
σ ¼1=2, meaning that A gets elected only when
she would get elected if reporting were unbiased, in which case the media owner has no
influence on elections. The maximal value occurs when
σ KðÞ1, meaning that A is
always elected, regardless of how bad she is in comparison to B.
The power index π corresponds to the maximal welfare loss that voters can experi-
ence as a result of biased reporting: instead of having B elected and receiving σ, they
receive 1 σ, generating a difference 2σ 1. This can be computed by summing the vote
shares over ...