def grofman(votes, seats, parties="votes"):
r"""Calculate the Grofman index of disproportionality.
.. math::
N \sum_{i=1}^n |v_i - s_i|
where N is :math:`\sum_{i=1}^n v_i^2` if ``parties == 'votes'`` or
:math:`\sum_{i=1}^n s_i^2` if ``parties == 'seats'``.
:param list votes: a list of vote counts
:param list seats: a list of seat counts
:param str parties: ``votes`` or ``seats`` to use to calculate the
effective number of parties
"""
votes = normalize(votes)
seats = normalize(seats)
if parties == "votes":
n = sum([v**2 for v in votes])
elif parties == "seats":
n = sum([s**2 for s in seats])
else:
raise ValueError("Parties argument must be either votes or seats.")
return n * sum([abs(v - s) for v, s in zip(votes, seats)])
def rae(votes, seats):
r"""Calculate Rae's index of disproportionality.
.. math::
\frac{1}{n} \sum_{i=1}^n |v_i - s_i|
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return 1.0 / len(votes) * sum([abs(v - s) for v, s in zip(votes, seats)])
def loosemore_hanby(votes, seats):
r"""Calculate Loosemore-Hanby index of disproportionality.
.. math::
\frac{1}{2} \sum_{i=1}^n |v_i - s_i|
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return 1.0 / 2 * sum([abs(v - s) for v, s in zip(votes, seats)])
def sainte_lague(votes, seats):
r"""Calculate the Sainte-Lague index of disproportionality.
.. math::
\sum_{i=1}^n \frac{(v_i - s_i)^2}{v_i}
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return sum(1.0 / v * (v - s)**2 for v, s in zip(votes, seats))
def dhondt(votes, seats):
r"""Calculate the D'Hondt index of disproportionality.
.. math::
\max \frac{s_i}{v_i}
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return max([1.0 * s / v for v, s in zip(votes, seats)])
def gallagher(votes, seats):
r"""Calculate the Gallagher index of disproportionality.
.. math::
\sqrt{\frac{1}{2} \sum_{i=1}^n (v_i - s_i)^2}
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return sqrt(1.0 / 2) * least_square(votes, seats)
def least_square(votes, seats):
r"""Calculate the least squares index of disproportionality.
.. math::
\sqrt{\sum_{i=1}^n (v_i - s_i)^2}
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return sqrt(sum([(v - s)**2 for v, s in zip(votes, seats)]))
def rose(votes, seats):
r"""Calculate the Rose index of proportionality.
.. math::
100 - \frac{1}{2} \sum_{i=1}^n |v_i - s_i|
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return 100 - loosemore_hanby(votes, seats)
def lijphart(votes, seats):
r"""Calculate the Lijphart index of disproportionality.
.. math::
\max | v_i - s_i |
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
return max([abs(v - s) for v, s in zip(votes, seats)])
def regression(votes, seats):
r"""Calculate the regression index of disproportionality.
.. math::
\frac{\sum_{i=1}^n v_i s_i}{\sum_{i=1}^n v_i^2}
:param list votes: a list of vote counts
:param list seats: a list of seat counts
"""
votes = normalize(votes)
seats = normalize(seats)
num = sum([v * s for v, s in zip(votes, seats)])
denom = sum([v**2 for v in votes])
return 1.0 * num / denom
def adjusted_loosemore_hanby(votes, seats, parties="votes"):
r"""Calculate the adjusted Loosemore-Hanby index of disproportionality.
.. math::
N \sum_{i=1}^n |v_i - s_i|
where N is :math:`\sum_{i=1}^n v_i` if ``parties == 'votes'`` or
:math:`\sum_{i=1}^n s_i` if ``parties == 'seats'``.
:param list votes: a list of vote counts
:param list seats: a list of seat counts
:param str parties: ``votes`` or ``seats`` to use to calculate the
effective number of parties
"""
votes = normalize(votes)
seats = normalize(seats)
return grofman(votes, seats, parties)
def shannon(groups):
r"""Calculate the Shannon index.
.. math::
\sum_{i=1}^n p_i \ln (p_i)
:param list groups: a list of integers representing populations of groups
"""
groups = normalize(groups)
return sum([g * log(g) for g in groups])
def berger_parker(groups):
r"""Calculate the Berger-Parker index.
.. math::
max(p_i)
:param list group: a list of integers representing populations of groups
"""
groups = normalize(groups)
return max(groups)
def laakso_taagepera(groups):
r"""Calculate the effective number of parties using Laakso-Taagepera.
.. math::
\frac{1}{\sum_{i=1}^n p_i^2}
:param list group: a list of integers representing populations of groups
"""
groups = normalize(groups)
return 1.0 / sum([g**2 for g in groups])
def simpson(groups):
r"""Calculate the Simpson index.
.. math::
\sum_{i=1}^n p_i^2
:param list groups: a list of integers representing populations of groups
"""
groups = normalize(groups)
return sum([g**2 for g in groups])
def general(groups, q=1):
r"""Calculate the general diversity index.
.. math::
\left( \sum_{i=1}^n p_i^q \right) ^ {1/(1-q)}
:param list groups: a list of integers representing populations of groups
:param float q: weight value
"""
if q == 1:
return exp(shannon(groups))
groups = normalize(groups)
return sum([g**q for g in groups])**(1.0 / (1 - q))
def golosov(groups):
r"""Calculate the effective number of parties using Golosov.
.. math::
\sum_{i=1}^n \frac{p_i}{p_i + p_1^2 - p_i^2}
where :math:`p_1` is the largest proportion.
:param list group: a list of integers representing populations of a group
"""
groups = normalize(groups)
p1 = max(groups)
return sum([g / (g + p1**2 - g**2) for g in groups])
def renyi(groups, q=0):
r"""Calculate the Renyi entropy.
.. math::
\frac{1}{1-q} \ln \left( \sum_{i=1}^n p_i ^ q \right)
:param list groups: a list of integers representing populations of groups
:param float q: weight value
"""
if q == 1:
return shannon(groups)
groups = normalize(groups)
return 1.0 / (1 - q) * log(sum([g**q for g in groups]))
