def func():
count = defaultdict(dict)
for n_cands in n_cands_list:
utilities = random_utilities(n_voters, n_cands)
# Find the social utility winner and accumulate utilities
UW = utility_winner(utilities)
count['UW'][n_cands] = utilities.sum(axis=0)[UW]
for name, method in rated_methods.items():
try:
winner = method(utilities, tiebreaker='random')
count[name][n_cands] = utilities.sum(axis=0)[winner]
except ValueError:
# Skip junk cases like vote-for-2 with 2 candidates
count[name][n_cands] = np.nan
rankings = honest_rankings(utilities)
for name, method in ranked_methods.items():
winner = method(rankings, tiebreaker='random')
count[name][n_cands] = utilities.sum(axis=0)[winner]
return count
start_time = time.monotonic()
for iteration in range(n):
for n_cands in n_cands_list:
utilities = random_utilities(n_voters, n_cands)
# Find the social utility winner and accumulate utilities
UW = utility_winner(utilities)
count['UW'][n_cands] += utilities.sum(axis=0)[UW]
for name, method in rated_methods.items():
winner = method(utilities, tiebreaker='random')
count[name][n_cands] += utilities.sum(axis=0)[winner]
rankings = honest_rankings(utilities)
for name, method in ranked_methods.items():
winner = method(rankings, tiebreaker='random')
count[name][n_cands] += utilities.sum(axis=0)[winner]
elapsed_time = time.monotonic() - start_time
print('Elapsed:', time.strftime("%H:%M:%S", time.gmtime(elapsed_time)), '\n')
plt.figure(f'Effectiveness, {n_voters} voters, {n} iterations')
plt.title('The Effectiveness of Several Voting Systems')
for name, method in (('Standard', eff_standard),
('Vote-for-half', eff_vote_for_half),
('Borda', eff_borda)):
plt.plot(n_cands_list, method(np.array(n_cands_list))*100, ':', lw=0.8)
# Restart color cycle, so result colors match
def impartial_culture(n_voters, n_cands, random_state=None):
"""
Generate ranked ballots using the impartial culture / random society model.
The impartial culture model selects complete preference rankings from the
set of all possible preference rankings using a uniform distribution.
This model is unrealistic, but is commonly used because it has some
worst-case properties and is comparable between researchers.[2]_
Parameters
----------
n_voters : int
Number of voters
n_cands : int
Number of candidates
random_state : {None, int, np.random.Generator}, optional
Initializes the random number generator. If `random_state` is int, a
new Generator instance is used, seeded with its value. (If the same
int is given twice, the function will return the same values.)
If None (default), an existing Generator is used.
If `random_state` is already a Generator instance, then
that object is used.
Returns
-------
election : numpy.ndarray
A collection of ranked ballots.
Rows represent voters and columns represent rankings, from best to
worst, with no tied rankings.
Each cell contains the ID number of a candidate, starting at 0.
For example, if a voter ranks Curie > Avogadro > Bohr, the ballot line
would read ``[2, 0, 1]`` (with IDs in alphabetical order).
Notes
-----
This implementation first generates a set of independent, uniformly
distributed random utilities, which are then converted into rankings.[1]_
It can (extremely rarely) generate tied utilities, which are always ranked
in order from lowest to highest, so there is a very slight bias in favor of
lower-numbered candidates?
References
----------
.. [1] S. Merrill III, "A Comparison of Efficiency of Multicandidate
Electoral Systems", American Journal of Political Science, vol. 28,
no. 1, p. 26, 1984. :doi:`10.2307/2110786`
.. [2] A. Lehtinen and J. Kuorikoski, "Unrealistic Assumptions in Rational
Choice Theory", Philosophy of the Social Sciences vol. 37, no. 2,
p 132. 2007. :doi:`10.1177/0048393107299684`
Examples
--------
Generate an election with 4 voters and 3 candidates:
>>> impartial_culture(4, 3)
array([[0, 1, 2],
[2, 0, 1],
[2, 1, 0],
[1, 0, 2]], dtype=uint8)
Here, Voter 1 prefers Candidate 2, then Candidate 0, then Candidate 1.
"""
# This method is much faster than generating integer sequences and then
# shuffling them.
utilities = random_utilities(n_voters, n_cands, random_state)
rankings = honest_rankings(utilities)
return rankings