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Fix winner distribution plots: center on voter median (#22) #45

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Fix winner distribution plots: center on voter median (#22) #45

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ab3a8d5
Plot winner positions relative to voter median per election
cursoragent May 11, 2026
c3ea34f
Scope voter-median centering to Tomlinson extended example only
cursoragent May 11, 2026
438e16c
Anchor Tomlinson Figure 3 draws to voter median like updated script
cursoragent May 11, 2026
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17 changes: 9 additions & 8 deletions examples/tomlinson_2023_figure_3.py
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Original file line number Diff line number Diff line change
Expand Up @@ -48,14 +48,15 @@ def simulate_batch(n_cands):
winners = defaultdict(list)
for iteration in range(batch_size):

# "voters and candidates come from the uniform distribution on [0, 1]"
v = np.random.uniform(0, 1, n_voters)
# But remove any run-to-run random bias, because we want to match ideal
# points of the actual set of voters, not their expected value.
v = (v - v.mean() + 0.5)[:, np.newaxis]

c = np.random.uniform(0, 1, n_cands)
c = (c - v.mean() + 0.5)[:, np.newaxis]
# Uniform on [0, 1]. Same translation for voters and candidates so
# pairwise distances are unchanged; anchor the draw to the voter median
# at 0.5 (issue #22, consistent with tomlinson_2023_figure_3_updated.py).
v_flat = np.random.uniform(0, 1, n_voters)
ref = np.median(v_flat)
v = (v_flat - ref + 0.5)[:, np.newaxis]

c_flat = np.random.uniform(0, 1, n_cands)
c = (c_flat - ref + 0.5)[:, np.newaxis]

# FPTP voting method
utilities = normed_dist_utilities(v, c)
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27 changes: 15 additions & 12 deletions examples/tomlinson_2023_figure_3_updated.py
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Original file line number Diff line number Diff line change
Expand Up @@ -64,53 +64,56 @@ def simulate_batch(n_cands):
c = np.random.uniform(-u_width/2, +u_width/2, n_cands)
c = np.atleast_2d(c).T

# Center each election on the voter median so Condorcet-style winners
# match the "nearest median" benchmark (issue #22).
ref = np.median(v[:, 0])

# FPTP voting method
utilities = normed_dist_utilities(v, c)
rankings = honest_rankings(utilities)
winner = fptp(rankings, tiebreaker='random')
winners['First Past The Post / Plurality'].append(c[winner][0])
winners['First Past The Post / Plurality'].append(c[winner][0] - ref)

# Top-two runoff
utilities = normed_dist_utilities(v, c)
rankings = honest_rankings(utilities)
winner = runoff(rankings, tiebreaker='random')
winners['Top-Two Runoff/Primary / Two-Round System / '
'Contingent Vote'].append(c[winner][0])
'Contingent Vote'].append(c[winner][0] - ref)

# Instant-runoff
winner = irv(rankings, tiebreaker='random')
winners['Ranked-Choice Voting (Hare) / '
'Alternative Vote / Instant-Runoff'].append(c[winner][0])
'Alternative Vote / Instant-Runoff'].append(c[winner][0] - ref)

# Approval voting
winner = approval(approval_optimal(utilities), tiebreaker='random')
winners['Approval Voting ("optimal" strategy)'].append(c[winner][0])
winners['Approval Voting ("optimal" strategy)'].append(c[winner][0] - ref)

# Approval voting
winner = approval(vote_for_k(utilities, vote_for), tiebreaker='random')
winners[f'Approval Voting "(Vote-for-{vote_for}"'
' strategy)'].append(c[winner][0])
' strategy)'].append(c[winner][0] - ref)

# STAR voting
ballots = honest_normed_scores(utilities)
winner = star(ballots, tiebreaker='random')
winners['STAR Voting'].append(c[winner][0])
winners['STAR Voting'].append(c[winner][0] - ref)

# Borda count
winner = borda(rankings, tiebreaker='random')
winners['Borda count'].append(c[winner][0])
winners['Borda count'].append(c[winner][0] - ref)

# Coombs method
winner = coombs(rankings, tiebreaker='random')
winners["Coombs' method"].append(c[winner][0])
winners["Coombs' method"].append(c[winner][0] - ref)

# Condorcet RCV
winner = black(rankings, tiebreaker='random')
winners['Condorcet Ranked-Choice Voting (Black)'].append(c[winner][0])
winners['Condorcet Ranked-Choice Voting (Black)'].append(c[winner][0] - ref)

# Ideal winner method. Votes don't matter at all; pick the center.
winner = np.argmin(abs(c))
winners['Best possible winner (nearest center)'].append(c[winner][0])
winner = int(np.argmin(np.abs(c[:, 0] - ref)))
winners['Best possible winner (nearest voter median)'].append(c[winner][0] - ref)

return winners

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