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epacuit merged 3 commits into from
Dec 27, 2025
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Updated axiom tables and added Positive Responsiveness #172

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ad0547d
Updated axiom tables
wesholliday Dec 25, 2025
3375ca1
Added Positive Responsiveness axiom
wesholliday Dec 25, 2025
0cf9e7e
Further updates to axiom tables
wesholliday Dec 26, 2025
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147 changes: 75 additions & 72 deletions axiom_tables/axiom_violations_dominance_axioms_profile.html
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23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Anti_Plurality_reinforcement.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Anti-Plurality – Reinforcement (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
</style>
</head><body><h1>Anti-Plurality</h1>
<h2>Citation for Reinforcement</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Young (1975) states that every scoring rule satisfies reinforcement (also called &#x27;consistency&#x27;). Anti-plurality is a scoring rule; hence it satisfies reinforcement.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='http://www.jstor.org/stable/2100365' target='_blank'>http://www.jstor.org/stable/2100365</a></li>
</ul>
</body></html>
24 changes: 24 additions & 0 deletions ...tables/citation_details/citation_profile_Anti_Plurality_weak_positive_responsiveness.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Anti-Plurality – Weak Positive Responsiveness (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
</style>
</head><body><h1>Anti-Plurality</h1>
<h2>Citation for Weak Positive Responsiveness</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Holliday and Pacuit (2025) note that all proper scoring rules (in the sense of Zwicker 2016, Def. 2.9) satisfy weak positive responsiveness. As a positional scoring rule, this covers the method.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://link.springer.com/article/10.1007/s00355-025-01598-7' target='_blank'>https://link.springer.com/article/10.1007/s00355-025-01598-7</a></li>
<li><a href='https://arxiv.org/abs/2312.14256' target='_blank'>https://arxiv.org/abs/2312.14256</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Baldwin_condorcet_winner.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Baldwin – Condorcet Winner (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
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</head><body><h1>Baldwin</h1>
<h2>Citation for Condorcet Winner</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Schulze (2011, Table 2) notes that Baldwin is a Condorcet method.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/s00355-010-0475-4' target='_blank'>https://doi.org/10.1007/s00355-010-0475-4</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Beat_Path_condorcet_winner.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Beat Path – Condorcet Winner (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
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</head><body><h1>Beat Path</h1>
<h2>Citation for Condorcet Winner</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Schulze (2011, Sect. 4.7) proves that Beat Path satisfies the Condorcet criterion (as a special case of the Smith criterion).</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/s00355-010-0475-4' target='_blank'>https://doi.org/10.1007/s00355-010-0475-4</a></li>
</ul>
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23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Beat_Path_monotonicity.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Beat Path – Monotonicity (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
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</head><body><h1>Beat Path</h1>
<h2>Citation for Monotonicity</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Schulze (2011, Sect. 4.5) proves that Beat Path satisfies monotonicity.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/s00355-010-0475-4' target='_blank'>https://doi.org/10.1007/s00355-010-0475-4</a></li>
</ul>
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23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Beat_Path_neutral_reversal.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Beat Path – Neutral Reversal (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
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</head><body><h1>Beat Path</h1>
<h2>Citation for Neutral Reversal</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Here we are assuming the margin-based version of Beat Path, and all margin-based methods satisfy neutral reversal.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://arxiv.org/abs/2501.08595' target='_blank'>https://arxiv.org/abs/2501.08595</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Beat_Path_pareto_dominance.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Beat Path – Pareto Dominance Criterion (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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ul { margin: 0.5em 0; padding-left: 2em; }
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</style>
</head><body><h1>Beat Path</h1>
<h2>Citation for Pareto Dominance Criterion</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Schulze (2011, Sect. 4.3) proves that Beat Path satisfies the Pareto criterion.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/s00355-010-0475-4' target='_blank'>https://doi.org/10.1007/s00355-010-0475-4</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Beat_Path_smith.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Beat Path – Smith (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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</head><body><h1>Beat Path</h1>
<h2>Citation for Smith</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Schulze (2011, Sect. 4.7) proves that Beat Path satisfies the Smith criterion.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/s00355-010-0475-4' target='_blank'>https://doi.org/10.1007/s00355-010-0475-4</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_condorcet_loser.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Condorcet Loser (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
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</head><body><h1>Borda</h1>
<h2>Citation for Condorcet Loser</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Felsenthal (2012, Table 3.2) states that Borda does not elect Condorcet losers.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/978-3-642-20441-8_3' target='_blank'>https://doi.org/10.1007/978-3-642-20441-8_3</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_monotonicity.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Monotonicity (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
</style>
</head><body><h1>Borda</h1>
<h2>Citation for Monotonicity</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Felsenthal (2012, Table 3.2) states that Borda satisfies monotonicity.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/978-3-642-20441-8_3' target='_blank'>https://doi.org/10.1007/978-3-642-20441-8_3</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_neutral_reversal.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Neutral Reversal (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
</style>
</head><body><h1>Borda</h1>
<h2>Citation for Neutral Reversal</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Saari (2003) notes that Borda satisfies neutral reversal.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1086/342857' target='_blank'>https://doi.org/10.1086/342857</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_pareto_dominance.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Pareto Dominance Criterion (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

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a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
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</head><body><h1>Borda</h1>
<h2>Citation for Pareto Dominance Criterion</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Felsenthal (2012, Table 3.2) states that Borda satisfies Pareto dominance.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/978-3-642-20441-8_3' target='_blank'>https://doi.org/10.1007/978-3-642-20441-8_3</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_reinforcement.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Reinforcement (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
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</head><body><h1>Borda</h1>
<h2>Citation for Reinforcement</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Young (1975) states that every scoring rule satisfies reinforcement (also called &#x27;consistency&#x27;). Borda is a scoring rule; hence it satisfies reinforcement.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='http://www.jstor.org/stable/2100365' target='_blank'>http://www.jstor.org/stable/2100365</a></li>
</ul>
</body></html>
24 changes: 24 additions & 0 deletions axiom_tables/citation_details/citation_profile_Borda_weak_positive_responsiveness.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Borda – Weak Positive Responsiveness (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
li { margin: 0.3em 0; }
</style>
</head><body><h1>Borda</h1>
<h2>Citation for Weak Positive Responsiveness</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Holliday and Pacuit (2025) note that all proper scoring rules (in the sense of Zwicker 2016, Def. 2.9) satisfy weak positive responsiveness. As a positional scoring rule, this covers the method.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://link.springer.com/article/10.1007/s00355-025-01598-7' target='_blank'>https://link.springer.com/article/10.1007/s00355-025-01598-7</a></li>
<li><a href='https://arxiv.org/abs/2312.14256' target='_blank'>https://arxiv.org/abs/2312.14256</a></li>
</ul>
</body></html>
23 changes: 23 additions & 0 deletions axiom_tables/citation_details/citation_profile_Bucklin_monotonicity.html
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<!DOCTYPE html><html><head><meta charset='utf-8'><title>Bucklin – Monotonicity (citation)</title>
<style>
body, table, h1, h2, p, ul, li { font-family: Arial, sans-serif; }

h1 { margin-bottom: .2em; }
h2 { margin-top: 0; font-size: 1.1em; color: #444; }

a { color: #0066cc; text-decoration: none; }
a:hover { text-decoration: underline; }

ul { margin: 0.5em 0; padding-left: 2em; }
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</head><body><h1>Bucklin</h1>
<h2>Citation for Monotonicity</h2>
<p><b>Profile&nbsp;type:</b> Profile</p>
<p><b>Notes:</b></p>
<p>Felsenthal (2012, Table 3.2) states that Bucklin satisfies monotonicity.</p>
<p><b>Sources:</b></p>
<ul>
<li><a href='https://doi.org/10.1007/978-3-642-20441-8_3' target='_blank'>https://doi.org/10.1007/978-3-642-20441-8_3</a></li>
</ul>
</body></html>
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