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<title>Nanson's method</title>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">A joint <a href="Portal%3APolitics" title="Portal:Politics">Politics</a> and <a href="Portal%3AEconomics" title="Portal:Economics">Economics</a> series</td></tr><tr><th class="sidebar-title-with-pretitle" style="border-top:1px #fafafa solid; border-bottom:1px #fafafa solid; background:#efefef; background: var(--background-color-interactive, #efefef); color: var(--color-base, #000); padding:0.2em;"><a href="Social_choice_theory" title="Social choice theory">Social choice</a> and <a href="Electoral_system" title="Electoral system">electoral systems</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-above">

<div class="hlist"><ul><li><a href="Social_choice_theory" title="Social choice theory">Social choice</a></li><li><a href="Mechanism_design" title="Mechanism design">Mechanism design</a></li><li><a href="Comparative_politics" title="Comparative politics">Comparative politics</a></li><li><a href="Comparison_of_voting_rules" title="Comparison of voting rules">Comparison</a></li><li><a href="List_of_electoral_systems" title="List of electoral systems">List</a><span class="nowrap"> </span>(<a href="List_of_electoral_systems_by_country" title="List of electoral systems by country">By country</a>)</li></ul></div></td></tr><tr><td class="sidebar-content" style="text-align:left;">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="Single-member_district" title="Single-member district">Single-winner methods</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Single vote – <a href="Plurality_voting" title="Plurality voting">plurality</a> methods</b>

<ul><li><a href="First-past-the-post_voting" title="First-past-the-post voting">First preference plurality (FPP)</a></li>

<li><a href="Two-round_system" title="Two-round system">Two-round</a> (<abbr style="font-size:85%" title=""><a href="American_English" title="American English">US</a>:</abbr> <a href="Nonpartisan_primary" title="Nonpartisan primary">Jungle primary</a>)

<ul><li><a href="Partisan_primary" class="mw-redirect" title="Partisan primary">Partisan primary</a></li></ul></li>

<li><a href="Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a>

<ul><li><abbr style="font-size:85%" title=""><a href="British_English" title="British English">UK</a>:</abbr> Alternative vote (AV)</li>

<li><abbr style="font-size:85%" title=""><a href="American_English" title="American English">US</a>:</abbr> Ranked-choice (RCV)</li></ul></li>

<li><a href="Party_block_voting" class="mw-redirect" title="Party block voting">Party block voting</a></li>

<li><a href="Plurality_block_voting" title="Plurality block voting">Plurality block voting</a></li></ul>

<hr>

<p><b><a href="Condorcet_method" title="Condorcet method">Condorcet methods</a></b>

</p>

<ul><li><a href="Tideman_alternative_method" title="Tideman alternative method">Condorcet-IRV</a></li>

<li><a href="Round-robin_voting" title="Round-robin voting">Round-robin voting</a>

<ul><li><a href="Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax</a></li>

<li><a href="Kemeny_method" title="Kemeny method">Kemeny</a></li>

<li><a href="Schulze_method" title="Schulze method">Schulze</a></li>

<li><a href="Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li>

<li><a href="Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li></ul></li></ul>

<hr>

<p><b><a href="Positional_voting" title="Positional voting">Positional voting</a></b>

</p>

<ul><li><a href="First-preference_plurality" class="mw-redirect" title="First-preference plurality">Plurality</a> (<abbr style="font-size:85%" title=""><a href="Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="Instant-runoff_voting" title="Instant-runoff voting">IRV</a>)</li>

<li><a href="Borda_count" title="Borda count">Borda count</a> (<abbr style="font-size:85%" title=""><a href="Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="Baldwin's_method" class="mw-redirect" title="Baldwin's method">Baldwin</a>, <abbr style="font-size:85%" title=""><a href="Highest_median_voting_rules" title="Highest median voting rules">Mdn.</a></abbr> <a href="Bucklin_voting" title="Bucklin voting">Bucklin</a>)</li>

<li><a href="Anti-plurality_voting" title="Anti-plurality voting">Antiplurality</a> (<abbr style="font-size:85%" title=""><a href="Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="Coombs_method" class="mw-redirect" title="Coombs method">Coombs</a>)</li></ul>

<hr>

<p><b><a href="Rated_voting" title="Rated voting">Cardinal voting</a></b>

</p>

<ul><li><a href="Score_voting" title="Score voting">Score voting</a></li>

<li><a href="Approval_voting" title="Approval voting">Approval voting</a></li>

<li><a href="Highest_median_voting_rules" title="Highest median voting rules">Majority judgment</a></li>

<li><a href="STAR_voting" title="STAR voting">STAR voting</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content" style="text-align:left;">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="Proportional_representation" title="Proportional representation">Proportional representation</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></b>

<ul><li><a href="Apportionment_(politics)" title="Apportionment (politics)">Apportionment</a>

<ul><li><a href="Highest_averages_method" title="Highest averages method">Highest averages</a></li>

<li><a href="Largest_remainder_method" class="mw-redirect" title="Largest remainder method">Largest remainders</a></li>

<li><a href="National_remnant" title="National remnant">National remnant</a></li>

<li><a href="Biproportional_apportionment" title="Biproportional apportionment">Biproportional</a></li></ul></li>

<ul><li><a href="Closed_list" title="Closed list">Closed list</a></li>

<li><a href="Panachage" title="Panachage">Panachage</a></li>

<li><a href="Localized_list" title="Localized list">Localized list</a></li></ul></li></ul>

<hr>

<p><b><a href="Electoral_quota" title="Electoral quota">Quota-remainder methods</a></b>

</p>

<li><a href="Schulze_STV" title="Schulze STV">Schulze STV</a></li>

<li><a href="Quota_Borda_system" title="Quota Borda system">Quota Borda</a></li></ul>

<hr>

<p><b><a href="Approval-based_committee" class="mw-redirect" title="Approval-based committee">Approval-based committees</a></b>

</p>

<ul><li><a href="Proportional_approval_voting" title="Proportional approval voting">Thiele's method</a></li>

<li><a href="Phragmen's_voting_rules" title="Phragmen's voting rules">Phragmen's method</a></li>

<li><a href="Expanding_approvals_rule" title="Expanding approvals rule">Expanding approvals rule</a></li>

<li><a href="Method_of_equal_shares" title="Method of equal shares">Method of equal shares</a></li></ul>

<hr>

<p><b><a href="Fractional_social_choice" title="Fractional social choice">Fractional social choice</a></b>

</p>

<ul><li><a href="Direct_representation" title="Direct representation">Direct representation</a>

<ul><li><a href="Interactive_representation" title="Interactive representation">Interactive representation</a></li>

<li><a href="Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li></ul></li>

<li><a href="Fractional_approval_voting" title="Fractional approval voting">Fractional approval voting</a></li>

<li><a href="Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li>

<li><a href="Random_ballot" title="Random ballot">Random ballot</a></li></ul>

<hr>

<p><b><a href="Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional representation</a></b>

</p>

<ul><li><a href="Cumulative_voting" title="Cumulative voting">Cumulative</a>

<li><a href="Limited_voting" title="Limited voting">Limited voting</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content" style="text-align:left;">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="Mixed_electoral_system" title="Mixed electoral system">Mixed systems</a></div><div class="sidebar-list-content mw-collapsible-content"><b>By results of combination</b>

<ul><li><a href="Mixed-member_majoritarian_representation" title="Mixed-member majoritarian representation">Mixed-member majoritarian</a></li>

<li><a href="Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member proportional</a></li></ul>

<hr><b>By mechanism of combination</b>

<ul><li><b>Non-<a href="Compensation_(electoral_systems)" title="Compensation (electoral systems)">compensatory</a></b>

<ul><li><a href="Parallel_voting" title="Parallel voting">Parallel (superposition)</a></li>

<li><a href="Coexistence_(electoral_systems)" title="Coexistence (electoral systems)">Coexistence</a></li>

<li>Conditional</li>

<li><a href="Majority_bonus_system" title="Majority bonus system">Fusion (majority bonus)</a></li></ul></li>

<li><b><a href="Compensation_(electoral_systems)" title="Compensation (electoral systems)">Compensatory</a></b>

<ul><li>Seat linkage system

<li><a href="Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage system</a>

<ul><li><a href="Scorporo" title="Scorporo">Negative vote transfer</a></li>

<li><a href="Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot</a></li></ul></li></ul></li>

<li><a href="Mixed_electoral_system" title="Mixed electoral system">Supermixed systems</a>

<ul><li><a href="Dual-member_proportional_representation" class="mw-redirect" title="Dual-member proportional representation">Dual-member proportional</a></li>

<li><a href="Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban proportional</a></li>

<li><a href="Majority_jackpot_system" title="Majority jackpot system">Majority jackpot</a></li></ul></li></ul>

<hr>

<p><b>By ballot type</b>

</p>

<ul><li><a href="Mixed_single_vote" title="Mixed single vote">Single vote</a>

<ul><li><a href="Double_simultaneous_vote" title="Double simultaneous vote">Double simultaneous vote</a></li></ul></li>

</tr><tr><td class="sidebar-content" style="text-align:left;">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="Pathological_(mathematics)#Voting" title="Pathological (mathematics)">Paradoxes and pathologies</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Spoiler effects</b>

<ul><li><a href="Spoiler_effect" title="Spoiler effect">Spoiler effect</a></li>

<li><a href="Independence_of_clones" class="mw-redirect" title="Independence of clones">Cloning paradox</a></li>

<li><a href="Condorcet_winner_criterion" title="Condorcet winner criterion">Frustrated majorities paradox</a></li>

<li><a href="Center_squeeze" title="Center squeeze">Center squeeze</a></li></ul>

<hr>

<p><b>Pathological response</b>

</p>

<ul><li><a href="Perverse_response" class="mw-redirect" title="Perverse response">Perverse response</a></li>

<li><a href="Best-is-worst_paradox" class="mw-redirect" title="Best-is-worst paradox">Best-is-worst paradox</a></li>

<li><a href="No-show_paradox" class="mw-redirect" title="No-show paradox">No-show paradox</a></li>

<li><a href="Multiple_districts_paradox" class="mw-redirect" title="Multiple districts paradox">Multiple districts paradox</a></li></ul>

<hr>

<p><b><a href="Strategic_voting" title="Strategic voting">Strategic voting</a></b>

</p>

<ul><li><a href="Sincere_favorite_criterion" title="Sincere favorite criterion">Lesser evil voting</a></li>

<li><a href="Strategic_voting#Exaggeration" title="Strategic voting">Exaggeration</a></li>

<li><a href="Truncation_(voting)" class="mw-redirect" title="Truncation (voting)">Truncation</a></li>

<li><a href="Turkey-raising" class="mw-redirect" title="Turkey-raising">Turkey-raising</a></li>

<li><a href="Wasted_vote" title="Wasted vote">Wasted vote</a></li></ul>

<hr>

<p><b>Paradoxes of <a href="Majority_rule" title="Majority rule">majority rule</a></b>

</p>

<ul><li><a href="Tyranny_of_the_majority" title="Tyranny of the majority">Tyranny of the majority</a></li>

<li><a href="Discursive_dilemma" class="mw-redirect" title="Discursive dilemma">Discursive dilemma</a></li>

<li><a href="Condorcet_paradox" title="Condorcet paradox">Conflicting majorities paradox</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content" style="text-align:left;">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="Social_choice_theory" title="Social choice theory">Social and collective choice</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="Proof_of_impossibility" title="Proof of impossibility">Impossibility theorems</a></b>

<ul><li><a href="Arrow's_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's theorem</a></li>

<li><a href="Condorcet_paradox" title="Condorcet paradox">Majority impossibility</a></li>

<li><a href="Moulin's_impossibility_theorem" class="mw-redirect" title="Moulin's impossibility theorem">Moulin's impossibility theorem</a></li>

<li><a href="McKelvey%E2%80%93Schofield_chaos_theorem" title="McKelvey–Schofield chaos theorem">McKelvey–Schofield chaos theorem</a></li>

<li><a href="Gibbard's_theorem" title="Gibbard's theorem">Gibbard's theorem</a></li></ul>

<hr>

<p><b>Positive results</b>

</p>

<ul><li><a href="Median_voter_theorem" title="Median voter theorem">Median voter theorem</a></li>

<li><a href="Condorcet's_jury_theorem" title="Condorcet's jury theorem">Condorcet's jury theorem</a></li>

<li><a href="May's_theorem" title="May's theorem">May's theorem</a></li>

<li><a href="Arrow's_theorem" class="mw-redirect" title="Arrow's theorem">Condorcet dominance theorems</a></li>

<li>Harsanyi's utilitarian theorem</li>

<li><a href="Vickrey-Clarke-Groves_mechanism" class="mw-redirect" title="Vickrey-Clarke-Groves mechanism">VCG mechanism</a></li>

<li><a href="Quadratic_voting" title="Quadratic voting">Quadratic voting</a></li></ul></div></div></td>

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<div class="hlist"><ul><li><span class="nowrap"><span class="mw-image-border noviewer" typeof="mw:File"></span> </span><a href="Portal%3APolitics" title="Portal:Politics">Politics portal</a></li><li><span class="nowrap"><span class="noviewer" typeof="mw:File"></span> </span><a href="Portal%3AEconomics" title="Portal:Economics">Economics portal</a></li></ul></div><span class="nowrap"><span class="skin-invert-image noviewer" typeof="mw:File"></span> </span><a href="Portal%3AMathematics" title="Portal:Mathematics">Mathematics portal</a></td></tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r1239400231">

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<p>The <a href="Borda_count" title="Borda count">Borda count</a> <a href="Electoral_system" title="Electoral system">electoral system</a> can be combined with an <a href="Instant-runoff_voting" title="Instant-runoff voting">instant-runoff</a> procedure to create hybrid election methods that are called <b>Nanson method</b> and <b>Baldwin method</b> (also called <b>Total Vote Runoff</b> or <b>TVR</b>). Both methods are designed to satisfy the <a href="Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet criterion</a>, and allow for incomplete ballots and equal rankings.

</p>

<div class="mw-heading mw-heading2"><h2 id="Nanson_method">Nanson method</h2></div>

<p>The Nanson method is based on the original work of the <a href="Mathematician" title="Mathematician">mathematician</a> <a href="Edward_J._Nanson" title="Edward J. Nanson">Edward J. Nanson</a> in 1882.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Nanson's method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains.

</p><p>If a <a href="Condorcet_winner" class="mw-redirect" title="Condorcet winner">Condorcet winner</a> exists, they will be elected. If not, (there is a <a href="Condorcet_cycle" class="mw-redirect" title="Condorcet cycle">Condorcet cycle</a>) then the preference with the smallest majority will be eliminated.<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 214">: 214 </span></sup>

</p><p>Nanson's method can be adapted to handle incomplete ballots (including "<a href="Bullet_voting" title="Bullet voting">plumping</a>") and equal rankings ("bracketing"), though he describes two different methods to handle these cases: a theoretically correct method involving fractions of a vote, and a practical method involving whole numbers (which has the side effect of diminishing the voting power of voters who plump or bracket).<sup id="cite_ref-:0_1-3" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 231, 235">: 231, 235 </span></sup> This then allows the use of <a href="Approval_voting" title="Approval voting">Approval</a>-style voting for uninformed voters who merely wish to approve of some candidates and disapprove of others.<sup id="cite_ref-:0_1-4" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 236">: 236 </span></sup>

</p><p>The method can be adapted to multi-winner elections by removing the name of a winner from the ballots and re-calculating, though this just elects the highest-ranked <i>n</i> candidates and does not result in proportional representation.<sup id="cite_ref-:0_1-5" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 240">: 240 </span></sup>

</p><p>Schwartz in 1986 studied a slight variant of Nanson's rule, in which candidates less than <i>but not equal to</i> the average Borda count score are eliminated in each round.<sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Baldwin_method">Baldwin method</h2></div>

<p>Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.

</p><p>This method actually predates Nanson's, who notes it was already in use by the <a href="Trinity_College%2C_Cambridge" title="Trinity College, Cambridge">Trinity College</a> Dialectic Society.<sup id="cite_ref-:0_1-6" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 217">: 217 </span></sup>

</p><p>It was systematized by <a href="Joseph_M._Baldwin" title="Joseph M. Baldwin">Joseph M. Baldwin</a><sup id="cite_ref-:2_3-0" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> in 1926, who incorporated <a href="Condorcet_method#Pairwise_counting_and_matrices" title="Condorcet method">a more efficient matrix tabulation</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and extended it to support incomplete ballots and equal rankings, by counting fractional points in such cases.

</p><p>The two methods have been confused with each other in some literature.<sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>This system has been proposed for use in the United States under the name "Total Vote Runoff", by <a href="Edward_B._Foley" title="Edward B. Foley">Edward B. Foley</a> and <a href="Eric_Maskin" title="Eric Maskin">Eric Maskin</a>, as a way to fix problems with the <a href="Instant-runoff_voting" title="Instant-runoff voting">instant-runoff method</a> in U.S. jurisdictions that use it.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Satisfied_and_failed_criteria">Satisfied and failed criteria</h2></div>

<p>The Nanson method and the Baldwin method satisfy the <a href="Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet criterion</a>.<sup id="cite_ref-:1_2-2" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Because Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated.

</p><p>They do not satisfy the <a href="Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">independence of irrelevant alternatives</a> criterion, the <a href="Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">monotonicity criterion</a>, the <a href="Participation_criterion" title="Participation criterion">participation criterion</a>, the <a href="Consistency_criterion" title="Consistency criterion">consistency criterion</a> and the <a href="Independence_of_clones_criterion" title="Independence of clones criterion">independence of clones criterion</a>, while they do satisfy the <a href="Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">majority criterion</a>, the <a href="Mutual_majority_criterion" title="Mutual majority criterion">mutual majority criterion</a>, the <a href="Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a> and the <a href="Smith_set" title="Smith set">Smith criterion</a>. The Nanson method satisfies and the Baldwin method violates <a href="Reversal_symmetry" title="Reversal symmetry">reversal symmetry</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>Both the Nanson and the Baldwin methods can be run in <a href="Time_complexity" title="Time complexity">polynomial time</a> to obtain a single winner. For the Baldwin method, however, at each stage, there might be several candidates with lowest Borda score. In fact, it is <a href="NP-completeness" title="NP-completeness">NP-complete</a> to decide whether a given candidate is a Baldwin winner, i.e., whether there exists an elimination sequence that leaves a given candidate uneliminated.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

</p><p>Both methods are computationally more difficult to manipulate than Borda's method.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Use_of_Nanson_and_Baldwin">Use of Nanson and Baldwin</h2></div>

<p>Nanson's method was used in city elections in the <a href="United_States" title="United States">U.S.</a> town of <a href="Marquette%2C_Michigan" title="Marquette, Michigan">Marquette, Michigan</a> in the 1920s.<sup id="cite_ref-Marquette_13-0" class="reference"><a href="#cite_note-Marquette-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> It was formerly used by the <a href="Anglican" class="mw-redirect" title="Anglican">Anglican</a> Diocese of <a href="Melbourne" title="Melbourne">Melbourne</a> and in the election of members of the University Council of the <a href="University_of_Adelaide" title="University of Adelaide">University of Adelaide</a>. It was used by the <a href="University_of_Melbourne" title="University of Melbourne">University of Melbourne</a> until 1983.

</p>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFNanson1882" class="citation journal cs1">Nanson, E. J. (1882). <a rel="nofollow" class="external text" href="https://archive.org/details/transactionsproc1719roya/page/197">"Methods of election"</a>. <i>Transactions and Proceedings of the Royal Society of Victoria</i>. <b>19</b>: <span class="nowrap">197–</span>240.</cite></span>

</li>

<li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFNiou1987" class="citation journal cs1">Niou, Emerson M. S. (1987). "A Note on Nanson's Rule". <i>Public Choice</i>. <b>54</b> (2): <span class="nowrap">191–</span>193. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.8191">10.1.1.460.8191</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00123006">10.1007/BF00123006</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0048-5829">0048-5829</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:154538772">154538772</a>.</cite></span>

</li>

<li id="cite_note-:2-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-:2_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFBaldwin1926" class="citation journal cs1">Baldwin, J. M. (1926). <a rel="nofollow" class="external text" href="https://archive.org/details/proceedingsroyaxxxvroyaa/page/42">"The technique of the Nanson preferential majority system of election"</a>. <i>Proceedings of the Royal Society of Victoria</i>. <b>39</b>: <span class="nowrap">42–</span>52. <q>In each case where on a voting paper no preference is expressed as between two candidates, half a preference is to be credited to each of the two candidates … For each paper where any number, p, of candidates are placed equal with a preference ranking as first, 1/p is to be credited to each of the candidates so placed.</q></cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFHogben1913" class="citation journal cs1">Hogben, G. (1913). <a rel="nofollow" class="external text" href="http://rsnz.natlib.govt.nz/volume/rsnz_46/rsnz_46_00_005780.html">"Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes"</a>. <i>Transactions and Proceedings of the Royal Society of New Zealand</i>. <b>46</b>: <span class="nowrap">304–</span>308.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFFoleyMaskin2022" class="citation news cs1"><a href="Edward_B._Foley" title="Edward B. Foley">Foley, Edward B.</a>; <a href="Eric_Maskin" title="Eric Maskin">Maskin, Eric S.</a> (November 1, 2022). <a rel="nofollow" class="external text" href="https://www.washingtonpost.com/opinions/2022/11/01/alaska-final-four-primary-begich-palin-peltola/">"Alaska's ranked-choice voting is flawed. But there's an easy fix"</a>. <i>Washington Post</i>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0190-8286">0190-8286</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-11-09</span></span>. <q>the way Alaska uses ranked-choice voting also caused the defeat of Begich, whom most Alaska voters preferred to Democrat Mary Peltola … A candidate popular only with the party's base would be eliminated early in a Total Vote Runoff, leaving a more broadly popular Republican to compete against a Democrat.</q></cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFEdward_B._Foley2023" class="citation journal cs1">Edward B. Foley (2023-03-01). <a rel="nofollow" class="external text" href="https://scholars.unh.edu/unh_lr/vol21/iss2/5">"Total Vote Runoff: A Majority-Maximizing Form of Rank Choice Voting"</a>. <i>The University of New Hampshire Law Review</i>. <b>21</b> (2): 323. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2325-7318">2325-7318</a>.</cite></span>

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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFFoley2022" class="citation web cs1"><a href="Edward_B._Foley" title="Edward B. Foley">Foley, Ned</a> (November 1, 2022). <a rel="nofollow" class="external text" href="https://electionlawblog.org/?p=132792">""Total Vote Runoff" tweak to Ranked Choice Voting"</a>. <i>Election Law Blog</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-11-09</span></span>. <q>a small but significant adjustment to the "instant runoff" method … equivalent to a candidate's Borda score, and eliminating sequentially the candidate with the lowest total votes</q></cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFFoley2022" class="citation web cs1"><a href="Edward_B._Foley" title="Edward B. Foley">Foley, Ned</a> (November 8, 2022). <a rel="nofollow" class="external text" href="https://electionlawblog.org/?p=132963">"An Additional Detail about "Total Vote Runoff""</a>. <i>Election Law Blog</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-11-09</span></span>. <q>Begich and Peltola each get half a vote by being tied for second place on this ballot</q></cite></span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFFoley" class="citation web cs1">Foley, Ned. <a rel="nofollow" class="external text" href="https://electionlawblog.org/?p=133027">""Total Vote Runoff" & Baldwin's method"</a>. <i>Election Law Blog</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-11-20</span></span>. <q>In this respect, TVR differs from Baldwin's method, which without checking whether any candidate has more than 50% of first-place votes would immediately recalculate Borda scores</q></cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mail-archive.com/election-methods@lists.electorama.com/msg00625.html">"Re: [Election-Methods] Borda-elimination, a Condorcet method for public elections?"</a>. <i>www.mail-archive.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-06-19</span></span>.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFMatteiNarodytskaWalsh2014" class="citation journal cs1">Mattei, Nicholas; Narodytska, Nina; Walsh, Toby (2014-01-01). "How Hard is It to Control an Election by Breaking Ties?". <i>Proceedings of the Twenty-First European Conference on Artificial Intelligence</i>. ECAI'14. <b>263</b> (ECAI 2014). Amsterdam, the Netherlands, The Netherlands: IOS Press: <span class="nowrap">1067–</span>1068. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1304.6174">1304.6174</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3233%2F978-1-61499-419-0-1067">10.3233/978-1-61499-419-0-1067</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781614994183</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1399756">1399756</a>.</cite></span>

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<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFDaviesKatsirelosNarodytskaWalsh2014" class="citation journal cs1">Davies, Jessica; Katsirelos, George; Narodytska, Nina; Walsh, Toby; Xia, Lirong (2014-12-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.artint.2014.07.005">"Complexity of and algorithms for the manipulation of Borda, Nanson's and Baldwin's voting rules"</a>. <i>Artificial Intelligence</i>. <b>217</b>: <span class="nowrap">20–</span>42. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.artint.2014.07.005">10.1016/j.artint.2014.07.005</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0004-3702">0004-3702</a>.</cite></span>

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<li id="cite_note-Marquette-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Marquette_13-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMcLean2002" class="citation web cs1">McLean, I. (2002). <a rel="nofollow" class="external text" href="http://www.nuff.ox.ac.uk/Politics/papers/2002/w23/mclean.pdf">"Australian electoral reform and two concepts of representation"</a> <span class="cs1-format">(PDF)</span>.</cite></span>

</li>

</ol></div></div>

<ul><li><a href="Duncan_Sommerville" title="Duncan Sommerville">Duncan Sommerville</a> (1928) "Certain hyperspatial partitionings connected with preferential voting", <a href="Proceedings_of_the_London_Mathematical_Society" class="mw-redirect" title="Proceedings of the London Mathematical Society">Proceedings of the London Mathematical Society</a> 28(1):368–82.</li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Electoral_systems390" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Electoral_systems390" style="font-size:114%;margin:0 4em"><a href="Electoral_system" title="Electoral system">Electoral systems</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>Part of the <a href="Portal%3APolitics" title="Portal:Politics">politics</a> and <a href="Portal%3AEconomics" title="Portal:Economics">Economics</a> series</i></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Single-winner_voting_system" class="mw-redirect" title="Single-winner voting system">Single-winner</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Approval_voting" title="Approval voting">Approval voting</a>

<ul><li><a href="Combined_approval_voting" title="Combined approval voting">Combined approval voting</a></li>

<li><a href="Unified_primary" title="Unified primary">Unified primary</a></li></ul></li>

<li><a href="Borda_count" title="Borda count">Borda count</a></li>

<li><a href="Bucklin_voting" title="Bucklin voting">Bucklin voting</a></li>

<li><a href="Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet methods</a>

<ul><li><a href="Copeland's_method" title="Copeland's method">Copeland's method</a></li>

<li><a href="Dodgson's_method" title="Dodgson's method">Dodgson's method</a></li>

<li><a href="Kemeny_method" title="Kemeny method">Kemeny method</a></li>

<li><a href="Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a></li>

<li><a href="Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li>

<li><a href="Schulze_method" title="Schulze method">Schulze method</a></li></ul></li>

<li><a href="Exhaustive_ballot" title="Exhaustive ballot">Exhaustive ballot</a></li>

<li><a href="First-past-the-post_voting" title="First-past-the-post voting">First-past-the-post voting</a></li>

<li><a href="Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a>

<ul><li><a href="Coombs'_method" title="Coombs' method">Coombs' method</a></li>

<li><a href="Contingent_vote" title="Contingent vote">Contingent vote</a></li>

<li><a href="Supplementary_vote" class="mw-redirect" title="Supplementary vote">Supplementary vote</a></li></ul></li>

<li><a href="Majority_rule" title="Majority rule">Simple majoritarianism</a></li>

<li><a href="Plurality_voting_system" class="mw-redirect" title="Plurality voting system">Plurality</a></li>

<li><a href="Positional_voting_system" class="mw-redirect" title="Positional voting system">Positional voting system</a></li>

<li><a href="Score_voting" title="Score voting">Score voting</a></li>

<li><a href="STAR_voting" title="STAR voting">STAR voting</a></li>

<li><a href="Two-round_system" title="Two-round system">Two-round system</a></li>

<li><a href="Graduated_majority_judgment" title="Graduated majority judgment">Graduated majority judgment</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Proportional_representation" title="Proportional representation">Proportional</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member</a></li>

<li><a href="Mixed_single_vote#Proportional_systems" title="Mixed single vote">Mixed single vote</a></li>

<li><a href="Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></li>

<li><a href="Proportional_approval_voting" title="Proportional approval voting">Proportional approval voting</a></li>

<li><a href="Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban</a></li>

<li><a href="Sequential_proportional_approval_voting" title="Sequential proportional approval voting">Sequential proportional approval voting</a></li>

<li><a href="Single_transferable_vote" title="Single transferable vote">Single transferable vote</a>

<li><a href="Hare%E2%80%93Clark_electoral_system" title="Hare–Clark electoral system">Hare–Clark</a></li>

<li><a href="Schulze_STV" title="Schulze STV">Schulze STV</a></li></ul></li>

<li><a href="Spare_vote" title="Spare vote">Spare vote</a></li>

<li><a href="Indirect_single_transferable_voting" title="Indirect single transferable voting">Indirect single transferable voting</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Allocation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Highest_averages_method" title="Highest averages method">Highest averages method</a>

<ul><li><a href="Sainte-Lagu%C3%AB_method" title="Sainte-Laguë method">Webster/Sainte-Laguë</a></li>

<li><a href="D'Hondt_method" title="D'Hondt method">D'Hondt</a></li></ul></li>

<li><a href="Largest_remainders_method" class="mw-redirect" title="Largest remainders method">Largest remainders method</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quotas</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Droop_quota" title="Droop quota">Droop quota</a></li>

<li><a href="Hagenbach-Bischoff_quota" class="mw-redirect" title="Hagenbach-Bischoff quota">Hagenbach-Bischoff quota</a></li>

<li><a href="Hare_quota" title="Hare quota">Hare quota</a></li>

<li><a href="Imperiali_quota" title="Imperiali quota">Imperiali quota</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Mixed_electoral_system" title="Mixed electoral system">Mixed</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Parallel_voting" title="Parallel voting">Parallel voting</a></li>

<li><a href="Additional_member_system" class="mw-redirect" title="Additional member system">Additional member system</a></li>

<li><a href="Alternative_vote_plus" title="Alternative vote plus">Alternative vote plus</a></li>

<li><a href="Mixed_single_vote" title="Mixed single vote">Mixed single vote</a></li>

<li><a href="Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot transferable vote</a></li>

<li><a href="Scorporo" title="Scorporo">Scorporo</a></li>

<li><a href="Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage mixed system</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Single_non-transferable_vote" title="Single non-transferable vote">Single non-transferable vote</a></li>

<li><a href="Limited_voting" title="Limited voting">Limited voting</a></li>

<li><a href="Cumulative_voting" title="Cumulative voting">Cumulative voting</a></li>

<li><a href="Satisfaction_approval_voting" title="Satisfaction approval voting">Satisfaction approval voting</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Criteria</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a></li>

<li><a href="Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a></li>

<li><a href="Consistency_criterion" title="Consistency criterion">Consistency criterion</a></li>

<li><a href="Independence_of_clones_criterion" title="Independence of clones criterion">Independence of clones</a></li>

<li><a href="Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">Independence of irrelevant alternatives</a></li>

<li><a href="Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Independence of Smith-dominated alternatives</a></li>

<li><a href="Later-no-harm_criterion" title="Later-no-harm criterion">Later-no-harm criterion</a></li>

<li><a href="Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">Majority criterion</a></li>

<li><a href="Majority_loser_criterion" title="Majority loser criterion">Majority loser criterion</a></li>

<li><a href="Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotonicity criterion</a></li>

<li><a href="Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority criterion</a></li>

<li><a href="Participation_criterion" title="Participation criterion">Participation criterion</a></li>

<li><a href="Plurality_criterion" class="mw-redirect" title="Plurality criterion">Plurality criterion</a></li>

<li><a href="Resolvability_criterion" class="mw-redirect" title="Resolvability criterion">Resolvability criterion</a></li>

<li><a href="Reversal_symmetry" title="Reversal symmetry">Reversal symmetry</a></li>

<li><a href="Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a></li>

<li><a href="Seats-to-votes_ratio" title="Seats-to-votes ratio">Seats-to-votes ratio</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Ballot" title="Ballot">Ballot</a></li>

<li><a href="Election_threshold" class="mw-redirect" title="Election threshold">Election threshold</a></li>

<li><a href="First-preference_votes" class="mw-redirect" title="First-preference votes">First-preference votes</a></li>

<li><a href="Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li>

<li><a href="Spoilt_vote" title="Spoilt vote">Spoilt vote</a></li>

<li><a href="Sortition" title="Sortition">Sortition</a></li>

<li><a href="Unseating" title="Unseating">Unseating</a></li>

<li><a href="Wasted_vote" title="Wasted vote">Wasted vote</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Comparison</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_voting_rules" title="Comparison of voting rules">Comparison of voting systems</a></li>

<li><a href="List_of_electoral_systems_by_country" title="List of electoral systems by country">Voting systems by country</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><a href="Portal%3APolitics" title="Portal:Politics">Portal</a></b> — <b>Project</b></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-02-24" href="https://en.wikipedia.org/wiki/?title=Nanson's_method&oldid=1277438043">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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