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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Quota method</span></span>
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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>
<li><a href="Electoral_list" title="Electoral list">List type</a>
<ul><li><a href="Closed_list" title="Closed list">Closed list</a></li>
<li><a href="Open_list" title="Open list">Open list</a></li>
<li><a href="Panachage" title="Panachage">Panachage</a></li>
<li><a href="Justified_representation" title="Justified representation">List-free PR</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>
<ul><li><a href="Single_transferable_vote" title="Single transferable vote">Hare STV</a></li>
<li><a href="Schulze_STV" title="Schulze STV">Schulze STV</a></li>
<li><a href="CPO-STV" title="CPO-STV">CPO-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>
<ul><li><a href="Single_non-transferable_vote" title="Single non-transferable vote">SNTV</a></li></ul></li>
<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
<ul><li><abbr style="font-size:85%" title=""><a href="British_English" title="British English">UK</a>:</abbr> <a href="Additional_member_system" class="mw-redirect" title="Additional member system">'AMS'</a></li>
<li><abbr style="font-size:85%" title=""><a href="New_Zealand_English" title="New Zealand English">NZ</a>:</abbr> <a href="Mixed-member_proportional" class="mw-redirect" title="Mixed-member proportional">'MMP'</a></li></ul></li>
<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>
<li><a href="Mixed_electoral_systems" class="mw-redirect" title="Mixed electoral systems">Dual-vote</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="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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<p>The <b>quota</b> or <b>divide-and-rank methods</b> make up a category of <a href="Apportionment_(politics)" title="Apportionment (politics)">apportionment rules</a>, i.e. algorithms for allocating seats in a legislative body among multiple groups (e.g. <a href="Political_party" title="Political party">parties</a> or <a href="Federal_state" class="mw-redirect" title="Federal state">federal states</a>). The quota methods begin by calculating an <a href="Entitlement_(fair_division)" title="Entitlement (fair division)">entitlement</a> (basic number of seats) for each party, by dividing their vote totals by an <a href="Electoral_quota" title="Electoral quota">electoral quota</a> (a fixed number of votes needed to win a seat, as a unit). Then, leftover seats, if any are allocated by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular <a href="Highest_averages_method" title="Highest averages method">highest averages methods</a> (also called divisor methods).<sup id="cite_ref-:12_1-0" class="reference"><a href="#cite_note-:12-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>By far the most common quota method are the <b>largest remainders</b> or <b>quota-shift methods</b>, which assign any leftover seats to the "plurality" winners (the parties with the largest <a href="Remainder" title="Remainder">remainders</a>, i.e. most leftover votes).<sup id="cite_ref-:02_2-0" class="reference"><a href="#cite_note-:02-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p><p>When using the <a href="Hare_quota" title="Hare quota">Hare quota</a>, this rule is called <b><a href="Alexander_Hamilton" title="Alexander Hamilton">Hamilton</a>'s method</b>, and is the third-most common apportionment rule worldwide (after <a href="Jefferson's_method" class="mw-redirect" title="Jefferson's method">Jefferson's method</a> and <a href="Webster's_method" class="mw-redirect" title="Webster's method">Webster's method</a>).<sup id="cite_ref-:12_1-1" class="reference"><a href="#cite_note-:12-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>Despite their intuitive definition, quota methods are generally disfavored by <a href="Social_choice_theory" title="Social choice theory">social choice theorists</a> as a result of <a href="Apportionment_paradox" title="Apportionment paradox">apportionment paradoxes</a>.<sup id="cite_ref-:12_1-2" class="reference"><a href="#cite_note-:12-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:52_3-0" class="reference"><a href="#cite_note-:52-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In particular, the largest remainder methods exhibit the <a href="Participation_criterion" title="Participation criterion">no-show paradox</a>, i.e. voting <i>for</i> a party can cause it to <i>lose</i> seats.<sup id="cite_ref-:52_3-1" class="reference"><a href="#cite_note-:52-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:02222_4-0" class="reference"><a href="#cite_note-:02222-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The largest remainders methods are also vulnerable to <a href="Spoiler_effect" title="Spoiler effect">spoiler effects</a> and can fail <a href="Resource_monotonicity" title="Resource monotonicity">resource</a> or <a href="House_monotonicity" title="House monotonicity">house monotonicity</a>, which says that increasing the number of seats in a legislature should not cause a party to lose a seat (a situation known as an <a href="Alabama_paradox" class="mw-redirect" title="Alabama paradox">Alabama paradox</a>).<sup id="cite_ref-:52_3-2" class="reference"><a href="#cite_note-:52-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:02222_4-1" class="reference"><a href="#cite_note-:02222-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: Cor.4.3.1">: Cor.4.3.1 </span></sup>
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="Method">Method</h2></div>
<p>The largest remainder method divides each party's vote total by a <i>quota</i>. Usually, quota is derived by dividing the number of valid votes cast, by the number of seats. The result for each party will consist of an <a href="Integer" title="Integer">integer</a> part plus a <a href="Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fractional</a> <a href="Remainder" title="Remainder">remainder</a>. Each party is first allocated a number of seats equal to their integer. This will generally leave some remainder seats unallocated. To apportion these seats, the parties are then ranked on the basis of their fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all seats have been allocated. This gives the method its name - largest remainder.
</p><p>Largest remainder methods produces similar results to <a href="Single_transferable_vote" title="Single transferable vote">single transferable vote</a> or the <a href="Quota_Borda_system" title="Quota Borda system">quota Borda system</a>, where voters organize themselves into <a href="Solid_coalition" title="Solid coalition">solid coalitions</a>. The <a href="Single_transferable_vote" title="Single transferable vote">single transferable vote</a> or the <a href="Quota_Borda_system" title="Quota Borda system">quota Borda system</a> behave like the largest-remainders method when voters all behave like strict partisans (i.e. only mark preferences for candidates of one party).<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>
</p>
<div class="mw-heading mw-heading2"><h2 id="Quotas">Quotas</h2></div>
<style data-mw-deduplicate="TemplateStyles:r1236090951">
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electoral_quota" title="Electoral quota">Electoral quota</a></div>
<p>There are several possible choices for the <a href="Electoral_quota" title="Electoral quota">electoral quota</a>. The choice of quota affects the properties of the corresponding largest remainder method, and particularly the <a href="Seat_bias" title="Seat bias">seat bias</a>. Smaller quotas allow small parties to pick up seats, while larger quotas leave behind more votes. A somewhat counterintuitive result of this is that a <i>larger</i> quota will always be more favorable to <i>smaller</i> parties.<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> A party hoping to win multiple seats sees fewer votes captured by a single popular candidate when the quota is small.
</p><p>The two most common quotas are the <a href="Hare_quota" title="Hare quota">Hare quota</a> and the <a href="Droop_quota" title="Droop quota">Droop quota</a>. The use of a particular quota with one of the largest remainder methods is often abbreviated as "LR-[quota name]", such as "LR-Droop".<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>
</p><p>The Hare (or simple) quota is defined as follows:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\text{total votes}}{\text{total seats}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mtext>total votes</mtext>
<mtext>total seats</mtext>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{total votes}}{\text{total seats}}}}</annotation>
</semantics>
</math></span><img src="./b052857e63f0b31691b3438f19561bf20047bcd4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.441ex; height:5.509ex;" alt="{\displaystyle {\frac {\text{total votes}}{\text{total seats}}}}" loading="lazy"></span></dd></dl>
<p>LR-Hare is sometimes called Hamilton's method, named after <a href="Alexander_Hamilton" title="Alexander Hamilton">Alexander Hamilton</a>, who devised the method in 1792.<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>
</p><p>The <a href="Droop_quota" title="Droop quota">Droop quota</a> is given by:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\text{total votes}}{{\text{total seats}}+1}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mtext>total votes</mtext>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mtext>total seats</mtext>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{total votes}}{{\text{total seats}}+1}}}</annotation>
</semantics>
</math></span><img src="./dd4da80289ea2f04d6c71094346c820a22baa3a0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.133ex; height:5.676ex;" alt="{\displaystyle {\frac {\text{total votes}}{{\text{total seats}}+1}}}" loading="lazy"></span></dd></dl>
<p>and is applied to elections in <a href="South_Africa" title="South Africa">South Africa</a>.
</p><p>The Hare quota is more generous to less-popular parties and the Droop quota to more-popular parties. Specifically, the Hare quota is <a href="Unbiased_estimate" class="mw-redirect" title="Unbiased estimate"><i>unbiased</i></a> in the number of seats it hands out, and so is more proportional than the Droop quota (which tends to give more seats to larger parties). The Hare suffers the disproportionality that it sometimes allocates a majority of seats to a party with less than a majority of votes in a district.<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="Examples">Examples</h2></div>
<p>The following example allocates 11 seats using the largest-remainder method by Droop quota.
</p>
<table class="wikitable">
<tbody><tr>
<th>Party
</th>
<th>Votes
</th>
<th><a href="Entitlement_(fair_division)" title="Entitlement (fair division)">Entitlement</a>
</th>
<th>Remainder
</th>
<th>Total seats
</th></tr>
<tr>
<th>Yellows
</th>
<td>47,000
</td>
<td>5.170
</td>
<td>0.170
</td>
<td>5
</td></tr>
<tr>
<th>Whites
</th>
<td>16,000
</td>
<td>1.760
</td>
<td>0.760
</td>
<td>2
</td></tr>
<tr>
<th>Reds
</th>
<td>15,800
</td>
<td>1.738
</td>
<td>0.738
</td>
<td>2
</td></tr>
<tr>
<th>Greens
</th>
<td>12,000
</td>
<td>1.320
</td>
<td>0.320
</td>
<td>1
</td></tr>
<tr>
<th>Blues
</th>
<td>6,100
</td>
<td>0.671
</td>
<td>0.671
</td>
<td>1
</td></tr>
<tr>
<th>Pinks
</th>
<td>3,100
</td>
<td>0.341
</td>
<td>0.341
</td>
<td>0
</td></tr>
<tr>
<th><b>Total</b>
</th>
<td><b>100,000</b>
</td>
<td><b>8/11</b>
</td>
<td><b>3</b>
</td>
<td><b>11</b>
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Pros_and_cons">Pros and cons</h2></div>
<p>It is easy for a voter to understand how the largest remainder method allocates seats. Moreover, the largest remainder method satisfies the <a href="Quota_rule" title="Quota rule">quota rule</a> (each party's seats are equal to its ideal share of seats, either rounded up or rounded down) and was designed to satisfy that criterion. However, this comes at the cost of greater inequalities in the <a href="Seats-to-votes_ratio" title="Seats-to-votes ratio">seats-to-votes ratio</a>, which can violate the principle of <a href="One_man%2C_one_vote" title="One man, one vote">one man, one vote</a>.
</p><p>However, a greater concern for social choice theorists, and the primary cause behind its abandonment in many countries, is the tendency of such rules to produce erratic or irrational behaviors called <a href="Apportionment_paradox" title="Apportionment paradox">apportionment paradoxes</a>:
</p>
<ul><li><i>Increasing</i> the number of seats in a legislature can <i>decrease</i> a party's apportionment of seats, called the <a href="Alabama_paradox" class="mw-redirect" title="Alabama paradox">Alabama paradox</a>.</li>
<li>Adding more parties to the legislature can cause a bizarre kind of <a href="Spoiler_effect" title="Spoiler effect">spoiler effect</a> called the <a href="New_states_paradox" class="mw-redirect" title="New states paradox">new state paradox</a>.
<ul><li>When Congress first admitted <a href="Oklahoma" title="Oklahoma">Oklahoma</a> to the Union, the House was expanded by 5 seats, equal to Oklahoma's apportionment, to ensure it would not affect the seats for any existing states. However, when the full apportionment was recalculated, the House was stunned to learn Oklahoma's entry had caused New York to lose a seat to Maine, despite there being no change in either state's population.<sup id="cite_ref-Caulfield22_10-0" class="reference"><a href="#cite_note-Caulfield22-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Stein200822_11-0" class="reference"><a href="#cite_note-Stein200822-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 232–233">: 232–233 </span></sup></li>
<li>By the same token, apportionments may depend on the precise order in which the apportionment is calculated. For example, identifying winning independents first and electing them, then apportioning the remaining seats, will produce a different result from treating each independent as if they were their own party and then computing a single overall apportionment.<sup id="cite_ref-:52_3-3" class="reference"><a href="#cite_note-:52-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul></li></ul>
<p>Such paradoxes also have the additional drawback of making it difficult or impossible to generalize procedure to more complex apportionment problems such as <a href="Biproportional_apportionment" title="Biproportional apportionment">biproportional apportionments</a> or <a href="Vote_linkage" title="Vote linkage">partial vote linkage</a>. This is in part responsible for the extreme complexity of administering elections by quota-based rules like the single transferable vote (see <a href="Counting_single_transferable_votes" title="Counting single transferable votes">counting single transferable votes</a>).
</p>
<div class="mw-heading mw-heading3"><h3 id="Alabama_paradox">Alabama paradox</h3></div>
<p>The <a href="Alabama_paradox" class="mw-redirect" title="Alabama paradox">Alabama paradox</a> is when an <i>increase</i> in the total number of seats leads to a <i>decrease</i> in the number of seats allocated to a certain party. In the example below, when the number of seats to be allocated is increased from 25 to 26, parties D and E end up with fewer seats, despite their entitlements increasing.
</p><p>With 25 seats, the results are:
</p>
<table class="wikitable">
<tbody><tr>
<th>Party
</th>
<th>A
</th>
<th>B
</th>
<th>C
</th>
<th>D
</th>
<th>E
</th>
<th>F
</th>
<th>Total
</th></tr>
<tr>
<th>Votes
</th>
<td>1500
</td>
<td>1500
</td>
<td>900
</td>
<td>500
</td>
<td>500
</td>
<td>200
</td>
<td>5100
</td></tr>
<tr>
<th>Quotas received
</th>
<td>7.35
</td>
<td>7.35
</td>
<td>4.41
</td>
<td>2.45
</td>
<td>2.45
</td>
<td>0.98
</td>
<td>25
</td></tr>
<tr>
<th>Automatic seats
</th>
<td>7
</td>
<td>7
</td>
<td>4
</td>
<td>2
</td>
<td>2
</td>
<td>0
</td>
<td>22
</td></tr>
<tr>
<th>Remainder
</th>
<td>0.35
</td>
<td>0.35
</td>
<td>0.41
</td>
<td>0.45
</td>
<td>0.45
</td>
<td>0.98
</td>
<td>
</td></tr>
<tr>
<th>Surplus seats
</th>
<td>0
</td>
<td>0
</td>
<td>0
</td>
<td>1
</td>
<td>1
</td>
<td>1
</td>
<td>3
</td></tr>
<tr>
<th>Total seats
</th>
<td>7
</td>
<td>7
</td>
<td>4
</td>
<td><i><b>3</b></i>
</td>
<td><i><b>3</b></i>
</td>
<td>1
</td>
<td>25
</td></tr></tbody></table>
<p>With 26 seats, the results are:
</p>
<table class="wikitable">
<tbody><tr>
<th>Party
</th>
<th>A
</th>
<th>B
</th>
<th>C
</th>
<th>D
</th>
<th>E
</th>
<th>F
</th>
<th>Total
</th></tr>
<tr>
<th>Votes
</th>
<td>1500
</td>
<td>1500
</td>
<td>900
</td>
<td>500
</td>
<td>500
</td>
<td>200
</td>
<td>5100
</td></tr>
<tr>
<th>Quotas received
</th>
<td>7.65
</td>
<td>7.65
</td>
<td>4.59
</td>
<td>2.55
</td>
<td>2.55
</td>
<td>1.02
</td>
<td>26
</td></tr>
<tr>
<th>Automatic seats
</th>
<td>7
</td>
<td>7
</td>
<td>4
</td>
<td>2
</td>
<td>2
</td>
<td>1
</td>
<td>23
</td></tr>
<tr>
<th>Remainder
</th>
<td>0.65
</td>
<td>0.65
</td>
<td>0.59
</td>
<td>0.55
</td>
<td>0.55
</td>
<td>0.02
</td>
<td>
</td></tr>
<tr>
<th>Surplus seats
</th>
<td>1
</td>
<td>1
</td>
<td>1
</td>
<td>0
</td>
<td>0
</td>
<td>0
</td>
<td>3
</td></tr>
<tr>
<th>Total seats
</th>
<td>8
</td>
<td>8
</td>
<td>5
</td>
<td><i><b>2</b></i>
</td>
<td><i><b>2</b></i>
</td>
<td>1
</td>
<td>26
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
<ol class="references">
<li id="cite_note-:12-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:12_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:12_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:12_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFPukelsheim2017" class="citation cs2">Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-3-319-64707-4_5">"Quota Methods of Apportionment: Divide and Rank"</a></span>, <i>Proportional Representation: Apportionment Methods and Their Applications</i>, Cham: Springer International Publishing, pp. <span class="nowrap">95–</span>105, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-64707-4_5">10.1007/978-3-319-64707-4_5</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-64707-4</bdi><span class="reference-accessdate">, retrieved <span class="nowrap">2024-05-10</span></span></cite></span>
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<li id="cite_note-:52-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:52_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:52_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:52_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:52_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFPukelsheim2017" class="citation cs2">Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-3-319-64707-4_9">"Securing System Consistency: Coherence and Paradoxes"</a></span>, <i>Proportional Representation: Apportionment Methods and Their Applications</i>, Cham: Springer International Publishing, pp. <span class="nowrap">159–</span>183, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-64707-4_9">10.1007/978-3-319-64707-4_9</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-64707-4</bdi><span class="reference-accessdate">, retrieved <span class="nowrap">2024-05-10</span></span></cite></span>
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<li id="cite_note-:02222-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:02222_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:02222_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFBalinskiYoung1982" class="citation book cs1">Balinski, Michel L.; Young, H. Peyton (1982). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/fairrepresentati00bali"><i>Fair Representation: Meeting the Ideal of One Man, One Vote</i></a></span>. New Haven: Yale University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-300-02724-9</bdi>.</cite></span>
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<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="CITEREFGallagher1992" class="citation journal cs1">Gallagher, Michael (1992). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/194023">"Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities"</a>. <i>British Journal of Political Science</i>. <b>22</b> (4): <span class="nowrap">469–</span>496. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0007123400006499">10.1017/S0007123400006499</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/0007-1234">0007-1234</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/194023">194023</a>.</cite></span>
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<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="CITEREFGallagher1992" class="citation journal cs1">Gallagher, Michael (1992). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/194023">"Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities"</a>. <i>British Journal of Political Science</i>. <b>22</b> (4): <span class="nowrap">469–</span>496. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0007123400006499">10.1017/S0007123400006499</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/0007-1234">0007-1234</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/194023">194023</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="CITEREFGallagherMitchell2005" class="citation book cs1">Gallagher, Michael; Mitchell, Paul (2005-09-15). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Igdj1P4vBwMC"><i>The Politics of Electoral Systems</i></a>. OUP Oxford. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-153151-4</bdi>.</cite></span>
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<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="CITEREFEerik_Lagerspetz2015" class="citation book cs1">Eerik Lagerspetz (26 November 2015). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RNcLCwAAQBAJ&q=alexander+hamilton+invented+the+largest+remainder+method&pg=PA130"><i>Social Choice and Democratic Values</i></a>. Studies in Choice and Welfare. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9783319232614</bdi><span class="reference-accessdate">. Retrieved <span class="nowrap">2017-08-17</span></span>.</cite></span>
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<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="CITEREFHumphreys1911" class="citation book cs1">Humphreys (1911). <i>Proportional Representation</i>. p. 138.</cite></span>
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<li id="cite_note-Caulfield22-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Caulfield22_10-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFCaulfield2010" class="citation journal cs1">Caulfield, Michael J. (November 2010). <a rel="nofollow" class="external text" href="http://www.maa.org/publications/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-paradoxes-of-apportionment">"Apportioning Representatives in the United States Congress – Paradoxes of Apportionment"</a>. <i>Convergence</i>. Mathematical Association of America. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4169%2Floci003163">10.4169/loci003163</a> (inactive 1 July 2025).</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite journal}}</code>: CS1 maint: DOI inactive as of July 2025 (link)</span></span>
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<li id="cite_note-Stein200822-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Stein200822_11-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFStein2008" class="citation book cs1">Stein, James D. (2008). <i>How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics</i>. New York: Smithsonian Books. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780061241765</bdi>.</cite></span>
</li>
</ol>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/SocialScience/AHamilton.shtml">Hamilton method experimentation applet</a> at <a href="Cut-the-knot" class="mw-redirect" title="Cut-the-knot">cut-the-knot</a></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="Nanson's_method" title="Nanson's method">Nanson's 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>
<ul><li><a href="CPO-STV" title="CPO-STV">CPO-STV</a></li>
<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="Mixed-member_proportional_representation" title="Mixed-member proportional representation">MMP</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><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2025-07-12" href="https://en.wikipedia.org/wiki/?title=Quota_method&oldid=1300123385">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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