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Tideman alternative method
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<h2 id="procedure">Procedure</h2> <p>The procedure for Tideman's rule is as follows: </p> <ol><li>Eliminate all candidates who are not in the <a href="/facts/Top_cycle/t5upwUmp">top cycle</a> (most often defined as the <a href="/facts/Smith_set/t5upwUmp">Smith set</a>).</li> <li>If there is more than one candidate remaining, <a href="/facts/Instant_runoff_voting/td1Q35Wg">eliminate the candidate ranked first by the fewest voters</a>.</li> <li>Repeat the procedure until there is a <a href="/facts/Condorcet_winner_criterion/p1pKVX0k">Condorcet winner</a>, at which point the Condorcet winner is elected.</li></ol> <p>The procedure can also be applied using <a href="/facts/Tournament_set/ChlRya7I">tournament sets</a> other than the Smith set, e.g. the <a href="/facts/Landau_set/q9xAoSIK">Landau set</a>, <a href="/facts/Copeland_set/KbogsCBg">Copeland set</a>, or <a href="/facts/Bipartisan_set/21r1kVTa">bipartisan set</a>. </p> <h2 id="features">Features</h2> <h3>Strategy-resistance</h3> <p>Tideman's Alternative strongly resists both <a href="/facts/Strategic_nomination/dsoCncgk">strategic nomination</a> and <a href="/facts/Strategic_voting/5cGzDa0c">strategic voting</a> by political parties or coalitions (although like every system, it <a href="/facts/Gibbard%25E2%2580%2593Satterthwaite_theorem/YPIeXAen">can still be manipulated</a> in some situations). The Smith and <a href="/facts/Instant-runoff_voting/td1Q35Wg">runoff</a> components of the system each cover the other's weaknesses: </p> <ol><li>Smith-efficient methods are difficult for any coalition to manipulate, because no majority-strength coalition will have an incentive to remove a Condorcet winner: if most voters prefer A to B, A can <i>already</i> defeat B. <ul><li>This reasoning does not apply to situations with a <a href="/facts/Condorcet_cycle/PXuWT0jl">Condorcet cycle</a>, however.</li> <li>While Condorcet cycles are rare in practice with honest voters, <a href="/facts/Strategic_voting/5cGzDa0c">burial</a> (ranking a strong rival last, below weak opponents) can often be used to manufacture a false cycle.</li></ul></li> <li><a href="/facts/Instant_run-off_voting/td1Q35Wg">Instant runoff voting</a> is resistant to burial, because it is only based on each voter's top preference in any given round. This means that burial strategies effective against the Smith-elimination step are not effective against the instant runoff step. <ul><li>On the other hand, instant-runoff voting is highly vulnerable to <a href="/facts/Strategic_voting/5cGzDa0c">compromising</a> strategy, where voters are incentivized to rank "lesser evils" higher in order to defeat a "greater evil".</li> <li>However, if a Condorcet winner exists, they're immune to compromising, so electing them reduces compromise incentive.</li></ul></li></ol> <p>The combination of these two methods creates a highly strategy-resistant system. </p> <h3>Spoiler effects</h3> <p>Tideman's Alternative fails <a href="/facts/Independence_of_irrelevant_alternatives/E5xfFDsC">independence of irrelevant alternatives</a>, meaning it can sometimes be affected by spoiler candidates. However, the method adheres to a weaker property that eliminates most spoilers, sometimes called <a href="/facts/Independence_of_Smith-dominated_alternatives/Kz1oWoWA">independence of Smith-dominated alternatives</a> (ISDA). This method states that if one candidate (X) wins an election, and a new alternative (Y) is added, X will still win the election as long as Y is not in the <a href="/facts/Smith_set/t5upwUmp">highest-ranked cycle</a>. </p> <h3>Comparison table</h3> <p>The following table compares Tideman's Alternative with other single-winner election methods: </p> Comparison of single-winner voting systems<table><tbody><tr><th>CriterionMethod</th><th><a href="/facts/Majority_winner_criterion/7ayptJfM">Majority winner</a></th><th><a href="/facts/Majority_loser_criterion/KKbWH41c">Majority loser</a></th><th><a href="/facts/Mutual_majority_criterion/3noJECSj">Mutual majority</a></th><th><a href="/facts/Condorcet_winner/p1pKVX0k">Condorcet winner</a><a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a></th><th><a href="/facts/Condorcet_loser/jQwkvzKS">Condorcet loser</a></th><th><a href="/facts/Smith_criterion/9pjF4olQ">Smith</a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a></th><th><a href="/facts/Independence_of_Smith-dominated_alternatives/Kz1oWoWA">Smith-IIA</a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></th><th><a href="/facts/Independence_of_irrelevant_alternatives/E5xfFDsC">IIA</a>/<a href="/facts/Independence_of_irrelevant_alternatives/E5xfFDsC">LIIA</a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></th><th><a href="/facts/Independence_of_clones/IcCrkyt6">Cloneproof</a></th><th><a href="/facts/Monotonicity_criterion/BruDjw6G">Monotone</a></th><th><a href="/facts/Participation_criterion/racmDXYL">Participation</a></th><th><a href="/facts/Later-no-harm/pWXycyIq">Later-no-harm</a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></th><th><a href="/facts/Later-no-help/geV4KrfD">Later-no-help</a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></th><th><a href="/facts/No_favorite_betrayal/R1s40J8Y">No favorite betrayal</a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></th><th>Ballot<p>type</p></th></tr><tr><th><a href="/facts/First-past-the-post_voting/RJ11du1H">First-past-the-post voting</a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Single mark</td></tr><tr><th><a href="/facts/Anti-plurality_voting/1QScubBj">Anti-plurality</a></th><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Single mark</td></tr><tr><th><a href="/facts/Two-round_system/2sFF4NBG">Two round system</a></th><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Single mark</td></tr><tr><th><a href="/facts/Instant-runoff_voting/td1Q35Wg">Instant-runoff</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Coombs%2527_method/Fh9knPby">Coombs</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Ranking</td></tr><tr><th><a href="/facts/Nanson%2527s_method/3rjmYCBE">Nanson</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Baldwin%2527s_method/3rjmYCBE">Baldwin</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th>Tideman alternative</th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Minimax_Condorcet/VqrAQEWo">Minimax</a></th><td>Yes</td><td>No</td><td>No</td><td>Yes<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a></td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Copeland%2527s_method/KbogsCBg">Copeland</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Black%2527s_method/Q44E0BXN">Black</a></th><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Kemeny-Young_method/F6eMjYBQ">Kemeny–Young</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>LIIA Only</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Ranked_pairs/B9z70acb">Ranked pairs</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>LIIA Only</td><td>Yes</td><td>Yes</td><td>No<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a></td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Schulze_method/6N0SMAY2">Schulze</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>No<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a></td><td>No</td><td>No</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Borda_count/0VK30c68">Borda</a></th><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Bucklin_voting/lQYCku6y">Bucklin</a></th><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Ranking</td></tr><tr><th><a href="/facts/Approval_voting/XBp98Jrf">Approval</a></th><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Approvals</td></tr><tr><th><a href="/facts/Majority_judgment/gby2PEMD">Majority Judgement</a></th><td>No</td><td>No<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></td><td>No<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></td><td>Yes</td><td>Yes</td><td>No<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></td><td>No</td><td>Yes</td><td>Yes</td><td>Scores</td></tr><tr><th><a href="/facts/Score_voting/hhpRqQny">Score</a></th><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Scores</td></tr><tr><th><a href="/facts/STAR_voting/gRPbXgjY">STAR</a></th><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Scores</td></tr><tr><th><a href="/facts/Quadratic_voting/h6Dg7rm3">Quadratic</a></th><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>N/A</td><td>N/A</td><td>No</td><td>Credits</td></tr><tr><th><a href="/facts/Random_ballot/NN3RdcaJ">Random ballot</a><a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></th><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Single mark</td></tr><tr><th><a href="/facts/Sortition/WSWzQfzj">Sortition</a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></th><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>None</td></tr><tr><th>Table Notes</th><td colspan="16"></td></tr></tbody></table> <ul><li>Green-Armytage, James. <a href="http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf">Four Condorcet-Hare Hybrid Methods for Single-Winner Elections</a>.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. <a href="/wiki/Condorcet_criterion" target="_blank">/wiki/Condorcet_criterion</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. <a href="/wiki/Approval_voting#Dichotomous_cutoff" target="_blank">/wiki/Approval_voting#Dichotomous_cutoff</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters. <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade. <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. <a href="/wiki/Approval_voting#Dichotomous_cutoff" target="_blank">/wiki/Approval_voting#Dichotomous_cutoff</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. <a href="/wiki/Approval_voting#Dichotomous_cutoff" target="_blank">/wiki/Approval_voting#Dichotomous_cutoff</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria. <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria. <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> </ol>