Ranked-choice voting is not a new idea. Plurality voting, a voting system in which the person who receives the most votes wins, is currently the predominate form of voting in the United States." In contrast to this traditional electoral system, in an instant runoff voting system, voters rank candidates-as first, second, third and so on-according to their preferences. The result was a one-election, plurality, winner-take-all vote for supreme court. With a traditional runoff system, a first election has multiple candidates, and if no candidate receives a majority of the vote, a second or runoff election is held between the top two candidates of the first election. If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election. The IRV algorithm, on the other hand, attempts to address these concerns by incorporating more information on voter preferences and cross-correlations in support among candidates. One might wonder how the concentration of votes (i.e., a situation where voters usually either support Candidate C over Candidate B over Candidate A, or support Candidate A over Candidate B over Candidate C) affects whether these two algorithms select the same candidate given a random election. Round 1: We make our first elimination. Notice that the first and fifth columns have the same preferences now, we can condense those down to one column. \hline & 9 & 11 \\ \hline 4^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ Enter the email address you signed up with and we'll email you a reset link. Candidate A wins under Plurality. In this election, Don has the smallest number of first place votes, so Don is eliminated in the first round. For example, consider the algorithm for Instant-Runoff Voting shown in Table 2, and the series of ballots shown in Table 3. The plurality with elimination method requires voters to rank their preferences. Minimizes strategic voting - Instead of feeling compelled to vote for the lesser of two evils, as in plurality voting, voters can honestly vote forwho they believe is the best candidate.\. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{C} & \mathrm{B} \\ If there are no primaries, we may need to figure out how to vet candidates better, or pass morerequirements for candidates to qualify to run. { "2.1.01:_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.02:_Preference_Schedules" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.03:_Plurality" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.04:_Whats_Wrong_with_Plurality" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.05:_Insincere_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.06:_Instant_Runoff_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.07:_Whats_Wrong_with_IRV" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.08:_Borda_Count" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.09:_Whats_Wrong_with_Borda_Count" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.10:_Copelands_Method_(Pairwise_Comparisons)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.11:_Whats_Wrong_with_Copelands_Method" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.12:_So_Wheres_the_Fair_Method" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.13:_Approval_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.14:_Whats_Wrong_with_Approval_Voting" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.15:_Voting_in_America" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.16:_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.17:_Concepts" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.1.18:_Exploration" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "2.01:_Voting_Theory" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.02:_Apportionment" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbysa", "showtoc:no", "transcluded:yes", "authorname:lippman", "Instant Runoff", "Instant Runoff Voting", "Plurality with Elimination", "source[1]-math-34181" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FAmerican_River_College%2FMath_300%253A_My_Math_Ideas_Textbook_(Kinoshita)%2F02%253A_Voting_Theory_and_Apportionment%2F2.01%253A_Voting_Theory%2F2.1.06%253A_Instant_Runoff_Voting, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org. We describe these relationships as candidate concordance. We use a Monte Carlo simulation to hold one million mock elections using both algorithms and then assess whether winner concordance occurred. The choice with the least first-place votes is then eliminated from the election, and any votes for that candidate are redistributed to the voters next choice. \hline \hline 3^{\text {rd }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ \end{array}\), G has the fewest first-choice votes, so is eliminated first. \hline 3^{\text {rd }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{C} & \mathrm{E} & \mathrm{C} & \mathrm{B} \\ Australia requires that voters do rank every candidate, even if they really dont want some of the candidates. \hline 3^{\text {rd }} \text { choice } & & \mathrm{D} & \mathrm{C} & & & \mathrm{D} \\ The concordance of election results based on the ballot HHI is shown in Figure 2. \end{array}\). Available: www.doi.org/10.1007/s11127-019-00723-2. But security and integrity of our elections will require having a paper trail so that we can do recounts, and know the results are, In the U.S., we have very few requirements for what a person must do to run for office and be on a ballot. McCarthy is declared the winner. Instant Runoff Voting (IRV), also called Plurality with Elimination, is a modification of the plurality method that attempts to address the issue of insincere voting. For the HHI, this point is located at 0.5, meaning that the Plurality and IRV algorithms with HHI above 0.5 are guaranteed to be concordant. Consider again this election. It refers to Ranked Choice Voting when there is only one candidate being elected. This is a problem. However, the likelihood of concordance drops rapidly when no candidate dominates, and approaches 50% when the candidate with the most first-choice ballots only modestly surpasses the next most preferred candidate. Lets return to our City Council Election. Consider again the election from Try it Now 1. The following video provides anotherview of the example from above. This is similar to the idea of holding runoff elections, but since every voters order of preference is recorded on the ballot, the runoff can be computed without requiring a second costly election. \hline & 44 & 14 & 20 & 70 & 22 & 80 & 39 \\ Choice E has the fewest first-place votes, so we remove that choice, shifting everyones options to fill the gaps. All of the data simulated agreed with this fact. \hline 5^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ 2. \hline \hline 3^{\text {rd }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{C} \\ Concordance rose from a 57% likelihood in bins where ballots had the highest levels of Shannon entropy to a 100% likelihood of concordance in the boundary case. The potential benefits of adopting an IRV algorithm over a Plurality algorithm must be weighed against the likelihood that the algorithms might produce different results. Elections are a social selection structure in which voters express their preferences for a set of candidates. Thus, greater preference dispersion results in lower concordance as hypothesized. The winner is determined by the algorithm outlined in Table 2. By the sixth and final round, the winner beat Santos by about 200 votes and had 51 percent to Santos' 49 percent of the remaining vote. This page titled 2.1.6: Instant Runoff Voting is shared under a CC BY-SA license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) . Expert Answer. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{E} & \mathrm{D} \\ This continues until a choice has a majority (over 50%). In the following video, we provide the example from above where we find that the IRV method violates the Condorcet Criterion in an election for a city council seat. There have been relatively few studies that use numerical simulations to test the behavior of election algorithms under different conditions. Also known as instant-runoff voting, RCV allows voters to rank candidates by preference. Review of Industrial Organization, 10, 657-674. Instant Runoff Voting (IRV), also called Plurality with Elimination, is a modification of the plurality method that attempts to address the issue of insincere voting. Electoral Studies, 42, 157-163. Instant Runoff Voting (IRV), also called Plurality with Elimination, is a modification of the plurality method that attempts to address the issue of insincere voting. If this was a plurality election, note that B would be the winner with 9 first-choice votes, compared to 6 for D, 4 for C, and 1 for E. There are total of 3+4+4+6+2+1 = 20 votes. 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