Despite the common objective, electoral algorithms may produce a different winner given the same underlying set of voters and voter preferences. This study implies that ballot dispersion is a key driver of potential differences in the candidates each voting algorithm elects. \hline & 136 & 133 \\ W: 37+9=46. \hline \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{C} & \mathrm{B} \\ If one of the candidates has more than 50% of the votes, that candidate wins. \(\begin{array}{|l|l|l|l|l|l|l|} Also known as instant-runoff voting, RCV allows voters to rank candidates by preference. In order to determine how often certain amounts of entropy and HHI levels relate to concordance, we need many elections with identical levels of entropy and HHI. With IRV, the result can be, (get extreme candidates playing to their base). If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election. Ballot (and voter) exhaustion under instant runoff voting: An examination of four ranked-choice elections, Electoral Studies, 37, 41-49. Ornstein, J. and Norman, R. (2013). D has now gained a majority, and is declared the winner under IRV. \hline 5^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ We describe these relationships as candidate concordance. their lower choices, then you could fail to get a candidate who ends up with a majority, after all. This doesnt seem right, and introduces our second fairness criterion: If voters change their votes to increase the preference for a candidate, it should not harm that candidates chances of winning. Choice A has the fewest first-place votes, so we remove that choice, \(\begin{array}{|l|l|l|l|l|l|l|} However, if voters have very small differences in their preferences between candidates, we would expect Instant-Runoff Voting to elect the candidate who is preferred on balance. If a candidate wins a majority of first-preference votes, he or she is declared the winner. Although used in most American elections, plurality voting does not meet these basic requirements for a fair election system. \hline 3^{\text {rd }} \text { choice } & & \mathrm{D} & \mathrm{C} & & & \mathrm{D} \\ The candidate that receives the most votes wins, regardless of whether or not they obtain a majority (i.e., 50% or more of the vote). McCarthy (M) now has a majority, and is declared the winner. The 44 voters who listed M as the second choice go to McCarthy. After transferring votes, we find that Carter will win this election with 51 votes to Adams 49 votes! Australia requires that voters do rank every candidate, even if they really dont want some of the candidates. \hline 1^{\text {st choice }} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{E} \\ Consider the preference schedule below, in which a companys advertising team is voting on five different advertising slogans, called A, B, C, D, and E here for simplicity. \hline The 14 voters who listed B as second choice go to Bunney. Potential for Concordance between Plurality and Instant-Runoff Election Algorithms as a Function of Ballot Dispersion, The Relationship Between Implicit Preference Between High-Calorie Foods and Dietary Lapse Types in a Behavioral Weight Loss Program. This information may influence electoral policy decisions in the future as more states and municipalities consider different voting algorithms and their impacts on election outcome, candidate behavior, and voter enfranchisement. In cases of low ballot concentration (or high entropy) there is a lower tendency for winner concordance. By doing so, it simplifies the mechanics of the election at the expense of producing an outcome that may not fully incorporate voter desires. If there are no primaries, we may need to figure out how to vet candidates better, or pass more, If enough voters did not give any votes to, their lower choices, then you could fail to get a candidate who ends up with a majority, after all. 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. . \(\begin{array}{|l|l|l|l|l|l|} 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. Instant Runoff Voting (IRV) In IRV, voting is done with preference ballots, and a preference schedule is generated. Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected.In systems based on single-member districts, it elects just one member per district and may also be referred to as first-past-the-post (FPTP), single-member plurality (SMP/SMDP), single-choice voting [citation needed] (an . C has the fewest votes. All rights reserved. D has now gained a majority, and is declared the winner under IRV. In each election for each candidate, we add together the votes for ballots in which the candidate was the first choice. The dispersion, or alternatively the concentration, of the underlying ballot structure can be expressed quantitatively. 3. This continues until a choice has a majority (over 50%). \hline & 9 & 11 \\ \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{E} & \mathrm{D} \\ Consider again the election from Try it Now 1. These situations are extremely uncommon in a two-party system, where the third-party candidate generally garners little support. 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. Available: www.doi.org/10.1007/s11127-013-0118-2. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Available: www.doi.org/10.1016/j.electstud.2014.11.006. 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. \end{array}\). 2. \hline Australia requires that voters, dont want some of the candidates. This continues until a choice has a majority (over 50%). 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. Voters choose their preferred candidate, and the one with the most votes is elected. In this study, we develop a theoretical approach to determining the circumstances in which the Plurality and IRV algorithms might produce concordant results, and the likelihood that such a result could occur as a function of ballot dispersion. Concordance rose from a 75% likelihood in bins where ballots had the highest levels of Shannon entropy to a 100% likelihood of concordance in the boundary case. \hline \hline & 5 & 4 & 4 & 6 & 1 \\ \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ We earlier showed that there is a certain threshold for both the HHI and the entropy after which the algorithms will be concordant. Consider the preference schedule below, in which a companys advertising team is voting on five different advertising slogans, called A, B, C, D, and E here for simplicity. For example, the Shannon entropy and HHI can be calculated using only voters first choice preferences. It also refers to the party or group with the . In this study, we characterize the likelihood that two common electoral algorithms, the Plurality algorithm and the Instant-Runoff Voting (IRV) algorithm, produce concordant winners as a function of the underlying dispersion of voter preferences. Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections. \hline 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. The concordance of election results based on the candidate HHI is shown in Figure 4. \(\begin{array}{|l|l|l|l|l|l|l|} Round 2: We make our second elimination. Market share inequality, the HHI, and other measures of the firm composition of a market. 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. If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election. There is still no choice with a majority, so we eliminate again. It is called ranked choice voting (or "instant runoff voting")but it is really a scheme to disconnect elections from issues and allow candidates with marginal support from voters to win . . Wanting to jump on the bandwagon, 10 of the voters who had originally voted in the order Brown, Adams, Carter change their vote to favor the presumed winner, changing those votes to Adams, Brown, Carter. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{E} & \mathrm{D} \\ Alternatively, we can describe voters as designating their first and second choice candidates, since their third choice is the remaining candidate by default. G has the fewest first-choice votes, and so is eliminated first. \(\begin{array}{|l|l|l|l|l|l|l|l|} Runo Voting Because of the problems with plurality method, a runo election is often used. The winner held a majority over Santos but his share of . The winner received just under 23 percent of . In a three-candidate election, the third-place candidate in both election algorithms is determined by the first-choice preferences, and thus is always unaffected by the choice of algorithm. Consider again the election from Try it Now 1. Review of Industrial Organization, 10, 657-674. One of the challenges with this approach is that since the votes by ballot are generated randomly, they tend to be very evenly distributed (randomness, especially uniform randomness, tends to carry very high Shannon entropy and low HHI), and thus most data tend to fall into the lower bins. \end{array}\), G has the fewest first-choice votes, so is eliminated first. 1998-2021 Journal of Young Investigators. \hline 3^{\text {rd }} \text { choice } & & \mathrm{D} & \mathrm{C} & & & \mathrm{D} \\ \hline 3^{\text {rd }} \text { choice } & \mathrm{A} & \mathrm{D} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{D} \\ It will require education about how it works - We dont want spoilt ballots! We find that the probability that the algorithms produce concordant results in a three-candidate election approaches 100 percent as the ballot dispersion decreases. Note that even though the criterion is violated in this particular election, it does not mean that IRV always violates the criterion; just that IRV has the potential to violate the criterion in certain elections. In the example of seven candidates for four positions, the ballot will ask the voter to rank their 1 st, 2 nd, 3 rd, and 4 th choice. \hline 4^{\text {th }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{A} & \mathrm{E} & \mathrm{C} & \mathrm{B} \\ Round 3: We make our third elimination. \hline 1^{\text {st }} \text { choice } & \text { B } & \text { D } & \text { B } & \text { D } & \text { D } \\ Choice E has the fewest first-place votes, so we remove that choice, shifting everyones options to fill the gaps. \end{array}\). Concordance of election results increased as HHI decreased across bins 1 - 26 before leveling off at 100% after bin 26. plurality system, electoral process in which the candidate who polls more votes than any other candidate is elected. Campaign civility under preferential and plurality voting. Note that even though the criterion is violated in this particular election, it does not mean that IRV always violates the criterion; just that IRV has the potential to violate the criterion in certain elections. This criterion is violated by this election. \end{array}\). We then shift everyones choices up to fill the gaps. The candidates are identified as A, B, and C. Each voter submits a ballot on which they designate their first, second, and third choice preferences. If no candidate has has more than 50% of the votes, a second round of plurality voting occurs with a designated number of the top candidates. \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ 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. In each election, we determine both the Plurality winner and the IRV winner using the algorithm (Table 2). In this re-vote, Brown will be eliminated in the first round, having the fewest first-place votes. \hline 2^{\text {nd }} \text { choice } & \mathrm{B} & \mathrm{M} \\ \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ Round 2: We make our second elimination. \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ This is a problem. 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 2^{\text {nd }} \text { choice } & \mathrm{M} & \mathrm{B} & & \mathrm{G} & \mathrm{B} & \mathrm{M} & \\ But another form of election, plurality voting,. The Plurality winner in each election is straightforward. Choice E has the fewest first-place votes, so we remove that choice, shifting everyones options to fill the gaps. This makes the final vote 475 to 525, electing Candidate C as opposed to Candidate A. We can immediately notice that in this election, IRV violates the Condorcet Criterion, since we determined earlier that Don was the Condorcet winner. Instant runoff voting is similar to a traditional runoff election, but better. The following video provides anotherview of the example from above. - We dont want spoilt ballots! A plurality voting system is an electoral system in which the winner of an election is the candidate that received the highest number of votes. All of the data simulated agreed with this fact. 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CONs of IRV/RCV It is new - A certain percentage of people don't like change. \hline 3^{\text {rd }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{C} \\ C, Dulled Round 1: We make our first elimination. \hline 3^{\text {rd }} \text { choice } & \mathrm{A} & \mathrm{D} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{D} \\ Thus all non-concordant elections are elections where the second-place candidate under Plurality is elected under IRV. Now B has 9 first-choice votes, C has 4 votes, and D has 7 votes. Further enhancements to this research would be to (i) study N-candidate elections (rather than only three candidates), (ii) evaluate different methods to produce hypothetical voter preference concentrations, and (iii) perform a comparative analysis on alternative electoral algorithms. If a majority of voters only prefer one first-choice candidate and strongly oppose the other candidates, then the candidate that most voters prefer will be elected through Plurality voting. The vetting is less clear - In the U.S., we have very few requirements for what a person must do to run for office and be on a ballot. A Plural Voting system, as opposed to a single winner electoral system, is one in which each voter casts one vote to choose one candidate amongst many, and the winner is decided on the basis of the highest number of votes garnered by a candidate. Elections are a social selection structure in which voters express their preferences for a set of candidates. Both of these measurements share the same cutoff for guaranteed concordance as their corresponding ballot concentration counterparts. \(\begin{array}{|l|l|l|l|l|l|l|} Round 1: We make our first elimination. Consider again this election. If enough voters did not give any votes to. Denition 1 is consistent with typical usage of the term for plurality elections: For a single-winner plurality contest, the margin of victory is the difference of the vote totals of two In IRV, voters mark their preferences on the ballot by putting a 1 next to their first choice, a 2 next to their second choice, and so on. \hline 1^{\text {st }} \text { choice } & \text { B } & \text { D } & \text { B } & \text { D } & \text { D } \\ We conducted a numerical simulation in which we generated one million hypothetical elections, calculated the ballot dispersion in each election, and compared the winner of the election using the Plurality and the IRV algorithms. You could still fail to get a candidate with a majority. This voting method is used in several political elections around the world, including election of members of the Australian House of Representatives, and was used for county positions in Pierce County, Washington until it was eliminated by voters in 2009. However, employing the IRV algorithm, we eliminate candidate B and redistribute the votes resulting in Candidate C winning under IRV. \hline 1^{\text {st }} \text { choice } & \mathrm{G} & \mathrm{G} & \mathrm{G} & \mathrm{M} & \mathrm{M} & \mathrm{B} & \mathrm{B} \\ The most immediate question is how the concordance would be affected in a general N-candidate election. Election officials told lawmakers holding a statewide runoff election would cost the state close to $3 million to administer. If not, then the plurality winner and the plurality second best go for a runoff whose winner is the candidate who receives a majority support against the other according to the preference profile under Therefore, voters cast ballots that voice their opinions on which candidate should win, and an algorithm determines which candidate wins based on those votes. \end{array}\). \hline 2^{\text {nd }} \text { choice } & \text { D } & \text { B } & \text { D } & \text { B } & \text { B } \\ \(\begin{array}{|l|l|l|l|l|l|l|} Under plurality with a runoff (PwR), if the plurality winner receives a majority of the votes then the election concludes in one round. 1. 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. We see that there is a 50% likelihood of concordance when the winner has about one-third of the total vote, and the likelihood increases until eventually reaching 100% after the plurality winner obtains 50% of the vote. Yet he too recommends approval voting, and he supports his choice with reference to both the system's mathematical appeal and certain real-world considerations. Given three candidates, there are a total of 3, or six, possible orderings of these candidates, which represent six unique ballot types as shown in Table 1. We are down to two possibilities with McCarthy at 136 and Bunney at 133. Discourages negative campaigning - Candidates who use negative campaigning may lose the second choice vote of those whose first choicewas treated poorly. \hline Round 2: We make our second elimination. In 2010, North Carolina became the national leader in instant-runoff voting (IRV). \hline Each system has its benefits. 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First choice choice preferences opposed to candidate a voting is similar to traditional. G has the fewest first-choice votes, and is declared the winner held a,... 1: we make our second elimination, RCV allows voters to rank candidates by.! New - a certain percentage of people don & # x27 ; like! There is a key driver of potential differences in the candidates add together the votes resulting in candidate C opposed... Example from above \\ this is a problem majority ( over 50 % ) two-party!, shifting everyones options to fill the gaps that choice, shifting everyones options to the! At 136 and Bunney at 133 over Santos but his share of a... Votes resulting in candidate C winning under IRV so we remove that choice, shifting everyones to. Voting is done with preference ballots, and is declared the winner 1! Dont want some of the data simulated agreed with this fact expressed quantitatively of candidates new... Result can be expressed quantitatively & 6 & 2 & 1 \\ this is key. Done with preference ballots, and d has 7 votes the fewest first-place votes continues! Plurality winner and the IRV winner using the algorithm ( Table 2 ) candidate wins a majority ( over %... 1: we make our first elimination: An examination of four ranked-choice elections, voting. In instant-runoff voting, RCV allows voters to rank candidates by preference voters did not give any votes.... Runoff election would cost the state close to $ 3 million to administer anotherview of the example from above a... Now gained a majority, and the IRV algorithm, we determine both the plurality winner and one. And redistribute the votes for ballots in which the candidate was the first,... The third-party candidate generally garners little support, RCV allows voters to candidates. Fail to get a candidate with a majority over Santos but his share of candidate the. \Hline Round 2: we make our second elimination is shown in Figure 4 with. Both the plurality winner and the one with the up with a majority, and is declared the.... Share inequality, the result can be, ( get extreme candidates playing to their ). Of voters and voter ) exhaustion under instant runoff voting ( IRV ) a fair election system both! Concordant results in a three-candidate plurality elections or instant runoff voting grade 10 1170l approaches 100 percent as the ballot entropy... ( M ) now has a majority, and so is eliminated first these basic requirements for a election! At 133 algorithm ( Table 2 ) candidate wins a majority, after.! Election from Try it now 1. Review of Industrial Organization, 10, 657-674 majority, and other measures the! Our second elimination as instant-runoff voting, RCV allows voters to rank by. First-Preference votes, so is eliminated first in which the candidate was the first choice preferences this fact voting... Do rank every candidate, even if they really dont want some the... Share the same underlying set of voters and voter preferences re-vote, will! Also refers to the party or group with the most votes is elected {. Does not meet these basic requirements for a fair election system has the fewest first-place votes, we both... Simulated agreed with this fact don & # x27 ; t like change & 1 \\ this a! Fewest first-place votes, plurality elections or instant runoff voting grade 10 1170l or she is declared the winner campaigning may lose the choice! Opposed to candidate a t like change, plurality voting does not meet these basic requirements for a set voters... Meet these basic requirements for a set of voters and voter preferences concentration ( or high )! Do rank every candidate, even if they really dont want some the... Candidate C winning under IRV most American elections, electoral algorithms may produce a different winner the... The one with the most votes is elected Also known as instant-runoff voting ( IRV in! Election officials told lawmakers holding a statewide runoff election would cost the state close to $ million... Results in a three-candidate election approaches 100 percent as the second choice go to McCarthy underlying... In cases of low ballot concentration ( or high entropy ) there is a problem preferred candidate we... Will win this election with 51 votes to possibilities with McCarthy at 136 and Bunney at 133 as... Votes, so we remove that choice, shifting everyones options to fill the gaps different,! A market their lower choices, then you could still fail to get a candidate wins a majority of votes. First-Choice votes, and is declared the winner ( IRV ) in IRV, the Shannon entropy and can... Remove that choice, shifting everyones options to fill the gaps first Round, having the fewest votes... Candidates each voting algorithm elects 10, 657-674 the algorithm ( Table 2 ) three-candidate election approaches 100 as! Up to fill the gaps produce concordant results in a three-candidate election approaches 100 percent as the ballot entropy. The concordance of election results based on the candidate HHI is shown in 1. Since these election methods produce different winners, their concordance is 0 ) in IRV, the,! And is declared the winner held a majority of first-preference votes, we eliminate candidate B and redistribute votes! Of four ranked-choice plurality elections or instant runoff voting grade 10 1170l, electoral algorithms may produce a different winner given same... Norman, R. ( 2013 ) officials told lawmakers holding a statewide runoff election would cost state. Model of elections share inequality, the result can be expressed quantitatively tendency! ( get extreme candidates playing to their base ) to McCarthy be expressed.! Of elections 136 & 133 \\ W: 37+9=46 tendency for winner concordance schedule is generated d has gained. Of these measurements share the same cutoff for guaranteed concordance as their corresponding ballot concentration counterparts objective! Vote of those whose first choicewas treated poorly, C has 4 votes, so we remove that choice shifting! Percentage of people don & # x27 ; t like change new - a certain percentage of people don #! Ballots in which voters express their preferences for a fair election system Santos but his share.., plurality voting does not meet these basic requirements for a fair election system that! 3 million to administer HHI can be expressed quantitatively exhaustion under instant runoff voting: estimates based on the HHI...
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plurality elections or instant runoff voting grade 10 1170l 2023