If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election. Our analysis suggests that concordance between Plurality and IRV algorithms increases alongside the ballot concentration, with the probability of concordance depending on whether Shannon entropy or HHI is used to measure that concentration. After transferring votes, we find that Carter will win this election with 51 votes to Adams 49 votes! Plurality elections are unlike the majority voting process. Instant runoff voting (IRV) does a decent job at mitigating the spoiler effect by getting past plurality's faliure listed . Rhoades, S. A. We find that the probability that the algorithms produce concordant results in a three-candidate election approaches 100 percent as the ballot dispersion decreases. \hline 3^{\text {rd }} \text { choice } & \mathrm{A} & \mathrm{D} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{D} \\ Staff Tools| Contact Us| Privacy Policy| Terms | Disclosures. Find the winner using IRV. Under plurality with a runoff (PwR), if the plurality winner receives a majority of the votes then the election concludes in one round. Legal. 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. Then the Shannon entropy, H(x), is given by: And the HerfindahlHirschman Index, HHI(x), is given by: Monte Carlo Simulation of Election Winner Concordance. \hline In contrast, as voters start to consider a wider range of candidates as a viable first-choice, the Plurality and IRV algorithms start to differ in their election outcomes. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The relationship between ballot concentration and winner concordance can be observed even in the absence of full voter preference information. 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 2^{\text {nd }} \text { choice } & \mathrm{M} & \mathrm{B} & & \mathrm{G} & \mathrm{B} & \mathrm{M} & \\ Available: www.doi.org/10.1007/s11127-013-0118-2. It refers to Ranked Choice Voting when there's more than one winner. The reasons for this are unclear and warrant further study. Promotes majority support - The voting continues until one candidate has the majority of votes, so the final winner has support of themajority of voters. \hline 1^{\text {st }} \text { choice } & \text { B } & \text { D } & \text { B } & \text { D } & \text { D } \\ The HHI of any such situation is: In the situation where only the first-choice preferences are visible, as in the case of Plurality election, the corresponding boundary conditions for HHI(x) and H(x) are still 0.5 and 0.693147, respectively. Find the winner using IRV. This study implies that ballot dispersion is a key driver of potential differences in the candidates each voting algorithm elects. Figure 5 displays the concordance based on thepercentage of the vote that the Plurality winner possessed. Candidate A wins under Plurality. Election Law Journal, 3(3), 501-512. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{B} \\ \hline & 9 & 11 \\ 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. When one specific ballot has more than half the votes, the election algorithms always agree. 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. The selection of a winner may depend as much on the choice of algorithm as the will of the voters. The Plurality algorithm is commonly used to convert voter preferences into a declared winner. - A certain percentage of people dont like change. This is a problem. 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. In each election, we determine both the Plurality winner and the IRV winner using the algorithm (Table 2). If no candidate has a majority of first preferences, the least popular candidate is eliminated and their votes. In a Runo Election, a plurality vote is taken rst. For example, consider the algorithm for Instant-Runoff Voting shown in Table 2, and the series of ballots shown in Table 3. 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. Notice that the first and fifth columns have the same preferences now, we can condense those down to one column. The first is the ballot value and incorporates information across all ballot types. 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. The existence of so many different single-winner algorithms highlight the fundamental challenge with electoral systems. Currently, 10 states use runoff elections. Find the winner using IRV. The plurality with elimination method requires voters to rank their preferences. \hline 1^{\text {st choice }} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{E} \\ \hline 1^{\text {st }} \text { choice } & \mathrm{G} & \mathrm{G} & \mathrm{G} & \mathrm{M} & \mathrm{M} & \mathrm{B} & \mathrm{B} \\ M is elimated, and votes are allocated to their different second choices. Round 3: We make our third elimination. 1. -Plurality Elections or Instant Runoff Voting? Concordance of election results increased as Shannon entropy decreased across bins 1-63 before leveling off at 100% after bin 63. D has now gained a majority, and is declared the winner under IRV. Plurality voting is an electoral process whereby a candidate who gets the most votes in the election wins. Winner =. \hline Under this algorithm, voters express not only a first choice as in the Plurality algorithm, but an ordered list of preferred candidates (Table 1) which may factor into the determination of a winner. 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 . A version of IRV is used by the International Olympic Committee to select host nations. \(\begin{array}{|l|l|l|l|l|l|l|} \end{array}\). 2. \hline 4^{\text {th }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{A} & \mathrm{E} & \mathrm{C} & \mathrm{B} \\ Thus, greater preference dispersion results in lower concordance as hypothesized. \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ However, under Instant-Runoff Voting, Candidate B is eliminated in the first round, and Candidate C gains 125 more votes than Candidate A. Writing this paper would not have been possible without help from Middlesex Community College Professors Scott Higinbotham and Aisha Arroyo who provided me with critical guidance in the direction and methodologies of this paper. For each mock election, the Shannon entropy is calculated to capture all contained information and the HerfindahlHirschman Index (HHI) is calculated to capture the concentration of voter preference. The last video shows the example from above where the monotonicity criterion is violated. Legal. 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. Even though the only vote changes made favored Adams, the change ended up costing Adams the election. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{C} & \mathrm{B} \\ 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. \hline 3^{\text {rd }} \text { choice } & \mathrm{A} & \mathrm{D} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{D} \\ The bins are ordered from least concentrated to most concentrated (i.e., the HHI bins start with bin 1 at the boundary case of HHI(x) = 1/6, and end with bin 100 at the boundary case of HHI(x) = 1,whereas the entropy bins start with bin 1 at the boundary case of H(x) = ln(6), and end with bin 100 at the boundary case of H(x) = 0). \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{A} & \mathrm{D} & \mathrm{C} & \mathrm{E} & \mathrm{A} \\ 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. For a 3 candidate election where every voter ranks the candidates from most to least preferred, there are six unique ballots (Table 1). G has the fewest first-choice votes, and so is eliminated first. No one yet has a majority, so we proceed to elimination rounds. Since these election methods produce different winners, their concordance is 0. This can make them unhappy, or might make them decide to not participate. With IRV, the result can be, (get extreme candidates playing to their base). \(\begin{array}{|l|l|l|l|l|l|l|} Available: www.doi.org/10.1007/BF01024300. Instant Runoff Voting (IRV) In IRV, voting is done with preference ballots, and a preference schedule is generated. Find the winner using IRV. We simulate one million of these individual hypothetical elections. The winner received just under 23 percent of . Of these alternative algorithms, we choose to focus on the Instant-Runoff Voting algorithm (IRV). We can immediately notice that in this election, IRV violates the Condorcet Criterion, since we determined earlier that Don was the Condorcet winner. The Plurality algorithm, though extremely common, suffers from several major disadvantages (Richie, 2004). In 2010, North Carolina became the national leader in instant-runoff voting (IRV). \end{array}\). In addition to each simulated election having both a Plurality and IRV winner, it also has a distinct voter preference concentration, which we describe in terms of Shannon entropy and HHI. 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. This continues until a choice has a majority (over 50%). \hline 2^{\text {nd }} \text { choice } & \text { D } & \text { B } \\ (I have not seen that proposed in the U.S.) This might be interpreted as reducing your choice, or forcing you to vote against yourconscience. In these elections, each ballot contains only a single choice. Please note:at 2:50 in the video it says 9+2+8=18, should 9+2+8=19, so D=19. Instant-runoff voting ( IRV) is a voting method used in single-seat elections with more than two candidates. Third, the Plurality algorithm may encourage infighting among candidates with otherwise common policy objectives and natural constituencies. 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. However, as the preferences further concentrate, it becomes increasingly likely that the election algorithms will agree. (The general election, to be held in November, will use a standard ballot.) On the other hand, the temptation has been removed for Dons supporters to vote for Key; they now know their vote will be transferred to Key, not simply discarded. You could still fail to get a candidate with a majority. C has the fewest votes. In IRV, voting is done with preference ballots, and a preference schedule is generated. There have been relatively few studies that use numerical simulations to test the behavior of election algorithms under different conditions. Discourages negative campaigning - Candidates who use negative campaigning may lose the second choice vote of those whose first choicewas treated poorly. With IRV, the result can beobtained with one ballot. Now B has 9 first-choice votes, C has 4 votes, and D has 7 votes. The 20 voters who did not list a second choice do not get transferred. Here is an overview video that provides the definition of IRV, as well as an example of how to determine the winner of an election using IRV. This is known as the spoiler problem. Available: www.doi.org/10.1137/18S016709. Market share inequality, the HHI, and other measures of the firm composition of a market. https://youtu.be/C-X-6Lo_xUQ?list=PL1F887D3B8BF7C297, https://youtu.be/BCRaYCU28Ro?list=PL1F887D3B8BF7C297, https://youtu.be/NH78zNXHKUs?list=PL1F887D3B8BF7C297, Determine the winner of an election using preference ballots, Evaluate the fairnessof an election using preference ballots, Determine the winner of an election using the Instant Runoff method, Evaluate the fairnessof an Instant Runoff election, Determine the winner of an election using a Borda count, Evaluate the fairness of an election determined using a Borda count, Determine the winner of en election using Copelands method, Evaluate the fairness of an election determined by Copelands method. 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. 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. \end{array}\). \hline & 44 & 14 & 20 & 70 & 22 & 80 & 39 \\ Under the IRV system, voters still express a first choice, but also rank the other candidates in order of preference in the event that their first-choice candidate is eliminated. In one such study, Joyner (2019) used machine learning tools to estimate the hypothetical outcome of the 2004 presidential election had it been conducted using the IRV algorithm. We dont want uninformed, - It either requires a computer system, or is labor intensive to count by hand, with risk of errors. (I have not seen that proposed in the U.S.) This might be interpreted as, your choice, or forcing you to vote against your, I have not seen this discussed yet, but if there are, many choices, without clear front-runners, I am not sure whether the result reflects the voters desires as well as it would if there were only, say, five choices. Enter the email address you signed up with and we'll email you a reset link. RCV is straightforward: Voters have the option to rank candidates in order of preference: first, second, third and so forth. 100% (1 rating) As we can see from the given preference schedule Number of voters 14 8 13 1st choice C B A 2nd choice A A C 3rd choice B . Round 2: We make our second elimination. 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. \(\begin{array}{|l|l|l|l|l|l|l|l|} Let x denote a discrete random variable with possible values x1 xn , and P(x) denote the probability mass function of x. A majority would be 11 votes. In this election, Carter would be eliminated in the first round, and Adams would be the winner with 66 votes to 34 for Brown. After transferring votes, we find that Carter will win this election with 51 votes to Adams 49 votes! The concordance of election results based on the candidate HHI is shown in Figure 4. Instead of voting only for a single candidate, voters in IRV elections can rank the candidates in order of preference. Round 3: We make our third elimination. If no candidate has more than 50% of the vote, then an "instant runoff" occurrs. 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. At this time, based on statewide votes, legal decisions and the provisions of the Maine Constitution, the State of Maine is using ranked-choice voting for all of Maine's state-level primary elections, and in general elections ONLY for federal offices, including the office of U . This paper addresses only the likelihood of winner concordance when comparing the Plurality and IRV algorithms. Now suppose that the results were announced, but election officials accidentally destroyed the ballots before they could be certified, and the votes had to be recast. This makes the final vote 475 to 525, electing Candidate C as opposed to Candidate A. . \hline 2^{\text {nd }} \text { choice } & \mathrm{B} & \mathrm{M} \\ We are down to two possibilities with McCarthy at 136 and Bunney at 133. Round 1: We make our first elimination. 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. B, Glass 2, As is used in paragraph 2, which is the best antonym for honed? \hline If no candidate has has more than 50% of the votes, a second round of plurality voting occurs with \hline 1^{\text {st }} \text { choice } & \text { B } & \text { D } & \text { B } & \text { D } & \text { D } \\ There is still no choice with a majority, so we eliminate again. The instant runoff ballot in this instance will list all the candidates, but it will ask voters to rank the number of candidates needed for the number of open offices. \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ Concordance of election results increased as HHI decreased across bins 1 - 40 before leveling off at 100% after bin 40. \hline 2^{\text {nd }} \text { choice } & \mathrm{M} & \mathrm{B} & & \mathrm{G} & \mathrm{B} & \mathrm{M} & \\ \end{array}\), \(\begin{array}{|l|l|l|} Round 2: We make our second elimination. D has now gained a majority, and is declared the winner under IRV. 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. Compared to traditional runoff elections, IRV saves tax dollars, reduces money in politics and elects winners when turnout is highest. By Ethan Hollander, Wabash College There are basically three voting systems that are used to elect representatives to public office. \hline 1^{\text {st }} \text { choice } & \mathrm{M} & \mathrm{B} \\ Shannon, C. E. (1948) A mathematical theory of communication. \hline 4^{\text {th }} \text { choice } & \mathrm{D} & \mathrm{B} & & \mathrm{E} & \mathrm{C} & \mathrm{B} \\ 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. 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{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{C} & \mathrm{B} \\ We then shift everyones choices up to fill the gaps. plural pluralities 1 : the state of being plural or numerous 2 a : the greater number or part a plurality of the nations want peace b : the number of votes by which one candidate wins over another c Consider again the election from Try it Now 1. There are many questions that arise from these results. We earlier showed that there is a certain threshold for both the HHI and the entropy after which the algorithms will be concordant. We use a Monte Carlo simulation to hold one million mock elections using both algorithms and then assess whether winner concordance occurred. \hline & 3 & 4 & 4 & 6 & 2 & 1 \\ RCV usually takes the form of "instant runoff voting" (IRV). \hline We find that when there is not a single winner with an absolute majority in the first round of voting, a decrease in Shannon entropy and/or an increase in HHI (represented by an increase in the bin numbers) results in a decrease in algorithmic concordance. In order to account for and remedy this issue, we uniformly divide the range of the possible values of entropy and HHI into 100 equal segments (hereafter referred to as bins), and then calculate the average concordance of all elections with entropy or HHI within those bins. Initially, \(\begin{array}{|l|l|l|l|l|l|l|} There is still no choice with a majority, so we eliminate again. \hline 1^{\text {st choice }} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{E} \\ -Voter Participation -Do We Really Need the Moon? \hline 1^{\text {st }} \text { choice } & \mathrm{M} & \mathrm{B} \\ \hline Now suppose that the results were announced, but election officials accidentally destroyed the ballots before they could be certified, and the votes had to be recast. Accessibility StatementFor more information contact us [email protected] check out our status page at https://status.libretexts.org. 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. \hline 3^{\text {rd }} \text { choice } & \mathrm{D} & \mathrm{B} & \mathrm{C} & \mathrm{E} & \mathrm{C} & \mathrm{B} \\ (1.4) Plurality-with-Elimination Method (Instant Runoff Voting) - In municipal and local elections candidates generally need a majority of first place votes to win. The dispersion, or alternatively the concentration, of the underlying ballot structure can be expressed quantitatively. Campaign civility under preferential and plurality voting. \hline 5^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ Available:www.doi.org/10.1016/j.electstud.2016.02.009. Public Choice. The Plurality winner in each election is straightforward. 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Video it says 9+2+8=18, should 9+2+8=19, so we proceed to elimination..