Of these alternative algorithms, we choose to focus on the Instant-Runoff Voting algorithm (IRV). 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 is still no choice with a majority, so we eliminate again. All of the data simulated agreed with this fact. 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 \(\begin{array}{|l|l|l|l|l|l|l|} However, we can calculate the HHI and Shannon entropy of these first choices and show how their dispersion relates to the probability of concordant election outcomes, had they been the first round in an IRV election. Provides an outcome more reflective of the majority of voters than either primaries (get extreme candidates playing to their base) or run-off elections (far lower turnout for run-offelections, typically). Election by a plurality is the most common method of selecting candidates for public office. Concordance of election results increased as HHI decreased across bins 1 - 26 before leveling off at 100% after bin 26. If a candidate wins a majority of first-preference votes, he or she is declared the winner. The following video provides anotherview of the example from above. In a three-candidate election, the third-place candidate in both election algorithms is determined by the first-choice preferences, and thus is always unaffected by the choice of algorithm. Consider the preference schedule below, in which a companys advertising team is voting on five different advertising slogans, called A, B, C, D, and E here for simplicity. The Plurality algorithm is far from the only electoral system. Ranked-choice voting is not a new idea. All rights reserved. The second is the candidate value and incorporates only information related to voters first choice. The choice with the least first-place votes is then eliminated from the election, and any votes for that candidate are redistributed to the voters next choice. \end{array}\). 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 . It refers to Ranked Choice Voting when there is only one candidate being elected. This paper presents only the initial steps on a longer inquiry. "We've had a plurality in general elections for quite some time. 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. Available: www.doi.org/10.1016/j.electstud.2014.11.006. \hline 1^{\text {st }} \text { choice } & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{D} \\ M: 15+9+5=29. Page 3 of 12 Instant Runoff Voting. 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. The 44 voters who listed M as the second choice go to McCarthy. Consider again this election. We simulate one million of these individual hypothetical elections. The most immediate question is how the concordance would be affected in a general N-candidate election. Even though the only vote changes made favored Adams, the change ended up costing Adams the election. Election Law Journal, 3(3), 501-512. 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 You could still fail to get a candidate with a majority. However, in terms of voting and elections, majority is defined as "a number of voters or votes, jurors, or others in agreement, constituting more than half of the total number.". Given the percentage of each ballot permutation cast, we can calculate the HHI and Shannon entropy: It should be noted that in order to reach certain levels of Shannon entropy and HHI, there must exist a candidate with more than half the votes, which would guarantee the algorithms are concordant. \hline In cases of low ballot concentration (or high entropy) there is a lower tendency for winner concordance. \hline 1^{\text {st choice }} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{E} \\ HGP Grade 11 module 1 - Lecture notes 1-10; 437400192 social science vs applied social science; . This is best demonstrated with the example of a close race between three candidates, with one candidate winning under Plurality, but a separate candidate gaining enough votes to win through IRV. 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. In IRV, voting is done with preference ballots, and a preference schedule is generated. So it may be complicated todetermine who will be allowed on the ballot. As a result, many of the higher bins did not receive any data, despite the usage of an exponential distribution to make the randomized data less uniform. If any candidate has a majority (more than 50%) of the first preference votes, that candidate is declared the winner of the election. In IRV, voting is done with preference ballots, and a preference schedule is generated. After transferring votes, we find that Carter will win this election with 51 votes to Adams 49 votes! 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. \hline 5^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ The 20 voters who did not list a second choice do not get transferred - they simply get eliminated, \(\begin{array}{|l|l|l|} \hline 2^{\text {nd }} \text { choice } & \text { D } & \text { B } \\ Under plurality with a runoff (PwR), if the plurality winner receives a majority of the votes then the election concludes in one round. Rep. Brady Brammer, R-Pleasant Grove, said he didn't see much urgency in addressing plurality in elections. A majority would be 11 votes. \hline 1^{\text {st }} \text { choice } & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{D} & \mathrm{B} & \mathrm{E} \\ RCV is straightforward: Voters have the option to rank candidates in order of preference: first, second, third and so forth. Instant runoff voting (IRV) does a decent job at mitigating the spoiler effect by getting past plurality's faliure listed . Still no majority, so we eliminate again. \(\begin{array}{|l|l|l|l|l|l|l|} their lower choices, then you could fail to get a candidate who ends up with a majority, after all. The reasons for this are unclear and warrant further study. - We dont want spoilt ballots! This page titled 2.6: Instant Runoff Voting is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. First, it explicitly ignores all voter preference information beyond the first preference. D has now gained a majority, and is declared the winner under IRV. The candidate Shannon entropy ranges from 0 to ln(3). People are less turned off by the campaign process andhappier with the election results. So Key is the winner under the IRV method. Notice that, in this example, the voters who ranked Montroll first had a variety of second choice candidates. There is still no choice with a majority, so we eliminate again. The last video shows the example from above where the monotonicity criterion is violated. Find the winner using IRV. Round 2: We make our second elimination. \hline 5^{\text {th }} \text { choice } & \mathrm{E} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{D} & \mathrm{C} \\ Second choices are not collected. 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. Runo Voting Because of the problems with plurality method, a runo election is often used. Third, the Plurality algorithm may encourage infighting among candidates with otherwise common policy objectives and natural constituencies. The candidate need not win an outright majority to be elected. With primaries, the idea is that there is so much publicity that voters in later primaries, and then in the general election, will have learned the candidates weaknesses and be better informed before voting. Higher degrees of voter preference concentration, or lower Shannon entropy, tends to increase the potential for winner concordance. - Voters can vote for the candidate they truly feel is best, - Instead of feeling compelled to vote for the lesser of two evils, as in plurality voting, voters can honestly vote for, (to narrow the field before the general election), (to chose a final winner after a general election, if no candidate has a majority, and if the law requires a majority for that office). But security and integrity of our elections will require having a paper trail so that we can do recounts, and know the results arevalid. Choice E has the fewest first-place votes, so we remove that choice, shifting everyones options to fill the gaps. The candidate HHI ranges from 1/3 to 1. Discourages negative campaigning - Candidates who use negative campaigning may lose the second choice vote of those whose first choicewas treated poorly. The Plurality algorithm is commonly used to convert voter preferences into a declared winner. \hline 2^{\text {nd }} \text { choice } & \mathrm{C} & \mathrm{D} & \mathrm{D} & \mathrm{C} & \mathrm{E} & \mathrm{D} \\ Australia requires that voters, dont want some of the candidates. \hline & 136 & 133 \\ 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. 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. However, under Instant-Runoff Voting, Candidate B is eliminated in the first round, and Candidate C gains 125 more votes than Candidate A. Both of these measurements share the same cutoff for guaranteed concordance as their corresponding ballot concentration counterparts. The first electoral system is plurality voting, also known as first-past-the-post; the second is the runoff system, sometimes called a two-round system; and the third is the ranked choice or the instant runoff. \hline 2^{\text {nd }} \text { choice } & \mathrm{B} & \mathrm{M} \\ 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 2^{\text {nd }} \text { choice } & \text { D } & \text { B } & \text { D } & \text { B } & \text { B } \\ No one yet has a majority, so we proceed to elimination rounds. Shannon, C. E. (1948) A mathematical theory of communication. Review of Industrial Organization, 10, 657-674. 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