In the wake of the 2016 US Presidential election, many Americans are wondering if there is a better way to elect political leaders. During the 2015 Canadian election, voters supported the Liberal party’s claim that 2015 would be the last time Canada would use archaic “first-past-the-post” voting. What other options do we have for electing an executive officer such as president, governor, mayor, secretary of state, or attorney general? This glossary summarizes how different voting systems for electing a mayor or president work, what supporters and critics say about them, and how they have played out in real life.
This document does not describe all the possible voting systems; there are far too many to list here. Nor does it detail all of the quirks of each system. Rather, it is meant as a quick reference guide to the different systems that have been used in Cascadia or that advocates propose for use here. To learn more about Sightline’s recommendations regarding these systems, see our Guide to Voting Systems for Electing an Executive Officer.
This Glossary and Guide are specifically about electing what we are calling “executive” positions that only one person holds at a time, such as a president or mayor. Different electoral systems can be used to elect legislative bodies made up of more than one person, such as a state house of representatives, city or county councils, and school boards. (To learn more about the options for electing legislative bodies, see our Glossary of Voting Systems for Electing a Legislative Body and our recommendations on those options next week.)
Considerations or tradeoffs
No voting system is perfect. Each system involves tradeoffs, which can be measured by how well the system complies with various mathematical criteria. But ultimately, the voting system you prefer will depend on which aspect is most important to you (see what is important to Sightline in our guide). Below are a few—though again, not all—criteria that supporters and critics may point to when comparing voting systems for electing an executive such as president or mayor.
(Click on the criteria below to expand or collapse each item.)
A simple ballot is easier for voters to understand and easier for counties to count. A more complex ballot gives voters the opportunity to express more nuanced views about the candidates.
If a voter would get a better election result by voting “strategically” or “tactically” instead of “honestly,” that system puts pressure on voters to figure out the best strategy and could give an unfair advantage to voters who do discover the best strategy.
Political scientists and mathematicians have described mathematical properties that might incentivize some form of strategic voting. They have also described criteria for determining whether a system is immune to that particular strategy (it passes) or could reward that type of strategy (it fails). These criteria can’t tell you how often an election using this method might pass or fail, or how likely voters are to strategically vote, it only says whether it could fail in some scenarios (in which case it fails) or would never fail in any scenario (in which case it passes).
- If you can safely vote for one of two similar or nearly identical candidates you prefer without fear of helping a different candidate win, the system is resistant to vote splitting, spoilers, and clones. In systems that fail, voters would need to organize around one of the similar candidates, or prevent similar candidates from running, to prevent a different, less popular candidate from winning. In systems that are resistant, voters can give high scores or ranks to similar candidates, confident that one of them will beat the different, less-preferred candidate.
- Pass: No system is completely immune to all spoilers, vote splitting, and clones
- Resistant to spoilers, vote splitting, and clones: Approval, Score, Score Runoff, Top-Two Runoff, Instant Runoff, Bucklin
- Fail: Plurality
- If you can safely rank or score additional less-preferred candidates without harming your favorite or more preferred candidates, the system passes the “Later-No-Harm” criterion. In systems that add your scores for all candidates, scoring a less preferred candidate could boost him past your favorite, causing your favorite to lose. In Approval, Bucklin, and Score, if your favorite was in first place, your vote for your less preferred candidate could vault him to first. In Score Runoff, if your favorite was in second place, your score for your less preferred candidate could vault him to second, bumping your favorite out of the runoff. When voters realize a system fails, they may vote like they would in a “vote for one” system—“bullet vote”—give a maximum score only to their favorite candidate. Voters are less likely to bullet vote in Score Runoff Voting because the runoff provides a countervailing motivation for voters to give at least some score to a backup candidate to make sure they have a vote in the runoff if only their backup makes it.
- Passes: Instant Runoff
- Fails: Approval, Score, Bucklin, Score Runoff
- Not applicable: Plurality, Top-Two Runoff
- If you can safely vote for or give a top-ranking or high score to your favorite candidate, the system passes the “Favorite Betrayal” criterion, so called because systems that fail this criterion may encourage voters who know their favorite can’t win to “betray” their favorite and instead vote for or score or rank a less-preferred but more likely to win candidate higher (for example, to “betray” Bernie and vote for Hillary). If it is clear to voters that their favorite can’t win but another candidate they like can win, they may strategically vote for their preferred viable candidate instead of their favorite in systems that fail this criterion.
- Passes: Approval, Score, Bucklin
- Fails: Plurality, Instant Runoff, Score Runoff
- If you can be sure that you would not counterintuitively cause a candidate to lose by ranking her higher or cause her to win by ranking her lower, the system passes the “monotonicity” criterion. These anomalous results are a product of the runoff: if ranking a candidate lower than a weaker opponent would help that weaker opponent make it to the runoff against her she can win, and if ranking her higher than a weaker opponent helps a stronger opponent instead reach the runoff, she could lose to the stronger candidate. Technically, this criterion only applies to ranking systems where ranking one candidate higher requires another candidate to move down the preference list. If the criterion applied to rating systems as causing a candidate to lose by rating them higher, without changing any other candidates’ scores, then all the rating systems pass. Score Runoff uses rating in the first round and ranking in the second round, so if the definition requires ranking one candidate higher than another to ensure your runoff vote would go to the candidate you decided to rank higher, then SRV fails. In systems that fail this criterion, if voters could know exactly how everyone else will vote, a group of voters could, in the small number of instances where this criterion comes into play, strategically try to elevate a weaker opponent to the runoff to help their favorite win. In reality, it would be difficult, if not impossible, to gain enough information about other voter’s behavior to develop a strategy based on monotonicity, and risky to do so in case you inadvertently cause your favorite to lose by strategically ranking him lower.
- Passes: Approval, Score, Plurality, Bucklin
- Fails: Instant Runoff, Top-Two Runoff
- Depends on the definition: Score Runoff
“Favorite Betrayal” and “Later-No-Harm” are two sides of the same coin. Which criterion you think is more important comes down to how strongly you think voters feel about their favorite candidate compared to their second-favorite. If you think most voters feel very strongly about their favorite and would not be willing to do anything that might hurt him (“I want Bernie to win, and even though Hillary is not terrible, I would not do anything that might help her beat Bernie”) then you prefer Instant Runoff Voting because it lets the Bernie voter safely express support for Hillary without hurting Bernie. In contrast, with Approval and Score Voting, giving a score to Hillary could hurt Bernie, so voters with a strong preference will only vote for Bernie, just like in a Plurality election.
On the other hand, if you think that voters only weakly prefer their favorite and would be willing for their favorite to lose to their second-favorite (“I like Bernie, but I’d also be happy if Hillary won”), or that they don’t particularly care who wins so longs as their least-favorite loses, then you prefer Approval and Score Voting, which makes it safe to give your favorite Bernie a top score without hurting your second-favorite, Hillary. In contrast, with Instant Runoff Voting, in the narrow case where Bernie is strong enough to make it to the runoff but sure to lose to Trump, and Hillary is too weak to make it to the runoff but could beat Trump if she did, Bernie voters who would be happy for Hillary to win or who mostly want Trump to lose would be better off ranking Hillary above Bernie.
The winner should be the candidate most voters support, right? But how do you measure what “most voters support” means? That could mean the candidate that a majority of voters prefer. Or it could mean the candidate with the most overall intensity of support—so a candidate that one group of voters loves, but whom the majority dislike, would win instead of a candidate that a majority of voters weakly prefer. Or it could mean victory for the candidate whom many voters love and a majority of voters find at least acceptable.
Different systems can guarantee that candidates meeting certain conditions will always win or never win, including:
- A system that meets the “Majority” criterion guarantees that, if a majority of voters choose a candidate as their favorite, she will win.
- Passes: Instant Runoff, Bucklin, Plurality, Top-Two Runoff
- Depends on the definition: Approval, Score Runoff
- Fails: Score
- A system that meets the “Mutual majority” criterion guarantees that, if there is a group of candidates that every voter prefers to every candidate outside that group, then one of the candidates in that group will win. In other words, if a majority of voters lean left, then one of the left-leaning candidates will win.
- Passes: Instant Runoff, Bucklin
- Fails: Plurality, Approval, Score
- A system that meets the “Condorcet Winner” criterion guarantees that, if a candidate would beat the other top candidates in a head-to-head contest, she will win. In other words, when offered only two options, most voters prefer her to the other option. This could be the most broadly acceptable candidate, or it could be the “lesser of two evils” for most voters.
- Passes: None
- A system that meets the “Condorcet Loser” criterion guarantees that, if a candidate would lose to the other top candidates in a head-to-head contest, he cannot win. In other words, when offered only two options, voters would never prefer him to the other option.
- Passes: Top-Two Runoff, Instant Runoff, Score Runoff
- Fails: Plurality, Approval, Score, Bucklin
Voting systems
(Click on the voting system below to expand or collapse each one.)
Also called: “first-past-the-post, “winner-take-all,” “simple majority,” or “vote for one.”
In Plurality Voting, each voter votes for just one candidate. The candidate with the most votes wins, even if he only won a plurality (more than any other candidate) and not a majority (more than half) of the votes. For example, in Oregon’s 1990 gubernatorial race a conservative independent pulled votes from the Republican, allowing the Democrat to win with just 46 percent of the vote.
Supporters say
- The Plurality Voting ballot is simple.
- The vote-counting is simple.
- Americans and Canadians all know how to do it.
- It seems fair: the person with the most votes wins.
Critics say
- Voters can’t vote for their favorite candidate under Plurality Voting: you have only one vote, so you may have to hold your nose and strategically give that vote to a candidate you think has a chance to win, which is almost always a major-party candidate. Many people feel they are voting for the lesser of two evils.
- If voters don’t strategically vote for a major-party candidate, a third-party candidate can “spoil” the election, splitting the majority of voters who supported either the third-party candidate or the most similar major-party candidate and electing the “wrong” candidate—the major-party candidate that a majority of voters did not want. The best-known example, of course, is when Nader split votes with Gore, allowing Bush to win the US presidency in 2000.
Experience says
The pressure to strategically vote for your preferred major-party candidate is real and common: commentators often (rightfully) brow-beat voters who consider voting for a third-party candidate, pointing out that by voting their conscience, they can throw the election to the candidate they like least: “A vote for Jill Stein is a vote for Donald Trump,” or “a vote for Gary Johnson is a vote for Hillary Clinton.” The spoiler effect is real and can elect a candidate that a majority of voters didn’t want.
Also called: Two-Round System, “majority threshold,” “absolute majority,” or top-two open primary.
Top-Two Runoff is also a “vote for one” system. All Washington elections (other than for the US president) and many non-partisan Oregon elections use Top-Two Runoff. Each voter votes for one candidate in an initial or primary election. In many Oregon cities, if one candidate wins a majority in the primary, she wins the race. If not, the top two vote-getters advance to the general election. In most Washington elections, the top two vote-getters in the open primary advance to the general election. In the general or runoff election, each voter again gets one vote, and the candidate with the most votes wins.
Supporters say
- The Top-Two Runoff ballot is simple.
- The vote-counting is simple.
- Americans and Canadians all know how to do it.
- It eliminates the spoiler effect because there are only two candidates in the general election, and it guarantees that the winner received more than half of the votes cast.
Critics say
- Few voters participate in primaries, and the voters who do participate are usually older, whiter, and more partisan than general election voters. As a result, a small, skewed group of voters selects the two candidates that general election voters must choose between, sometimes yielding unrepresentative or disappointing results. For example, far-right voters in the Republican primary might select a far-right candidate, and in a Republican-leaning city he might win a majority of votes in the general, but the majority of voters would not feel he represents them well.
- A spoiler effect can still occur in the Top-Two primary, forcing general election voters to choose between two unappealing candidates.
Experience says
In Washington State in 2016, the majority of voters split their votes between three Democratic candidates in the open primary election for State Treasurer, leaving two Republicans—who together won less than half the primary votes—to advance to the general ballot. General election voters had no choice but to vote for a Republican, even though all but one other statewide political offices in the state are held by Democrats. The three Democrats “spoiled” the primary for each other, leaving general election voters with an unsatisfactory choice between two candidates who both likely only appealed to a minority of voters.
Also called: “single-winner ranked-choice voting,” “preferential voting,” or “the Alternative Vote.”
Instant Runoff Voting (IRV) is a type of Ranked-Choice Voting (RCV). (The multi-winner form, used to elect legislative bodies, is called Single Transferable Vote.) Other election methods, such as Bucklin, also use a ranked ballot that allows voters to rank candidates in order of preference. Ranked ballots ask voters to make a comparative judgment: whom do you like more—Deborah Democrat or Ronald Republican?
Under Instant Runoff Voting, voters rank their candidates in order of preference. Votes are counted in rounds that simulate a series of runoffs: in the first round, everyone’s first-choice vote is counted. If no candidate wins a majority, the candidate with the fewest first-choice votes is eliminated, and her votes are transferred to her voters’ next-ranked candidate who is still in the race. Candidates with fewer votes continue getting eliminated and their votes transferred until a candidate wins a majority of the remaining active votes. (Sound complicated? It’s not. This one-minute video explains.)
Supporters say
Single-winner Ranked-Choice Voting, a.k.a. Instant Runoff Voting:
- has been used in thousands of public elections around the world.
- eliminates the spoiler effect.
- allows third-party candidates to run and voters to safely vote for them.
- elects leaders with majority support.
- encourages positive, inclusive, campaigns.
- Psychologists say people are more accurate in making comparative judgments between candidates (“I like Deborah Democrat more than Ronald Republican”) than in making absolute judgments about each candidate individually (“I think Deborah Democrat is an eight, and I think Ronald Republican is a four”).
- Ranking candidates allows voters to express their opinions about multiple candidates but also puts a low cognitive burden on voters because they don’t have to weigh who is viable and who is not and formulate a voting strategy accordingly; they only have to say whom they like, in order.
Critics say
Single-winner Ranked-Choice Voting, a.k.a. Instant Runoff Voting:
- does not completely eliminate the spoiler effect.
- does not guarantee a majority winner.
- sometimes elects the “wrong” winner. A candidate with broad but weak support—few give him a top ranking but many consider him an acceptable back-up choice—will lose because he will be eliminated for lack of top rankings.
- does not count all voters’ second and third choices. Voters only get one vote per round, so if their favorite candidate makes it all the way to the final round their second and third rankings will never be counted.
- sometimes creates counter-intuitive situations where ranking a candidate higher could cause him to lose or ranking him lower could cause him to win.
- requires votes to be centrally tabulated rather than summed at each precinct, creating added administrative burden. Some voting machines can’t handle a ranked ballot.
- Because of these faults, it is vulnerable to being repealed.
More information about supporters’ and critics’ claims
Single-winner Ranked-Choice Voting, a.k.a. Instant Runoff Voting, guarantees that:
- If a majority of voters choose a candidate as their favorite, she will win.
- If there is a group of candidates that every voter prefers to every candidate outside that group, then one of the candidates in that group will win.
- If a candidate would lose to the other top candidates in a head-to-head contest, he cannot win.
- The winner received a majority of the active ballots.
- Every voter who expresses a preference between the candidates in any round of runoffs gets one vote in that round (if a voter’s preferred candidate is not eliminated in one round, his vote will count for that candidate again in the next runoff round).
Single-winner Ranked-Choice Voting, a.k.a. Instant Runoff Voting, does not guarantee that:
- If a candidate would beat the other top candidates in a head-to-head contest, she will win. (A compromise candidate without enough top ranks to make it to the runoff will be eliminated, even if she could have won in the runoff).
- The winning candidate received votes from a majority of all voters. (The winning candidate must receive votes from a majority of all voters who ranked the candidates in the final round, but some voters may not have ranked either of the final candidates.)
Instant Runoff Voting eliminates what most people think of as the “spoiler effect”—where two similar candidates split the majority of votes, allowing a different candidate to win. (For example, in this video, the blueberry and peach are similar candidates splitting the fruit vote, allowing the less popular squash to win.) Usually, this happens when a minor-party candidate (Nader) pulls some votes from a similar major-party candidate (Gore), allowing the less popular, other major-party candidate (Bush) to win. Under Instant Runoff Voting, if a majority of voters prefer Gore or Nader over Bush, Bush cannot win. As a voter, this means you can safely rank a third-party candidate like Nader first and a major-party candidate like Gore second, knowing that once Nader is eliminated your vote will transfer to Gore, helping him win. If you rank Gore first and Nader second, your vote will count for Gore in the first round and again in the second round after Nader is eliminated.
However, Instant Runoff Voting does not eliminate a situation some call the “center squeeze.” When three candidates sit along an ideological spectrum and most voters prefer one of the candidates on the ends, the middle candidate who is everyone’s second choice will get squeezed out. For example, imagine a left-leaning city with three candidates for Mayor: Ronald Republican on the right, Deborah Democrat in the middle, and Priya Progressive on the left. In a spoiler situation, the majority of voters would split their votes between Deborah Democrat and Priya Progressive, allowing Ronald Republican to win. That can’t happen with IRV. In a “middle squeeze” situation, if most left-leaning voters prefer Priya Progressive, Priya would win, even though Deborah was more acceptable to the Republican voters.
This “center squeeze” situation happened in an IRV election in Burlington, Vermont, in 2009: the Republican and the Progressive each got a little more than one-third of the votes and the Democrat got about one-quarter and was eliminated. Most Democratic voters ranked the Progressive second, so the Progressive beat the Republican in the final runoff. Critics of IRV say the Republican “spoiled” the election for the Democrat. But if a spoiler is a similar candidate who splits the votes of a majority of like-minded voters allowing a different candidate to win, the Republican was not a spoiler for the Democrat. Democratic and Progressive voters in Burlington were like-minded, giving most of their back-up votes to the other, but Republican and Democratic voters were less similar; less than half of Republican voters chose the Democrat as a back-up and just 19 percent of Democrats chose the Republican as a back-up.
This video from a group that promotes Approval Voting illustrates a similar so-called “spoiler” effect in IRV from the point of view of a voter in the minority. In the video, imagine your “Ideal” candidate is the Republican, you think the Democrat is “Good” and you oppose the Progressive (“Bad” in the video). You and other voters in the conservative minority in this progressive town are upset that your least favorite candidate won. In Burlington, 17 percent of voters preferred the Republican first and the Democrat second, and were upset that their least favorite candidate, the Progressive, won. But from the perspective of the electorate as a whole, the result makes sense. Few voters felt strongly about the “center” Democrat, while a majority ranked the Progressive first or second.
Put another way, IRV narrows the field to the two candidates with the strongest support (the most high rankings) and then selects the most popular of those two. In a three-way race, a candidate who would lose in a head-to-head against both other contenders (the Condorcet Loser) can’t win, because he has to go head-to-head in the runoff). But a candidate who would win a head-to-head against both other contenders (the Condorcet Winner) won’t necessarily win, because he has to get enough high rankings to make it to the runoff. If the 17 percent of Burlington voters who preferred the Republican first and the Democrat second could have known that the Republican would be the Condorcet Loser and the Democrat would be the Condorcet Winner, they could have been wary of advancing their favorite to the runoff and instead tried to get their second-favorite to the runoff.
In IRV, votes have to be tabulated centrally, although this is not a problem for local elections in Oregon and Washington, where all vote-by-mail ballots are already sent to one county location for counting. For statewide elections, all counties would transmit their ballot data to the secretary of state. Counties could transmit the entire ballot information, or they could transmit their first-round totals, and then the state could add them and tell all counties which candidates to eliminate. The counties could then transfer the eliminated candidates’ votes and transmit second-round totals and so on.
Experience says
The following places currently use Instant Runoff Voting:
- 12 American cities and one county
- 50 American colleges and universities
- Australia, to elect members to the federal House of Representatives and some local offices
- Ireland, to elect the president
- The Academy Awards
In 2017, 18 states introduced ranked-choice voting bills—11 states have Republican co-sponsors, and 13 states have Democratic co-sponsors.
Instant Runoff Voting has been shown to reduce negative campaigning and produce more civil, less negative campaigns because candidates have an incentive to broaden their appeal and seek out second- and third-ranked votes.
In US cities that have used Instant Runoff Voting in the past decade, voters in IRV systems have elected more women and people of color.
In ten recent public IRV elections in US cities, between 54 percent and 85 percent of voters ranked two or more candidates, indicating most voters understand the ranked ballot and make use of it by expressing support for more than one candidate.
Out of 142 Instant Runoff Voting elections in the United States that released full data, including 86 with three or more candidates, all but one has elected the Condorcet Winner. In the 2009 election for Mayor of Burlington, Vermont, described above, the “center squeeze” eliminated the Condorcet winner before the final runoff. If the 17 percent of voters had known to strategically “betray” their favorite, the Republican, they could have at least helped their second-favorite, the Democrat, win and kept their least-favorite, the Progressive, out of office. But they could not have known the weak (third place in the polls) Democrat was a better bet than the strong (first place in the polls) Republican candidate. What if they misjudged and prevented their favorite from winning? Under Instant Runoff Voting, voters’ safest strategy is always honest rankings.
Nonetheless, candidates or parties may spread misinformation about Instant Runoff Voting. For example, in those parts of Australia where the Green Party regularly wins seats in the senate (elected with proportional voting) and sometimes in the lower house (elected with IRV), the Labor Party sometimes warns Green voters not to vote for their favorite Green Party candidate in Instant Runoff Voting elections for the lower house because they could “spoil” the election for the Labor candidate. So far as I can tell, this has never actually happened, and it has not discouraged third-party candidates from running nor voters from voting for them. Australia routinely has 5 or more candidates run for lower house seats, and minor-party candidates receive between 15 and 23 percent of first-ranked votes. But facts don’t stop major parties and critics from fearmongering.
Another example: some producers spread misinformation around the Academy Awards, erroneously telling people that Instant Runoff uses a “weighted” ballot. (They are basically describing another voting system called Borda Count, which translates ranks to scores and therefore fails the Later-No-Harm criterion.) This is not true; Instant Runoff Voting doesn’t use scores, but instead transfers your vote to your next-ranked candidate if your first-choice is eliminated, so it is always safe to rank more candidates. But this experience indicates the need for voter education.
Under Approval Voting, voters can vote for as many candidates as they find acceptable. Voters are implicitly assigning each candidate a score: either a 1 or a 0. All votes are added up and the candidate with the most total votes wins.
Supporters say
- The Approval Voting ballot is simple yet expressive.
- The vote-counting is easy.
- Voters can always vote for their favorite.
- Third-party candidates can run and win votes.
- It eliminates the spoiler effect.
- It tends to elect moderate candidates who would beat all other candidates in a head-to-head.
Critics say
- In practice, in high-stakes elections using Approval Voting, voters will only vote for their favorite candidate because a vote for a less-preferred candidate could cause your favorite to lose. In other words, Approval Voting fails the Later-No-Harm criterion, meaning that voters cannot honestly vote for a less-preferred candidate without risking causing their more preferred candidate to lose. When voters realize this, they often bullet vote (vote only for their favorite).
- If enough voters bullet vote, Approval Voting is no better than Plurality Voting: third parties get few votes, and similar candidates can split the majority of votes, electing a candidate whom a majority of voters did not want.
- To know whether it is safe to vote for more than one candidate, voters must figure out which candidates are viable and which are not. Making these calculations imposes a cognitive burden on voters.
More information about supporters’ and critics’ claims
When there are only two viable candidates, likely two major-party candidates, voters can safely vote for their preferred major-party candidate and also any weaker or third-party candidates they like but know can’t win (it is safe to approve both Nader and Gore, since Nader can’t win). But when there are three strong candidates, or if the voter isn’t sure who is viable and who is not, or if the voter honestly approves of both major-party candidates, he can only safely vote for his favorite. (In the Burlington example above, voters would most likely approve just one of the three strong candidates, and the Republican would have won with mere plurality support, even though, had voters who mildly approved of the Democrat voted for him in addition to their favorite, he would have won.)
Alternatively, if a voter does not care who wins, but only wants a particular candidate to lose, (for example, in this video, if a voter didn’t care whether peach or blueberry won, he only wanted squash to lose), he could vote for everyone other than the candidate he wants to lose.
To make the most of their Approval ballot, voters must know which candidates are viable and only vote for one of those. If they know which candidates can’t win, they can safely vote for any and all of those. Without this knowledge, voters’ safest strategy—the one that gives their favorite candidate the best chance to win—is to treat the Approval ballot like a Plurality ballot and only vote for one.
Experience says
Approval voting is not used in any governmental election. Although the Center for Election Science and Warren Smith say that the United Nations “uses Approval Voting to elect its Secretary General,” they don’t actually use an Approval Voting election. Rather, the UN Security Council discusses candidates over the course of many months, periodically using non-binding Approval Voting-style straw polls to help them converge on a candidate no one will veto. They unanimously recommend that candidate to the larger body to be appointed as the Secretary General.
Colorado Democrats introduced an Approval Voting bill in the 2017 session.
Several minor political parties, professional organizations, Dartmouth College, and San Francisco State University use Approval Voting.
Experience indicates that many voters “bullet vote”—vote for only one candidate—in Approval Voting elections. For example:
- The Institute of Electrical Engineers stopped using approval voting in 2002 because 80 percent of members were bullet voting.
- In a Mathematical Association of American election, 79 percent of voters bullet voted.
- The Independent Party of Oregon recently held an Approval Voting presidential primary, and more than 70 percent of voters bullet voted.
- Dartmouth College’s student body has used approval voting since 2011, and most voters for student body president bullet vote. In 2015 and 2017, likely everyone bullet voted (there were fewer votes than ballots cast), in 2016 more than 92 percent bullet voted, and in 2014 at least 82 pecent bullet voted.
- In a 2009 Dartmouth Alumni Association election that did not release full data, between 19 and 60 percent of voters bullet voted. However, a faction of Dartmouth alumni with extreme views apparently succeeded in electing several candidates to the Board of Trustees by getting their supporters to bullet vote while others naively approved more candidates. After several of these surprising wins, the association put a referendum on the alumni ballot in 2010, and alumni voted 81 percent to 19 percent to eliminate approval voting. In the 2010 plurality election, the extreme candidate lost by 70 percent to 30 percent, suggesting that strategic approval voting had elected unrepresentative candidates.
Approval Voting works well in many non-election scenarios, such as polls or ratings where people are expressing an opinion or narrowing in on satisfactory options (as in the UN Security Council process) but not electing a single winner. For example, in its online election, the Independent Party of Oregon also asked voters to use Approval Voting to identify multiple policy priorities, and voters averaged nearly four votes each. YouTube, and now Netflix use thumbs up or thumbs down rating systems where viewers can express approval or disapproval of multiple people, videos, or shows. Approval Voting can also be an easy and fair way to make decisions in lower-stakes group situations—everyone raises a hand for every option they find acceptable, and no compicated tallying is needed.
Also called: “Grand Junction Voting,” “preferential approval voting.”
Bucklin Voting uses a ranked (preferential) ballot but adds multiple votes together (like Approval Voting does), rather than transferring a single vote as Instant Runoff Voting does. Votes are summed in rounds: in the first round, only first-choice votes are counted. If no candidate wins a majority (at least half) of the votes, then all second-choice votes are added to the first-choice votes, then all third-choice votes are added, and so on until someone wins a majority.
Some versions of Bucklin Voting only allowed voters to rank two candidates.
Supporters say
- The counting method for Bucklin Voting is fairly easy to explain.
- Because you know your second-choice vote will only be counted after your first-choice, you are less likely to bullet vote than in pure Approval Voting.
- Because your votes for multiple candidates can all get counted simultaneously, it is more fair than Instant Runoff Voting, which only counts your second-choice ranking if your first-choice candidate gets eliminated.
Critics say
- Like Approval Voting, voters are likely to revert to bullet voting when they realize giving a rank to less-preferred candidates can hurt your favorite under Bucklin Voting.
Experience says
For a brief period at the beginning of the 20th century, several American cities, including Portland, Oregon, and Spokane, Washington, used Bucklin Voting. In 1932, Portland voted 81 percent to 19 percent to repeal Bucklin voting. A 1915 analysis of Cleveland, Columbus, Portland, and Spokane showed that between between 27 and 65 percent of voters ranked more than one candidate. However, in 16 Bucklin elections in Alabama, an average of just 13 percent of voters ranked more than one. Overall, more voters seem to rank multiple candidates under Bucklin Voting than under Approval Voting, but still rank fewer candidates than under Instant Runoff Voting.
Also called: “Range voting.”
Score Voting is also called Range Voting because voters can give each candidate a range of scores. Scoring or rating systems ask voters to make an absolute judgement about each candidate and give each an independent rating or grade: do you think Deborah Democrat is a 0, a 9, or some number in between? Same for every other candidate. Scores could range from 1 to 5 as on Yelp, or from 0 to 9, or some other range. The scores are added up or averaged, and the candidate with the highest total or average score wins.
Supporters say
The Center for Range Voting makes stronger claims about Score Voting’s benefits than does the Center for Election Science; following is a mix of claims from these two organizations.
- Score Voting, especially with a large range of numbers, allows voters maximal nuanced expression.
- Voters can always express themselves honestly, including always giving a top score to their favorite.
- The “human impulse for honesty” will ensure many voters will vote honestly, even when it is not in their interest to do so.
- Voters will give high scores to weak or “infant” third-parties because they know, if that candidate has no chance to win, it is safe to give them a high score.
- There are no “spoilers.”
- It will elect the most “utilitarian” candidate—the one whose win will inspire the highest average intensity of happiness among voters.
- It is the best voting system according to “Bayesian regret”—a model that proponents consider the “gold standard for comparing single-winner” methods—and its inverse “Voter Satisfaction Efficiency.”
- “Modern election machines” can count a scored ballot.
Critics say
- In Score Voting, it’s irrational to vote honestly. One strategy, as in Approval Voting, is to give a maximum score to your favorite and minimum to everyone else. Voters who don’t follow the strategy and instead give honest scores to all candidates will be at a disadvantage. Some voters will max out for their favorite viable candidate and be done. Voters who don’t care which of their preferred candidates win, or who just want to see a particular candidate lose, may give a max score to all candidates they approve of, or to all candidates other than their least favorite. Informed voters will give a max score to any weak third-party candidates, confident that doing so won’t sink their preferred viable candidate. What voters won’t do is honestly score all the candidates, because voting that way minimizes their influence over the outcome.
- Score Voting could elect extreme candidates opposed by the majority of voters. Because total intensity of voters’ support is more important than total numbers of voters who support a candidate, a minority that feels strongly can beat a majority that feels less strongly, an outcome that goes against most notions of democracy. For example, if 45 percent of voters gave the Republican a 9 and the Democrat a 0, and 55 percent of voters give the Democrat an 8 and the Republican a 1, the Republican would win, even though a majority of voters preferred the Democrat. (Note that, in the multi-winner form of Range Voting that could be used to elect legislatures, this is not a flaw because a group in the racial, political, or social minority should be able to have a voice in the legislature.)
- The way that Score Voting works, and the mathematical models used to prove it is the best voting system (Bayesian Regret and Voter Satisfaction Efficiency) are based on assumptions about voters that don’t apply to real people in the real world.
- If I don’t love her, but she’s okay, should I give her a four or a six? Does a one mean “I weakly support” or “I strongly oppose”? Because different voters will interpret the numbers differently, researchers who study measurement generally agree that raw scores cannot be added and compared across voters in the way Score Voting boosters’ models do.
- In the last election you voted in, for how many candidates did you know whether they were a 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9? Most voters know whom they like and whom they oppose—“I like Republicans” or “I don’t like Libertarians”—or whom they like most and whom they like second-most. Asking voters to give each candidate a precise score may be overwhelming.
- When you look at election results, is your happiness about who won based on their mathematical distance from you on an array of policy issues? Can you even name five policy positions held by your mayor, governor, attorney general, secretary of state, etc.? In reality, many voters’ perception of election results is shaped more by group identity—whether political, racial, religious, or geographic—than by personal views on multiple policy positions. Indeed, voters often shape their policy views based on their party, rather than picking their party or candidates based on unchanging personal policy positions, as evidenced by Republican’s dramatically changed views on Russia and Democrat’s flip-flop on state’s rights.
- Trying to calculate your honest scores for each candidate, and then also understand the best strategy under Score Voting, would put an even higher cognitive burden on voters than Approval Voting.
- No voting machines are yet able or certified to count score ballots.
More information about supporters’ and critics’ claims
Voters can always safely give their favorite a top score because Score Voting passes the “Favorite Betrayal” criterion. As with Approval Voting, if a voter knows which candidates are not viable (cannot win), he can safely give scores to those candidates, too. However, voters cannot safely give scores to viable candidates other than their favorite because Score Voting fails the Later-No-Harm criterion. Score Voting also fails the Majority, Mutual Majority, Condorcet Winner, and Condorcet Loser criteria, so it does not tend towards the candidate with majority support. Another drawback is that not all vote-counting machines can handle a score ballot.
Another drawback is that no vote-counting machines are certifed to count a score ballot.
Experience says
No governmental elections have ever used Score Voting. Amazon, Yelp, and other online platforms use a 5-star Score Voting system. YouTube and Netflix previously used a 5-star Score voting system, but both eventually switched to a simplified thumbs-up/thumbs-down Approval Voting system. In 2009, YouTube realized that most users of its 5-star Score Voting system were giving either 1 star or 5 stars. This year, Netflix also switched from Score to Approval Voting, perhaps in part because the company realized that a mobilized block of users who intensely disliked a particular show were able to damage its average rating. For example: far-right activists all gave Amy Schumer’s show 1 star, overwhelming her other positive ratings.
Even in a low-stakes situation like rating a TV show, users polarized around the highest and lowest scores. In a high-stakes election, the pressure to strategically vote is strong because giving a middling score to a candidate you moderately support could cause your favorite to lose. Voters in an election would likely give their favorite candidate the highest score and all other candidates the lowest.
Score Runoff Voting (SRV) is a new hybrid form of voting invented in Oregon. The ballot looks like a Score Voting ballot, where voters can give each candidate a score from, say, 0 to 5. The scores are added up, and the two candidates with the highest total scores advance to an automatic runoff. In the runoff, each voter’s vote counts for the candidate he or she rated higher. The candidate with the most votes in the runoff wins.
Supporters say
- Score Runoff Voting aka Star Voting is the best of both worlds: it lets voters express nuanced opinions about each candidate as in Score Voting, but it improves on Score Voting by ensuring, as does Instant Runoff Voting, that a candidate whom a majority of voters oppose can’t win. It improves on Instant Runoff Voting by counting, as Score and Approval do, each voter’s opinion of each candidate all at once (instead of just counting one vote for one candidate in each round, as in Instant Runoff).
- It allows voters to always vote honestly without fear of spoilers.
- It ensures that a candidate in the middle—one who is the second choice of most voters on both sides—will win if supporters give him good scores. Or, if supporters give him low scores and he loses, it will be clear that he was only a reluctant backup choice for most voters.
- The runoff incentivizes voters to give a non-zero score to more than one candidate, to ensure they get a vote in the runoff.
Critics say
- Under Score Runoff Voting, voters would likely not fill out their whole ballot with honest, nuanced scores for each candidate. Rather, voters would likely give a maximum score to their favorite and a minimum to their second-favorite, to get a vote in the runoff in case their favorite is eliminated, but still minimize the chance of helping their second-favorite make it to the runoff instead of their favorite. Savvy voters might also give a maximum score to a third-party candidate if they are sure that candidate can’t beat their favorite.
- This could lead to the “center squeeze” situation described under Instant Runoff Voting above: if you live in a right-leaning district where Ronald Republican sits in the ideological “center” between Terry Tea Party and Deborah Democrat, but voters give their respective favorites (Terry and Deborah) high scores and give Ronald low scores, then he could get squeezed out of the runoff, allowing Terry to win, even though left-leaning voters would have preferred the Republican to the Tea Party candidate. If voters figure this out, Tea Party voters will give Ronald minimal scores, to ensure he doesn’t beat out their favorite. Democratic voters might give Ronald higher scores, to try to keep the Tea Party out of office, but only if they are confident that their second-favorite, Ronald, can’t beat their favorite, Deborah Democrat, in the runoff.
- The calculations above put a large cognitive burden on voters.
- Like IRV, SRV does not guarantee that all voters have a say in the runoff or that the winner has majority support; any ballot without a score for either of the final two candidates will not count in the runoff.
- If a voter gives the same score to two candidates, his vote may not count in the runoff.
- No voting machines are yet able or certified to count SRV ballots.
More information about supporters’ and critics’ claims
Like IRV, SRV narrows the field to the two candidates with the strongest support (the most high scores) and then selects the most popular of those two. This ensures that, in a race with three strong candidates, one who would lose in a head-to-head against both other contenders can’t win (because he has to go head-to-head in the runoff). But it doesn’t guarantee that a candidate who would win a head-to-head against both contenders wins, because a candidate who doesn’t earn enough high scores to make it to the runoff can’t win. For those who are scrutinizing the election results, SRV has the advantage of showing that the head-to-head winner received low scores, making it seem more appropriate that he lost, whereas IRV only tells analysts that voters ranked him second, leaving ambiguity about whether he was a close second or a distant second.
No voting machines are yet able or certified to count SRV ballots.
Experience says
Score Runoff Voting has so far been used in a poll in a group meeting in Portland. It should be put to use in an election to see how real voters respond.
Note:
Anyone who wades into voting systems in the United States and Canada will soon discover strong divisions amongst voting advocates.
On one side is FairVote, a national advocacy group pushing for ranked-choice voting, in both its single-winner form (Instant Runoff Voting or IRV) and its multi-winner form (Single Transferable Vote or STV). FairVote also advocates for the National Popular Vote for US president, modernizing voter registration to ensure all American citizens are able to vote, and improving primaries.
On the other side, the Center for Election Science champions Approval Voting and Score Voting, and mathematician Warren Smith and his Center for Range Voting advocate for Score Voting (a.k.a. “Range Voting”).
A new player in the game, Oregon-based EqualVote Coalition, is pushing for Score Runoff Voting (SRV) in Oregon.
Clay Shentrup
> The “human impulse for honesty” will ensure voters will vote honestly, even when it is not in their interest to do so.
Without qualification, this could be interpreted as a claim that Score Voting will ensure all voters will be honest. Its proponents are not making that strong of a claim. Your link says, “score voters will be both honest and strategic”. It also says that the impulse for honesty is so strong that, “even after 100 years of future experience (and even though strategic voting is fairly simple in score voting) voters will still, in large numbers and in a large fraction, choose not to be fully strategic, and to include a large amount of honesty, in their score vote.”
> The best strategy is to give a maximum score to your favorite and minimum to everyone else, making Score Voting act like Plurality Voting
This is inaccurate. The very link you cite before that statement says, “ideal range voting strategy for well-informed voters is identical to ideal approval voting strategy, and a voter would want to give their least and most favorite candidates a minimum and a maximum score, respectively.”
That does not mean only voting for one’s favorite. For instance, say you honestly think Tea=10, Libertarian=8, GOP=7, Dem=3, Green=2. You’d want to “polarize” GOP and Dem, and push candidates in their paths along with them, like beads on an abacus. This would create a tactical vote: Tea=10, Libertarian=10, GOP=10, Dem=0, Green=0. That is dramatically different than simply giving the Tea Party candidate a 10 and zeroing everyone else.
> But when electing just one person, that person should represent the majority.
This is incorrect. It is mathematically proven that there’s no unambiguous definition of “majority winner” in the first place.
https://sites.google.com/a/electology.org/www/utilitarian-majoritarian
> Trying to calculate your honest scores for each candidate, and then also understand the best strategy under Score Voting, would put an even higher cognitive burden on voters than Approval Voting.
Actually it’s empirically simpler than ranking, based on order of complexity and Kolmogorov Complexity, standard measures of complexity used by computer scientists. Even if humans do the sorting in their heads, these still apply. And empirical evidence bears this out—voters experimentally fill out Score Voting ballots faster than ranked ballots or Approval Voting ballots. Voters also experimentally make fewer spoiled ballots with Approval Voting or Score Voting than with ranked ballots.
> The mathematical models used to prove it is the best voting system (Bayesian Regret and Voter Satisfaction Efficiency) are based on assumptions about voters that don’t apply to real people in the real world.
You say this, then you proceed to list out assumptions that those calculations didn’t actually make, as well as making statements which demonstrate you don’t understand the methodology behind these calculations. For example, “different voters will interpret the numbers differently”. This is irrelevant. The Bayesian Regret calculations use simulated humans, whose utilities are known with precision. There is then ample “ignorance” added in which represents the disparity between what voters expect and what they get. On top of that, there is normalization error.
Kristin Eberhard
Hi Clay,
I appreciate your tireless efforts for voting reform. To be sure there is no confusion, I added a few qualifiers to the passages you found objectionable, for example I qualified that score voting advocates think “most” voters will vote honestly.
But several of your comments seem to misread the article or assume that your own opinions are facts. For example, it is not “incorrect” that a mayor or president should represent the majority of voters, it is a matter of opinion. As the article makes clear (see the “considerations or tradeoffs” section), no voting system is perfect and which you prefer will depend on what you think is important. You, Clay, think that overall utility of a candidate, assuming scores can be translated to utility and compared, is more important than majority support. I disagree. Readers are welcome to draw their own conclusions.
As to your claim that I don’t understand that there is no single definition of majority winner, actually I do, as I explained in the section “Does the system elect the “right” winner?”
But let’s zoom out to the larger problem at hand, the one most Americans understand and perceive as a problem: that our voting systems are not producing elected officials who actually work toward the priorities of their diverse constituents. Because while you argue with me about mathematical proofs, the status quo continues to sit there, fat and happy, churning out unrepresentative election results. No voting system is perfect, but those of us who realize that the one we use in the US and Canada is the worst need to band together to change the status quo to something that works for We the People.
Clay Shentrup
> it is not “incorrect” that a mayor or president should represent the majority of voters, it is a matter of opinion.
No, it’s mathematically proven. See Arrow’s Theorem.
> Clay, think that overall utility of a candidate, assuming scores can be translated to utility and compared, is more important than majority support. I disagree.
You can’t “disagree” with something that’s mathematically proven. I know it’s unsettling that things like this can be objectively proven, but it is very much the case.
For instance, it’s possible for a majority of people to want Measure X to pass, regardless of wether Y passes, and for a majority to want Measure Y to pass, regardless of whether Measure X passes. Aaaand (wait for it) for a majority to simultaneously prefer that NEITHER measure passes vs. having them both pass. See trivial proof here.
http://scorevoting.net/XYvote.html
In that case, you have contradictory majorities, which mathematically proves that a majority view can be “wrong”.
I appreciate the pragmatism of your last paragraph, and I’m actually not in much disagreement with you there. I can see how you could accept that “a majority can be wrong”, but still push for “majority rule” out of political pragmatism, even though it’s a nonsensical concept in mathematical terms. But time and time again, you’ve actually challenged the underlying math and game theory, while making comments which demonstrate a profound lack of familiarity with elementary facets of social choice theory. You don’t simply say that Score Voting is concerning because of political practicalities. You assail it’s actual appropriateness, invoking superstitions like “Later-no-harm”. This is, scientifically speaking, just flat out nonsense. And that’s why you have a lot of very smart people, with deep expertise, arguing with you here.
Adam Zielinski
In the article it says,
“Immune to spoilers, vote splitting, and clones: None
Resistant to spoilers, vote splitting, and clones: Approval, Score, Score Runoff, Top-Two Runoff, Instant Runoff
Vulnerable to spoilers, vote splitting, and clones: Plurality, Bucklin”
However then in the graphic, the icons indicate the opposite of the above.
Kristin Eberhard
Thanks for the catch, Adam – this is fixed now!
Parker Friedland
Score Runoff Voting does not pass the Favorite Betrayal Criterion:
Example:
Red Blue Green
Voter 1: 1 10 0
Voter 2: 0 1 5
Voter 3: 8 0 1
Total: 9 11 6
Runoff: 1 2
Winner: Blue
However, if voter 3 betrays his favorite:
Red Blue Green
Voter 1: 1 10 0
Voter 2: 0 1 5
Voter 3: 0 0 1
Total: 1 11 6
Runoff: 1 2
Winner: Green
Score Runoff Voting is surprisingly monotonic though here is why:
giving any candidate a lower score will either have no effect on the election, prevent them from entering the runoff, or prevent them from winning the runoff. If you disagree, I dare you to provide a counter example proving SRV is not monotonic.
Parker Friedland
In my example of SRV failing Favorite Betrayal, I did not know your comment system automatically deletes extra spacing whenever more then one space is used, which ruins everything. I will try again using non-spaces.
Example:
““““`Red“Blue“Green
Voter 1:“`1““10 ““0
Voter 2:“`0““`1““5
Voter 3:“`8““`0““1
Total:““9““`11““6
Runoff:“1“““2“““
Winner: Blue
However, if voter 3 betrays his favorite:
““““`Red“Blue“Green
Voter 1:“`1““10 ““0
Voter 2:“`0““`1““5
Voter 3:“`0““`0““1
Total:““`1““11““6
Runoff:““““`1““2
Winner: Green
However some voting systems that fail the Favorite Betrayal Criterion are more resistant to favorite betrayals then others. Despite not passing this criterion, SRV is very resistant to favorite betrayals in comparison to IRV (It frustrates me that IRV is now called Ranked Choice Voting even though it is not the only ranked ballot voting system)
Kristin Eberhard
Voter 3 doesn’t have to betray his favorite, he can just increase his score for Green to 7 and Green will win.
Parker Friedland
Revised example of favorite betrayal in SRV election:
Voters 1 and 2:
Red – 9
Blue – 10
Green – 0
Voters 3 and 4:
Red – 0
Blue – 1
Green – 5
Voter 5:
Red – 10
Blue – 0
Green – 10
Total:
Red – 28
Blue – 22
Green – 20
Runoff:
Red – 1
Blue – 4
However if voter 5 betrays his favorite…
Voter 5:
Red – 0
Blue – 0
Green – 10
Total:
Red – 18
Blue – 22
Green – 20
Runoff:
Blue – 2
Green – 3
Thus favorite betrayal. However despite failing the favorite betrayal criterion, however unlike IRV, favorite betrayal violations are rare in SRV
Kristin Eberhard
Red was not Voter 5’s favorite in this example—he gave the exact same score to Green, meaning he did not prefer Red to Green. Is there an example where a voter has one favorite (a candidate he prefers to all others) and betrays him to get a better result?
Parker Friedland
You assume that voters are honest. Is it not plausible that Red is voter 5’s favorite and Green is voter 5’s compromise candidate?
The scenario I mentioned still fails the favorite betrayal criterion because it is possible that voter 5 prefers Red, and is strategically giving green a max score too. Unfortunately, giving a max score to Green will not help Green enough to win. Even after giving a maximum score to Green, voter 5 will have still have to sacrifice Red to stop Blue from winning.
Parker Friedland
As I had just explained in my previous comment, the previous example was an example of favorite betrayal where the candidate in question only had one favorite. My example compared a scenario where voter 5 was as strategic as he could be without betraying his favorite, and an example of him betraying his favorite.
However if you insist seeing a discrete comparison between when voter 5 is 100% honest to when he is 100% strategic (or at least strategic enough to get the most desired outcome he can get under the current circumstances), here you go:
Voters 1 and 2:
Red – 9
Blue – 10
Green – 0
Voters 3 and 4:
Red – 0
Blue – 1
Green – 5
Voter 5:
Red – 10
Blue – 0
Green – 2
Total:
Red – 28
Blue – 22
Green – 12
Runoff:
Red – 1
Blue – 4
However if voter 5 betrays his favorite (and votes more strategically at the same time)…
Voter 5:
Red – 0
Blue – 0
Green – 10
Total:
Red – 18
Blue – 22
Green – 20
Runoff:
Blue – 2
Green – 3
Kristin Eberhard
You are right – SRV fails favorite betrayal. I’ll fix it.
Parker Friedland
Yes, and as I have described in another comment, it also passes monotonicity.
And runoff voting also fails the favorite betrayal criterion. Pretty much every voting system that has the word “runoff” in it’s name fails the favorite betrayal criterion.
I have sent you a tweet showing you all the changes you need to make to your chart:
https://twitter.com/ElectoralRef0rm/status/877307359223099392
By the way, I was torn about whether I should indicate that plurality voting and runoff voting both pass the later no harm criterion because with the stranded definition of plurality and runoff voting, you only mark one x next to each candidate in each round, thus it makes no sense to evaluate these methods for a criterion that is about what ranking you give candidates that you indicate on your ballot that you prefer more then another candidate.
The later no harm criterion just doesn’t seem applicable to these two methods unless for the sake of being able to compare these voting systems to other voting systems, you redefine plurality voting as a ranked ballot system where only the first preferences are used to determine the winner.
In a similar way, runoff voting can be redefined as a single election where you rank all of your candidates. For the first round, only the first preference votes matter in determining who the two candidates entering the runoff are, and out of those two, the candidate that wins is the one ranked higher on more of the ballots.
If for the sake of being able to compare voting systems easier, you use these definitions of plurality and runoff voting, then both of these systems also pass the later no harm criterion. However that is up to you to decide. Oddly, when it comes to determining which voting methods pass which criteria, the table comparing single winner voting systems on Wikipedia is not consistent: it uses the stranded definition of plurality voting and the modified definition of runoff voting.
Kristin Eberhard
Monotonicity:
Red,Blue,Green
V1:10,1,0
V2:10,2,4
V3:10,2,4
V4:8,10,9
V5:0,5,10
Total:28,23,27
Runoff:2,X,3
Winner:Green
V2 instead ranks Green higher than Red, causing Green to lose.
Red,Blue,Green
V1:10,1,0
V2:0,2,4
V3:10,2,4
V4:8,10,9
V5:0,5,10
Total:18,23,27
Runoff:X,3,2
Winner:Blue
Parker Friedland
That is not an example of SRV failing monotonicity voter 2 did not give green a worse score. In both examples, voter 2 gave green a score of 4, and in cardinal voting, the monotonicity criterion is as fallows:
A candidate cannot improve their final standing by being rated lower by a voter and a candidate cannot hurt their final standing by being rated higher by a voter. SRV fallows this principle.
Kristin Eberhard
Hi Parker – if you define monotonicity as rating a candidate higher to make them lose, then SRV is non-monotonic. But I think monotonicity is defined as ranking a candidate higher. If a voter had given Blue a top score (say, 5) and decided to rank Red higher, simply rating Red 5 would not rank them higher–in the runoff based on rankings, your vote wouldn’t go to Red because Red and Blue would be ranked the same. To rank Red higher, the voter would have to reduce Blue’s score to something less than the maximum score.
#Voters: Red,Blue,Green
6: 5,1,0
2: 0,5,3
4: 0,5,1
5: 2,0,5
Totals: 40,36,35
Runoff: 11,6,X
Winner: Red
Two voters instead rank Red higher, causing him to lose.
6: 5,1,0
2: 5,4,3
4: 0,5,1
5: 2,0,5
Totals: 50,34,35
Runoff: 8,X,9
Winner: Green
I’ve changed the table to indicate SRV’s monotonicity depends on whether the definition is rating higher or ranking higher.
Parker Friedland
As I have stated in my last comment, you forgot that top-two runoff also fails the favorite betrayal criterion.
I described why I was torn about deciding on whether to indicate whether top-two runoff and plurality pass the later-no-harm criterion or are N/A to it. I have definitely changed my mind since about top-two runoff voting, because if you prefer Green > Blue > Red and you vote Green in the first election, and between Blue and Red, you vote Blue in the second election, this second vote can be viewed as expressing support to Blue but to a lesser extent then your support for Green (that is if you are an honest voter). Thus top-two runoff most definitely passes the later no harm criterion.
According to electrowiki though (http://wiki.electorama.com/wiki/Later-no-harm_criterion), plurality can be considered as either passing the later no harm criterion or being N/A to it depending on if you consider plurality voting as the equivalent to allowing voters to rank all of their choices and electing the candidate that has the most first preference support. I have since changed my mind and I believe that it makes more sense to say that plurality voting passes this criterion, however that is just my opinion.
Parker Friedland
Your ` character’s appeared as a very different length after I submitted my comment then when they appeared in this text box.
Parker Friedland
You have made some misconceptions that I would like to clear up.
You said:
If they know which candidates can’t win, they can safely vote for any and all of those. Without this knowledge, voters’ safest strategy—the one that gives their favorite candidate the best chance to win—is to treat the Approval ballot like a Plurality ballot and only vote for one.
This is so very far from the truth!
1. The Best Strategy:
When voters have no information about which candidates are the most likely to get elected, Approval Voting is actually more optimal then when voters have that information. This is because when voters have 0 information about each candidates chances of winning, the most strategic way to vote becomes simply voting for every candidate you like more then your average opinion of all the candidates. And in a contested election with many candidates, voters are bound to like many candidates more then their average opinion of all the candidates. If you are curious about why this happens, check out this page that explains the most strategic way to vote in score and approval voting: http://www.electology.org/score-voting-threshold-strategy. When voters have 0 information about the chance each candidate has of winning, they have to assume that each candidate has the same chance of winning, and when you use the strategic voting formula described in the link (while assuming everyone has an equal chance of winning) the most strategic way to vote becomes just voting for the candidates you like more then average.
2. The Safest Strategy:
When it comes to scenarios where voters have 0 information about each candidates chances of winning, you didn’t say that in bullet voting was the best strategy. No, you made an even more ridiculous claim. You said that it was the safest strategy. Correct me if I’m wrong but doesn’t the phrase “playing it safe” generally refer to reducing risk? If you had the ability to either win $2,000,000 or take a 50% 50% chance of either winning $5,000,000 or $0, which strategy would you call the safe strategy? Taking a chance between winning $5,000,000 or $0, or choosing the $2,000,000 reward instead? If you were only concerned with what strategy would give you the greatest amount of money on average, taking the risk may be the “best” strategy, but it certainly isn’t the greatest. Now suppose you were voting in an approval voting election and Bernie Sanders, Hillary Clinton, and Donald Trump were running. You happen to have 0 information about each candidates chances (meaning you never looked at the polls) but if you had to honestly rate the candidates, you would rate Bernie as 5 stars, Hillary as 2 stars, and Trump as 0 stars. Only voting for B would increase your chances of getting outcomes that you would rate as 0 stars and 5 stars, while voting for both B and H would increase your chances of getting an outcome that you would rate as 2 stars. Assuming that “playing it safe” means reducing the risk of a disastrous outcome, the safest strategy would actually be to vote for both Bernie and Hillary. So the safest strategy actually involves approving MORE candidates then the best strategy says you should approve of.
3. The Riskiest Strategy:
This is the strategy bullet voting actually is, and in plurality voting this is the strategy that is preferred by all of those third party voters that vote for third parties in swing states (like Florida in 2000). In reality, the ideal voting strategy lies somewhere in between the “best” voting strategy and and the safest voting strategy, and it depends on how accepting voters are of the risk of getting a really bad outcome.
Also, in your tab about approval voting, you have linked to a lot of places where a large portion of the electorate bullet voted. Those elections you linked to (with the exception of the Oregon presidential poll) were not political elections, so not many voters were devoted to the election results, and as a result, they voted the way they were used to voting, which was voting for 1. In actual contested elections, where voters understand approval voting and they are using it to actually elect or nominate politicians, it is a different story. According to an article released by approval voting SKEPTICS, less then 25% of voters bullet voted in approval voting primary elections in Philly: http://www.philly.com/philly/blogs/heardinthehall/New-study-shows-bullet-voting-common-in-Phila.html. What is even more interesting is that this article was intended to be a critical of approval voting, so the headline actually reads “New study shows bullet voting common in Phila”, despite the fact that the article says that the exact opposite was true. Infact, @progressnerd, a pro-IRV anti-approval twitter user actually linked me to this article in a twitter debate. I’m guessing he only read the headline.
Ciaran Dougherty
This is a remarkably biased “analysis.”
What sort of person uses bold in their analysis of only one method, and then exclusively in the “Con” section of that method?
Are you afraid that if you don’t artificially accentuate the cons of a method, that people will recognize that it’s not as bad as you claim?
Robert Bristow-Johnson
That you didn’t include any Condorcet-consistent method among all of the others is a shame.