Voting Systems
Approval Voting in Municipal and County Elections
Bart Ingles 9/12/1999 Latest Revision: 3/30/2001
Contents
Introduction
Single-winner elections involving three or more candidates can fail to elect a popular winner, even when using runoff elections. Approval Voting is a simple election method which avoids this problem, favoring consensus candidates where possible. The method is well known in academic circles, and is widely recognized as preferable to single-vote plurality elections (referred to here as Plurality), plurality with a runoff (here termed Runoff), and to equivalent instant runoff systems.
Approval Voting is no more expensive than simple Plurality elections and can be implemented on any existing voting equipment, but its real advantage is in the elegant way it uses the strengths of voters' preferences, and not just preference orders. This avoids some absurd results possible under Runoff and instant runoff, as shown in the example to follow.
The rules are: each voter is free to vote for as many candidates as she chooses, but is limited to one vote per candidate. Each vote counts fully, and the candidate with the most votes wins. This is similar to traditional Plurality voting, but without the vote-for-only-one rule.
Approval works by harnessing the voter's tendency to use strategy to achieve the best possible result. The voter is always free to vote for a favorite without penalty, and may vote for additional candidates if she thinks this will improve the chances of a desirable outcome. Voting for these additional candidates requires compromise, which can be viewed as a cost of strategy. This market-like weighing of strategic value against strategic cost insures that votes are only cast when they represent a meaningful level of support. This is not always true with runoff-based systems, and is one reason those systems sometimes perform worse than even simple Plurality.
In practice, Approval Voting strategy is simple, and generally consists of voting for all favorites down to and including the most preferred of two front-runners. In two-candidate races, this means that Approval is equivalent to the other voting systems mentioned here, since the most preferred front runner is the only favorite.
Approval Voting has been studied for 30 years, and has been in actual use for the past 12 years. It has been adopted by a number of professional societies since 1987, with a combined membership now in excess of 600,000. All groups who have adopted it continue to use it, including the Institute of Electrical and Electronics Engineers (IEEE), the Mathematical Association of America, and the American Statistical Association.(1) The U.N. Security Council uses Approval Voting to elect its Secretary-General (subject to a veto, and to ratification by the General Assembly).
Example Showing Limitations of Plurality and Runoff Methods
The following example produces absurd results under both Plurality and Runoff, with better results using Approval. While it would be unusual for a single election to manifest all of the problems described here, it would not be rare for an election to show at least one of these problems. In the example there are three voting factions, with groups of voters using classroom-style letter grades to show their true opinions of the candidates. The three candidates are Nora, Oscar, and Paul. Note that Oscar is a consensus candidate, with a rating of "B+" or better from all factions:
Percent of
Electorate Candidate (w/grade) in order of preference
Faction 1: 45% Nora (A), Oscar (B+), Paul (F)
Faction 2: 27% Oscar (A), Paul (D-), Nora (F)
Faction 3: 28% Paul (A), Oscar (B+), Nora (F)
Using Plurality voting, Nora wins with only 45% of the vote, even though 55% of the voters give this candidate an "F" grade.
Using Runoff (traditional or instant), Oscar is eliminated first, and then Paul defeats Nora in the runoff phase, 55% to 45%. There are four things wrong with this outcome:
(1) Paul wins even though 72% of the voters grade this candidate "D-" or lower.
(2) Consensus candidate Oscar is eliminated first, even though 100% of the voters rate Oscar "B+" or higher.
(3) Oscar would have easily defeated both Nora and Paul in separate head-to-head races.
(4) To keep Paul from winning, it is in the interest of the 45% who support Nora to instead throw their first choice support to consensus candidate Oscar. Thus Nora's supporters face a lesser-of-two-evils dilemma, even with a runoff in place!
Using Approval Voting, Oscar's supporters have little incentive to vote for more than one candidate, since they disapprove of the other two candidates almost equally. With no support from the moderates, Paul has no chance of winning, and so Paul's supporters compromise by voting for both Paul and Oscar in order to keep Nora from winning. Oscar wins with 27 + 28 = 55% approval, vs. Nora with 45% and Paul with 28%.
Extending the letter grade analogy, Approval winner Oscar has a Grade Point Average among all voters of 3.51, vs. 1.80 for the Plurality winner. The Runoff winner's GPA is actually lowest of all, at 1.30.(2)
Fortunately such scenarios are not the rule, and when they do occur voters are often able to compensate through the use of strategy. In the example above, under Runoff rules the Nora voters would be better off switching their first-choice votes to lesser-evil candidate Oscar, and under Plurality rules Paul's supporters should defect and support Oscar. In either case, the strategy is more difficult (and more painful for the voters) than it would have been using Approval, and it only works if the voters have accurate polling data and are willing to vote against their first-choice candidates.
Approval also adapts to situations where Runoff and Plurality are correct, and usually agrees with those methods. But the more extreme and polar the scenario (and thus the more critical the outcome), the more likely Plurality and Runoff are to break down, while Approval only becomes more sure-footed. In the trivial case where each voter rates every candidate as either "A" or "F", the only reasonable winner is the candidate with the most "A" votes. This requires that the voter be allowed to vote for all "A" choices equally, to avoid a situation where voters mistakenly hand the election to an opponent because they don't know which favorite to support. A method that permits only one first choice at a time, such as Plurality or Runoff, will produce essentially random results unless the voter knows in advance which of his "A" choices is the most viable.
Average Case and Computer Simulations
The above example deals with a near worst-case scenario in a three-candidate election. Computer simulations show that Approval also works well when results are averaged over a large number of trials, and when there are larger numbers of candidates. In contrast, the average performance of Plurality, Runoff, and even instant runoff can decline rapidly as the number of candidates grows. The simulations also show a tendency for these other methods to allow centrist candidates to be squeezed out by more extreme candidates. Approval Voting appears to be immune to this "squeeze" effect.(3)
Political and Practical Feasibility
Approval Voting is free of some practical and political considerations that have kept other voting systems from widespread use in the U.S. The choice voting method used in New York City school board elections is unpopular there because of its complexity. In 1996, San Francisco voters rejected a proposal for choice voting, apparently for similar reasons.
Systems such as choice voting and the related instant runoff voting require equipment specifically designed for the task. The cost of installing and operating this equipment is considerable, and would negate much of the savings expected from the elimination of separate runoff elections. In Santa Clara County, an independent audit studying instant runoff estimated an initial cost of up to $5.9 million for new voting equipment, and annual operating costs of $350,000 to $480,000 higher than the current system.(4) Subsequent estimates involving touch-screen equipment place the intial cost at closer to $20 million.
Again, Approval Voting is simple and requires no equipment upgrade. Existing voting equipment already allows voters to vote for multiple candidates in at-large multiple-seat elections. For Approval Voting, this same feature would be used to allow multiple choices in single-seat elections.
Costs and Savings
Assuming a ballot measure is needed to incorporate Approval Voting into the city or county charter, the approximate per-district cost of the election would be recovered with the first avoided runoff election in each district. There would be cost savings to the city or county with every subsequent avoided runoff election.
Additional Benefits
(1) Avoids the expense of runoff elections for candidates as well as public
The lack of necessity for runoff elections also means cost savings for candidates. This could be especially important for smaller, less publicized elections, where the likelihood of a runoff election may be harder to predict because of a lack of polling data, and where a candidate may be less able to afford an unexpected runoff campaign.
(2) Allows minority viewpoints to be heard; increases meaningful participation
Approval Voting also allows minority viewpoints to be heard. While the primary purpose of voting is to select public officials, there is from the voter's perspective a second reason for voting. The motive that keeps voters returning to the polls, often in the face of certain defeat, is the desire to make one's viewpoint known.
Vote-for-one election methods unfairly force minority and third-party voters to choose between expressing this viewpoint, and trying to influence the outcome in a meaningful way. It should be no surprise that these voters become so frustrated with the electoral process that many give up on it altogether. Allowing them to do both would help restore faith in the electoral process and improve satisfaction with the representatives that the process elects.
(3) Indirect Benefits
Approval Voting is uniquely suited for immediate use in state and federal elections, while other voting systems would require every single locality to install new voting equipment before those systems could be used in statewide or federal races. If local demonstrations of Approval Voting lead to adoption at state and federal level, this would also benefit local voters.
Options for Implementation
(1) Implement city- or county-wide, or pilot in selected races first?
Since no change of voting equipment is needed, a city or county would have maximum flexibility in deciding which elections could best be used as pilot programs for approval voting, before adopting the system in all single-seat races.
End notes
(1) Brams, Steven J. and Fishburn, Peter C., "Approval Voting in Scientific and Engineering Societies", Group Decision and Negotiation 1:41-55 (1992)
(2) GPA calculations used grade values of 4.0, 3.33, 0.67, and 0.0 for A, B+, D-, and F, respectively.
(3) Merrill, Samuel III, Making Multicandidate Elections More Democratic, Princeton University Press, 1988
(4) Harvey M. Rose Accountancy Corp., "Review of Proposed Instant Run-off System for County Elections", Memorandum to the Subcommittee on Governance and Organization of the Charter Review Committee (Santa Clara County), May 18 1998