A paean to Approval voting – "Count all the votes"

By Warren D. Smith. Also incorporates some ideas and/or verbatim sentences from Steven J. Brams, Catherine Kimport, Mike Ossipoff, Andrew Jennings, and Abd ul-Rahman Lomax. However, Brams may not entirely agree with the present page. The essay by Brams from which many sentences have been lifted verbatim (or nearly), is here. We in turn do not entirely agree with that essay. Brams is the coauthor of the book Approval Voting. See also Sanders' essay.

The simplest way to introduce approval voting to those familiar with the current plurality system is with the slogan "count all the votes." That is, if somebody in the current system votes for Nader and Bush, then her vote is discarded as an illegal "overvote" and not counted. With approval voting, overvotes are legal and all votes are counted.

So it is just like the current system, only SIMPLER, and it works with all today's voting equipment with no modification and no reprogramming needed.

If you want some other kind of voting reform, you definitely should want approval voting, because it gets a long way in the direction you want, doesn't hurt you, and it is so incredibly simple and easy.

Formal definition:

  1. In Approval Voting (AV), each voter approves or disapproves of every candidate.
  2. The most-approved candidate wins.

Set voting

Approval voting has also been called "set voting" because voters vote for whichever set of candidates they prefer versus the candidates they don't vote for. In this graphic, we can see there are 8 possible kinds of voters: those who approve Nader only, those who approve Gore only, those approving both Nader & Gore (but not Bush), and so on. With approval voting, all 8 kinds are capable of saying in their vote, which kind they are, and the election result takes account of how many voters of each kind are present. With old-fashioned plain-plurality voting, though, that information simply is not available and cannot be used to to help make the election decision.

[Venn diagram with Nader, Gore, Bush in svg graphics format; you need to click this to see the picture using FireFox]

Variants to try to make approval voting even better

1. We could add intermediate options between full approval and full disapproval. When you do that, you get range voting. The advantages of range voting versus AV are summarized here.

2. We could also, optionally, permit voters to express no opinion about a candidate. That is useful because a lot of voters are ignorant about a lot of candidates and in some cases would prefer to leave the decision about rating that candidate, to other, hopefully more-informed, voters. (In fact, there is evidence that the vast majority of US voters who are offered the chance to vote about judges, know essentially nothing about those judges.) The definition of range voting given on the main page in fact already incorporates the "no opinion" idea, and we could also add it to approval voting.

Indeed, AV is really just the special case of range voting (with or without "no opinion" scores permitted) in which the only allowed scores are 0 (disapprove) and 1 (approve).

3. Forest Simmons invented DYN (for Delegable Yes/No) voting. It is similar to Approval but more complicated to count. Almost as simple for the voter, however!) A related followup idea invented by Jameson Quinn was SODA voting. DYN's virtue is immunity to "media manipulation" of poll data; the question then is whether the extra complexity of DYN is worth the benefits arising from this immunity.

Approval overcomes a major flaw in plurality voting (while making it simpler)

In any race with more than two candidates, plurality may elect the candidate least acceptable to the majority of voters. This frequently happens in a three-way contest, when the majority splits its votes between two centrist candidates, allowing a more extreme candidate to win. Plurality also forces minor-party candidates into the role of spoilers, as we saw in USA 2000, which can be decisive in a close contest between the major-party candidates. That in turn causes many voters to refuse to vote for their true favorite (!) unless it coincides with one of the two candidates that seem most likely to win – out of a (justified) fear of creating a "spoiler" or "wasted vote" scenario. And that in turn causes third parties to die out over time, causing 2-party domination, which severely reduces voter choice and thus makes democracy work badly.

With approval voting, spoilers do not happen; approving your true favorite is never strategically unwise; approving candidates unlikely to win is no longer "throwing away your vote."

Approval gives voters much more expressivity

Instead of "name one candidate, then shut up," it is "express a yes/no opinion on all the candidates." You the voter, get to say much more. Why should less of your views be incorporated, when more of them can be?

Approval gives voters more power

Say we want to define a notion of "voting power." What quantity would make sense as that voting power? One way is to measure the number of pairs of candidates of unequal merit that your vote can discriminate between. The more such pairs there are, the more chance your vote will be able to have an effect by breaking a tie between that pair. (If there is no tie, then your vote has no effect.)

With plurality voting, your vote-for-one discriminates that one candidate versus the other N-1, for a "voting power" of N-1. With approval voting, you can approve of half the N candidates, discriminating N/2 of them from the other N/2, for a voting power of N²/4. The ratio between these two voting powers is N²/(4N-4). We exhibit that formula in this table:

N=#candidatesVoting Power Ratio
21
31.125
41.333
51.563
61.800
72.042
82.286
92.531
102.778
205.363
5012.76
10025.25

Approval voting is excellent for use in votes in meetings

You can just hold up your hand (or better, a red card) to approve of an option.

Actually, range voting on a 3-point scale {0,1,2} could also be thus-conducted using two red cards per voter, and a voter could hold them up using either zero, one, or two hands.

This is much simpler than plurality voting, where if you tried hand-raising voting, you'd pretty much have to trust people not to cheat by overvoting, since careful verification takes ages. Approval is the fastest, simplest, and most reliable method for voting in meetings.

What might an approval ballot look like?

An AV ballot could look almost exactly like a Plurality ballot. Here's a quick side-by-side comparison:

Plurality Vote

What is your favorite color?

Red
Orange
Yellow
Green
Blue
Violet
Black
White

Approval Vote

Which colors do you like?

Red
Orange
Yellow
Green
Blue
Violet
Black
White

A ballot for the variant-approval system (also allowing "no opinion" votes) could be like this:

Approval Vote II  –  Which colors do you like?

ColorYesNo"no opinion"
REDΟΟ
ORANGEΟΟ
YELLOWΟΟ
GREENΟΟ
BLUEΟΟ
INDIGOΟΟ
VIOLETΟΟ
WHITEΟΟ

Approval voting history

Approval and Range voting were the foundation of government in renaissance Venice, and Ancient Sparta respectively, two of the longest lasting (perhaps the two longest lasting) democracies ever. Also approval voting was used for centuries to elect the catholic pope (at the time the most powerful elected person on the planet) and was used in 1000s of elections in the USSR, and was used to elect the first 4 USA presidencies and is currently used to elect the UN secretary-general. (Approximately. The rules were slightly different in most of these cases, e.g. the first 4 US presidential elections had the undesirable twist that the second-place finisher became the vice president.)

Approval voting was apparently first explicitly invented in the modern era by Guy Ottewell in 1968 (albeit Ottewell has now endorsed range voting). Several political scientists and mathematicians then invented it independently during the 1970s. All of them at the time were unaware of that vast previous history. Two of them, S.Brams and P.Fishburn, published a book on it in 1983.

AV has been used in internal elections by the political parties in some US states, such as Pennsylvania, where a presidential straw poll using AV was conducted by the Democratic State Committee in 1983. Bills to implement AV have been introduced in several state legislatures. In 1987, a bill to enact AV in certain statewide elections passed the Senate but not the House in North Dakota. In 1990, Oregon used AV in a statewide advisory referendum on school financing, which presented voters with five different options and allowed them to vote for as many as they wished.

In the late 1980s, AV was used in thousands of competitive elections in countries in Eastern Europe and the Soviet Union (experiment in democratization initiated by M.Gorbachev) where it was effectively "disapproval voting" because voters were permitted to cross off names on ballots but not to vote for candidates. This procedure is logically equivalent to AV: candidates not crossed off are, in effect, approved of. However psychologically there is almost surely a difference between approving and disapproving of candidates.

Beginning in 1987, several scientific and engineering societies adopted AV:

Smaller societies that use AV include the Society for Judgment and Decision Making, the Social Choice and Welfare Society, the International Joint Conference on Artificial Intelligence, the Pubic Choice Society, and the European Association for Logic, Language and Information.

In the early 2000s the Boston Tea Party became apparently the first US political party in modern times to employ approval voting.

Additionally, the Econometric Society has used AV (with certain emendations) to elect fellows since 1980; likewise, since 1981 the selection of members of the National Academy of Sciences at the final stage of balloting has been based on AV. Coupled with many colleges and universities that now use AV – from the departmental level to the school-wide level – at least several hundred thousand individuals have had direct experience with AV.

Click these links to learn about the French study of AV and the other French study of Range Voting conducted during two real French Presidential elections. "Approval ratings" are nowadays produced all the time by pollsters such as Gallup for various political candidates, which allows you to tell approximately what would happen in an election if it were run with approval voting.

Some further comments

What about the "one person, one vote" principle? Approval voting can instead be thought of as implementing the more-fair principle that "one person gets one vote on each candidate." Another way to think of it is: it still is one person one vote, it is just that a "vote" is now a different thing – but still preserving the central idea that a "vote" is an expression of your views, it is now just a better expression of them. (And with range voting, even better still.) This, e.g, affords voters an opportunity to express their intensities of preference by approving of, for example, all candidates except the one they despise.

Incidentally, there is nothing unconstitutional about approval voting. The US constitution intentionally did not specify any voting method, and its writers were well aware there were many possible voting methods, and in fact approval voting basically was used in the first few USA presidential elections and several other (often more peculiar) voting methods have been used throughout US history.

You can also regard approval as obeying the same one-person-one-vote principle as plurality voting as follows: only one of your votes gets used: the one indicating your approval (or disapproval) of whoever wins the election.

Although AV encourages sincere voting, it does not altogether eliminate strategic calculations. Because approval of a less-preferred candidate can hurt a more-preferred approved candidate, the voter is still faced with the decision of where to draw the line between acceptable and nonacceptable candidates. A rational voter will vote for a second choice if his or her first choice appears to be a long shot – as indicated, for example, by polls – but the voter's calculus and its effects on outcomes is not yet entirely understood either for AV or especially for more complicated voting procedures.

While AV is a strikingly simple election reform for finding consensus choices in single-winner elections, in elections with more than one winner AV is not recommended if the goal is to mirror a diversity of views, especially of minorities; for this purpose, other voting systems should be considered. However Fishburn and Smith both have shown with computer simulations that approval still works well in 2-winner situations where a "second round" election is used to decide between the two winners in round 1. On the other hand, minorities may derive indirect benefit from AV in single-winner elections, because mainstream candidates, in order to win, will be forced to reach out to minority voters for the approval they (the mainstream candidates) need to win. While promoting majoritarian candidates, therefore, AV still induces them to be responsive to minority views.


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