My previous article took a close look at how the chicken dilemma, Approval voting’s worst case scenario can be dealt with in Approval or Score. As I showed in that article, while the chicken dilemma is the nearest thing to a problem that Approval has, it really isn’t much of a problem after all.  It’s fitting to start this new article with that reference to the previous article because this article’s title refers to the properties of Approval voting, the simplest voting system.

Approval is, in its worst case, certainly relevant to its overall properties situation.  So that previous article can be regarded as the first topic in this article about Approval’s properties.  Because properties are most relevant and useful in comparisons, this “Properties” article series will compare a set of voting systems that are popular or proposed, in terms of a set of properties. I use the word “properties” in a broad sense, to include everything from precisely-worded criteria, to general descriptions of a method’s strategy, to a method’s social optimizations, to its easy implementation and count-fraud vulnerability, and even its enactability.

In voting system discussions, the word “method” means voting system.  I’ll use the word “method.”  This article series starts with Approval: the simplest voting system. The following topics will be covered in this “Properties” article series:

Properties of Simplest Voting System

While topics 1 to 3 will be included in this article, I will begin with topic 4 with the properties of Approval and Score.  Subsequent articles will continue topic 4, discussing the properties of other methods, before topics 5 and 6.

1. Kinds of Properties – Main Categories of Properties and Criteria

Methods will be compared by the following kinds of properties, in the following order:

a) Important Strategy Criteria:

Yes/No, Pass/Fail tests for voting systems, in regards to strategy.

b) General Strategy Description:

What would it be like to use the method? How would you vote optimally, to get your best result possible?

c) Social Optimizations:

Are there ways in which the method as obviously right, fair or maximally beneficial for the members of society?  If so, then how?

d) Ease of Implementation, and Count-Fraud Vulnerability:

e) Enactabililty:

f) Embarrassment Criteria:

Criteria relating to inconsistency, and the resulting criticism-vulnerability in enactment campaigns.

2. List of Some Pass/Fail Criteria That Will Be Used (Without Definitions)

• Favorite-Betrayal Criterion (FBC)
• Later-No-Harm
• Later-No-Help
• Chicken Dilemma Criterion
• Condorcet Criterion
• 0-Info Later-No-Help.
• Strong 0-Info Later-No-Help
• Participation
• Mono-Add-Top
• Monotonicity
• Independence-from-Irrelevant-Alternatives
• Plurality
• Criterion
• Mono-Add-Plum
• Smith Criterion
• Mutual Majority Criterion.
• 0-Info Sincerity Criterion.

3. Cast of Characters: List of Methods Being Compared (Without Definitions):

• Approval
• Score
• Traditional unimproved Condorcet (TUC)
• Improved-Condorcet-Top (ICT)
• Symmetrical ICT
• Majority-Judgment.
• Approval-Optional-Conditional (AOC)
• Majority-Choice-Approval (MCA)
• Instant Runoff (IRV)
• MinMax-Pairwise-Opposition (MMPO)
• Majority-Defeat-Disqualification-Top-Ratings (MDDTR)

I should clarify that I don’t propose all of those methods for official public elections—only the first two: Approval and Score.  But, as I said, properties are most relevant and useful for comparison.

4. Methods, with Definitions, Properties, Criterion-Compliances and Criterion-Failures:

a) Approval and Score: 

First, the definition of a u/a election, and u/a strategy.  In this series of articles, the strategy compared will mostly be u/a Strategy; “u/a” stands for “unacceptable/acceptable”.  A u/a election is an election in which there are unacceptable candidates who could win. Unacceptable candidates are so undesirable (to some particular voters) that electing an acceptable instead of an unacceptable is the only important thing—as opposed to the matter of which acceptable or which unacceptable is elected.

In other words, the acceptables and the unacceptables are two sets in which the merit differences within the sets are negligible in comparison to the merit difference between the two sets.  u/a strategy is strategy for u/a elections.  I suggest that all of our official public elections are u/elections, making u/a strategy the most important kind.

Additionally, u/a strategy is emphasized in this series of articles, because u/a strategy is much simpler than other strategy. For many rank methods, u/a strategy is the only strategy known—to the extent that it can even be described for those methods.

Zero-information (0-info) u/a strategy will be sometimes mentioned too. That’s u/a strategy for a 0-info election. That’s an election about which all that is known is the candidates and the voting system. Nothing is known about the voters, their preferences, or how they are likely to vote.

Everyone, or nearly everyone, believes that there is information about candidates’ win-abilities, and that means that it therefore is not a 0-info election.  That’s probably true in all national and state official public elections. But, even if it weren’t, the fact that people believe it would make 0-info strategy not be the relevant kind.

In the U.S., nearly everyone believes that the TV’s information about candidates’ win-ability is correct. That alone is enough to suggest that 0-info strategy is not relevant for our elections. There are a few valid indications regarding voter-preference information, and so the elections probably really are not 0-info.  I’ve discussed this matter in more detail in previous articles.  Approval’s u/a strategy is to approve all of the acceptables, and none of the unacceptables.

That u/a strategy is simpler and easier than that of any other method: It’s a consequence of Approval’s compliance with FBC and LNHe. Approval’s u/a strategy is no different in a 0-info election.  Score’s u/a strategy is the same as that of Approval: Give top rating to the acceptables. Give bottom rating to the unacceptables. Score and Approval differ only in how they implement the strategic fractional ratings, for dealing with the chicken dilemma. But that topic was covered in the previous article, and needn’t be discussed here.

Social Optimizations of Approval and Score:

Obviously, Approval elects the candidate who has received approval from the most people. In a meaningful sense, Approval elects the most approved candidate, when “approve” is interpreted in the procedural sense—the most accepted candidate.

I’ve suggested that one should approve the candidates one likes and trusts. Obviously, then, Approval would elect the most liked and trusted candidate.

In general (not just u/a), Approval’s strategies amount to voting for the candidates who are better-than-expectation. Better than what the voter perceives as his statistical expectation for the election. When voters vote in that way, Approval elects the candidate who, for the most voters, is better than what they expected of the election. In other words, Approval maximizes the number of pleasantly-surprised people.

Those are a lot of valuable social optimizations for Approval.  Obviously, since Score (when optimally voted, at the extremes) an amount to the same thing as Approval, then Score has the same social optimizations and criterion-compliances that Approval has.

Approval’s ease of implementation and count-fraud vulnerability:

No other voting system even comes close to Approval’s ease of implementation. Therefore, no other voting system even comes close to Approval’s freedom from count-fraud vulnerability.

The more computation-intensive the count, the more it needs to be computerized, creating incomparably, qualitatively, more count-fraud vulnerability. And, even in hand-counts, the less work there is for the counters, the less count-fraud opportunity there is.  No other method can match Approval’s merit in that regard.

Score comes in second, in that regard. A Score hand-count doesn’t require any more tally-marks per ballot than Approval does. But 0-10 Score requires that 10 times as many tallies be kept. By increasing the work for that counters in that way, there could be some increase in count-fraud opportunity.  So, in the ease of count, and count-fraud, category, Approval is the clear winner by far.

An enactment of Approval would amount to nothing other than the repeal of Plurality’s forced falsification rule that I discussed in my first article published on Democracy Chronicles. That’s the rule that requires voters to give bottom rating (no vote) to all but one of the candidates. For more detail on that subject, see my article “Some Problems With Plurality.”  Therefore, Approval is the natural, obvious, minimal improvement on Plurality. Score is, of course, the familiar point system.

People are familiar with being asked to rate things from 1 to 10. Therefore, 0-10 Score would be entirely familiar to people, if it were proposed.  So both Approval and Score have very good enactability. No other voting system even comes close to them in that regard.

Embarrassment Criteria for Approval and Score:

Approval and Score, because of their simplicity and naturalness, meet all of the embarrassment criteria, so far as I’m aware. I’ll name a few of the ones that most distinguish between Approval, Score, and other methods:

Let’s compare Approval and Score to two other popular proposals now. Traditional Unimproved Condorcet (TUC) and Majority Judgment (MJ). (To be defined later, when we get to them in this topic #4).

As I said, Approval and Score meet all of the above-defined criteria: FBC, LNHe, Participation, Consistency, and IIAC.  TUC advocates will say that TUC meets the Condorcet Criterion (CC), Smith, and Mutual Majority and that Approval and Score don’t. This is true, however TUC’s failure of FBC and CD make meaningless its compliance with the Condorcet Criterion.  I’m getting ahead of the intended order of discussion. The method TUC and the criteria CC, Smith, Mutual Majority and CD will be defined later on in this article series.

As for 0-Info LNHe and Strong 0-Info LNHe, they’re complied with by every method that complies with LNHe. That includes Approval.  Approval meets Mono-Add-Top, which is a stronger version of Participation (and therefore is failed by TUC). The other criteria listed above don’t distinguish between Approval, Score, and TUC.  Majority Judgment (defined later, when this article series gets to it) fails Participation and Consistency. Here is a list of some of Approval’s criterion compliances and other desirable properties (the last two of which will be defined later in this article series):

• FBC
• LNHe
• 0-Info LNHe
• Strong 0-Info LNHe
• Participation,
• Mono-Add-Top
• Monotonicity
• Consistency
• IIAC
• Plurality Criterion
• Mono-Add-Plump

The simplest and easiest u/a strategy—several very desirable social optimizations (described above), easiest implementation, best enactability—passes all embarrassment criteria that I know of, due to simplicity and straightforwardness.  Approval is pretty damn impressive.