Recommendations for using the appropriate voting systems in small groups including voting in organizations, clubs, committees, meetings, and even families
(Style edits on 8-26-14)
For voting in organizations, clubs, committees, meeting and even families, election method choice is very important. The choice of voting systems (often referred to as “methods”) depends on how similar the alternatives are, how strongly their merit-differences are felt. That determines, for instance, whether you insist on automatic majority rule enforcement, as opposed to just maximizing the liked-ness of the outcome. The choice is also influenced by how amicable the organization or voting situation is. That determines how compromising the voting system should be.
But, whether the decision is by consensus or voting, discussion is often very desirable before the decision is made. But there are times when it might not be: Maybe when people express their wishes in the discussion, some of the participants will feel obligated to give others their way. In those types of situations, voting, by secret ballot, might be preferable.
So, in any group, big or small, there can be situations where voting is the best way to make a collective choice. So let me suggest voting systems for various conditions with two main distinctions. The first:
1. When maximizing overall satisfaction is the important thing, more important than automatic majority rule. …and/or maximum count-ease is desired:
Use Approval or Score.
In Approval, each voter can approve one or more alternatives–as many as s/he wants to approve. To avoid vulnerability to people strategically taking advantage of previous voting, the ballots shouldn’t be displayed until they’re all voted. A voter approves an alternative by writing its name, or by marking a box next to its name, on a ballot.
In Score each voter gives to each alternative a rating from 0 to N, where N can be any pre-specified number. For instance, in 0-10 Score, each voter rates each alternative from 0 to 10. In 0-100 Score, each voter rates each alternative from 0 to 100.
Of course Approval amounts to 0-1 Score. Approval has the simplest and easiest handcount, but Score adds flexibility, allowing built in fractional ratings , which are useful when Approval’s yes/no would be difficult to decide, or when one desires to strategically give somewhat less than full support to a potential rival.
2. When automatic majority rule is desired:
Automatic majority rule is achieved by compliance with the Mutual Majority Criterion. Here is that criterion’s definition:
But, compliance with MMC loses its meaning and value if members of a mutual majority are tempted to “defect” against each other, and/or are afraid to support each other’s alternatives because fear of being taken advantage of in that way. That situation is called the “chicken dilemma”. MMC compliance has value only with voting systems that don’t have the chicken dilemma.
That’s the chicken dilemma. For any method more complicated than Approval or Score, there’s no excuse to have the chicken dilemma. All of the voting systems recommended here, other than the simple Approval and Score, meet the Mutual Majority Criterion and don’t have the chicken dilemma. The choice among the voting systems that give automatic majority rule depends on certain conditions, listed below:
2a) When conditions are amicable:
Then, you want a method that elects the Condorcet winner (CW) compromise (defined below). To not do so would be uncompromising and a bit inimical.
Compliance with the Condorcet Criterion guarantees that all majorities will be satisfied, as opposed to only mutual majorities. That property is desirable for amicable organizations and amicable voting situations. Additionally, a voting system that dis-satisfies some majority, however constituted, is vulnerable to replacement, when a majority of the participants demand its replacement.
Here are a few suggested Condorcet-Criterion-complying voting systems for amicable conditions when automatic majority rule is desired (If you want show-of-hands voting (or its Internet equivalent), and/or if there are many alternatives, no counting software, and little time, then do Sequential Pairwise Voting):
SP has a number of important properties. Of course, like all of the voting systems recommended here, other than the simple Approval and Score, SP meets the Mutual Majority Criterion (MMC), and doesn’t have the chicken dilemma. Additionally, SP meets the Condorcet Criterion (defined above). It also meets the Smith Criterion, defined as the smallest set of alternatives that all are socially preferred to everything outside that set. If everyone votes sincerely, then the winner should come from the Smith set. Every method that meets the Smith Criterion also meets the Mutual Majority Criterion.
If you’re interested in an explanation of why SP doesn’t have the chicken dilemma, then here’s why:
If the B voters defect against A before it’s time to vote on B, then you (as an A-preferrer) will notice that, and you can penalize them by refusing to support B when it’s time to vote on B. If you’ve already helped B, before it’s time to vote on A, then the B voters will have no reason to defect against A, because B must have already been eliminated by losing its 2-way vote. …unless B’s 1st vote, after you’ve helped B, is between B and A, in which case it isn’t defection when the B voters sincerely vote B over A. In short, SP has no chicken dilemma.
Admittedly, if protection from defection is necessary, then SP requires you to protect yourself against that defection. Your protection consists of deterrence, where the would-be defector knows that you’ll retaliate if s/he defects. For that threat to be credible, it must be known that you’d retaliate even if it worsens your outcome. That need to protect yourself from defection, and that potential need to retaliate in a way that worsens your result, are a disadvantage of SP. But simplicity has its price. SP is simple and easily-counted, in comparison to the rank methods defined below.
Deluxe features, such as automatic defection-deterrence by the voting system, requires more elaborateness and count-labor. The deluxe methods described below are suitable if you have count software, or very few alternatives to choose among, or plenty of time for a time-consuming hand count. For the purpose of the rank methods defined below, X “beats” Y if more ballots rank X over Y than rank Y over X.
(Of course, as soon as an alternative tops a majority of the rankings, that alternative is assured a win, by the above-stated rule, and so it can be immediately declared the winner.)
I recommend a website that will conduct, for you, a fully-automated poll, using Benham (also called Condorcet-IRV). The website has complete instructions for setting up a poll. As is pointed out at the website, its automated polling service can be used for voting by organizations and families. For those purposes, the website provides private polls, in which only certain selected individuals (members of the organization or family) can vote. Of course the results of those polls aren’t publicly viewable.
That website also allows you to set up a public poll, in which anyone can participate, and whose results anyone can view. But our topic here is voting in organizations and families, and, for that purpose, you want a private poll. I highly recommend the Condorcet Internet Voting Service, linked to above. It is operated by a Cornell University professor. Actually, polls at that website are countable by any of a variety of rank-count rules. To achieve the desirable criteria stated in this article, the best count rule at that website is Condorcet-IRV.
The way it works, when you set up your poll, you don’t specify a voting system (but of course you should tell the voters what count rule is official for that vote). When looking at the poll’s results, you choose count method by which you want the result to be displayed. Of course, because you’ve told your voters that it’s a Condorcet-IRV poll, then the relevant count-result to look at is the Condorcet-IRV count result.
Therefore, when you’re at the “results” page, check the box in the right margin, near the top. It will have a list of several rank-count rules. One of them is Condorcet-IRV. Each has a box in front of it that you can click on, to select that count rule.
The default count rule is “Schulze”. You want Condorcet-IRV, so click on Condorcet-IRV. Then the results displayed will be the Condorcet-IRV count results. In this article, that voting system is also referred to as “Benham”. So, the Condorcet Internet Voting Service makes it easy for an organization or family to very easily use one of the most deluxe voting systems.
Now, if you want to count the ballots yourself, then actually, SP is as good as Benham, and a lot easier to count. But Benham is deluxe, in the sense that it isn’t necessary for voters to observe and penalize defection, because Benham automatically penalizes defection. In Benham, it’s simply a matter of sincere ranking. A mutual majority have no reason to do other than rank sincerely. In fact no one has need to do other than rank sincerely. That’s also true of Woodall and Schwartz. Woodall is defined immediately below:
Though both Benham and Woodall always choose from the Smith set, Woodall is more particular about which Smith set member it chooses. For that reason, Woodall achieves slightly better social utility than does Benham.
Those 2 sets are identical if there are no pairwise ties. But when there aren’t many voters, there can be pairwise ties. Then, the Schwartz set is a bit more exclusive than the Smith set. You can get into the Smith set by tying one of its members and beating all the non-Smith-set alternatives. That won’t get you into the Schwartz set. So the Schwartz set is more deluxe, for small-electorate voting.
Let me define the Schwartz set. It has 2 equivalent definitions. Both definitions define the same set:
That is the end of Schwartz set definitions. I recommend Schwarz Woodall as the deluxe voting system for amicable conditions. Sequential Pairwise is really just as good, though not as deluxe. Sequential Pairwise is, of course, much easier to count. Benham and Woodall are discussed in a journal article by James Green-Armytage.
2b) When conditions are not amicable:
The a) methods (for amicable conditions) are ok under inimical conditions too. But the methods described below might be preferred.
Plain IRV, instead of Schwartz Woodall:
Plain IRV (defined above), like all of the methods recommended here, other than Approval and Score, meets the Mutual Majority Criterion and doesn’t have the chicken dilemma. IRV doesn’t always elect the CW compromise (defined above), making IRV less compromising, and maybe a bit inimical. But IRV is simpler to count than Schwartz Woodall, or Benham.
And, in inimical conditions, the CW compromise might even not be desired. It might be felt that only mutual majorities should be honored, and that there’s no need to compromise with voters who aren’t in a mutual majority, and that it isn’t necessary to let voters outside the mutual majority have a say in which mutual-majority-preferred alternative wins.
But be aware that a method that doesn’t meet the Condorcet Criterion could (as stated above) be vulnerable to replacement, if it results in a dis-satisfied majority who insist on replacing it with a method that meets the Condorcet Criterion (and therefore doesn’t dis-satisfy any majority, however constituted).
What if the organization or voting situation is inimical, and show-of-hands voting is desired, or there are many alternatives, no count-softare, and little time? Then I suggest:
Exhaustive Balloting, also called “Elimination Voting”:
Do a Vote-For-1 vote among all the alternatives. Eliminate the alternative that gets fewest votes. Repeat till only one alternative remains. (Actually, you might as well stop as soon as an alternative gets votes from a majority, because that alternative will win anyway.) Of course this could be done by show-of-hands, or its Internet equivalent. It’s even easier to count than IRV.
An advantage of Exhaustive Balloting, over Sequential Pairwise, is that Exhaustive Balloting automatically deters defection, and the voter doesn’t have to protect himself via a deterrent threat to retaliate. If the organization or voting situation is inimical, then there’s be greater chance of a need for that concern. That’s why Exhaustive balloting is likely to be better than Sequential Pairwise (SP) for inimical organizations or voting situations.
And, of course, an inimical organization or voting situation doesn’t need the compromising-ness of methods that meet the Condorcet Criterion. That’s why, when automatic majority rule is desired, and a simple and easy show-of-hands count is desired, I recommend SP for amicable organizations and voting situations, and Exhaustive Balloting (Elimination Voting) for inimical organizations and voting situations.
Those are my recommendations. All of them except for Approval and Score meet the Mutual Majority Criterion, and have no chicken dilemma.
Also see our entire section called Voting Methods Central.