[EM] Improved organizational voting recommendations article

Tue Apr 30 08:07:09 PDT 2013

*Recommendations for Voting in Organizations, Clubs, Committees, Meetings,
and Families*

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 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..

Before I start, of course small groups, such as families don’t always use
voting in their decision-making. Often decisions in such small groups are
made by consensus, after discussion. That can be a good system, but not
always. Sometimes consensus decision making just means that the most
assertive get their way, and the most co-operative get taken advantage of.
That’s why often voting is better than “consensus”.

But, whether the decision is by consensus or voting, discussion is often
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
situations, voting, by secret ballot, might be preferable.

So, in any group, there can be situations where voting is the best way to
make a collective choice.

So let me suggest voting systems for various conditions:

*1. Maximizing overall satisfaction is the important thing, more
important than automatic majority rule. ...&/or maximum count-ease
is desired:*

Use Approval or Score.

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.

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. Automatic majority rule is desired*

Automatic majority rule is achieved by compliance with the Mutual Majority
Criterion. Here is that criterion’s definition:

Mutual Majority Criterion:

A mutual majority (MM) is a set of voters, comprising a majority of

the voters, who all prefer a certain same set of alternatives to all

of the other alternatives. That set of alternatives is their

MM-preferred set.

If a MM vote sincerely, then the winner should come from their MM-preferred
set.

[end of Mutual Majority Criterion definition]

Definition of sincere voting:

A voter votes sincerely if s/he doesn’t vote an unfelt preference, or

fail to vote a felt preference that the voting system in use would

have allowed hir to vote in addition to the preferences that s/he

actually did vote.

To vote a felt preference is to vote X over Y when preferring  X to Y.

To vote an unfelt preference is to vote X over Y when not preferring X to Y.

[end of sincerity definition]

SP meets the Mutual Majority Criterion (MMC).

But, compliance with MMC loses its meaning and value if members of a mutual
majority are tempted to “defect” against eachother, &/or are afraid to
support eachother’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.

The chicken dilemma:

Say your faction prefer A, and another faction prefer B. Your 2

factions, combined are a majority, and both detest C, strongly

preferring A and B to C.

But if you support B, the B voters can take advantage of your

co-operativeness, by withholding support for A, and thereby winning at

your expense, even if A has more 1st choice support than B. They can

do so because you helped B. You don’t know if they’re going to

“defect” in that way, and that makes you hesitate to help B. But if

neither A not B voters help eachother’s alternative, the detested C

will win.

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:

.

*1a) 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. .
I’ll define the CW:

X is socially preferred to Y if more voters prefer X to Y than prefer Y to
X.

The CW is an alternative that is socially preferred to each one of the
other alternatives.

The Condorcet Criterion says:

If there's a CW, and if everyone votes sincerely, then that CW should win.

[end of Condorcet Criterion definition]

Definition of sincere voting:

A voter votes sincerely if s/he doesn’t vote an unfelt preference, or
fail to vote a felt preference that the voting system in use would
have allowed hir to vote in addition to the preferences that s/he
actually did vote.

To vote a felt preference is to vote X over Y when preferring X to Y.

To vote an unfelt preference is to vote X over Y when not preferring X to Y.

[end of sincerity definition]

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), &/or if
there are many alternatives, no counting software, and little time,
then do Sequential Pairwise Voting:

 Sequential Pairwise Voting (SP):

Arrange the alternatives in a vertical list, in reverse order of their
order of proposal. …or hold a Vote-For-1 balloting, and order the
alternatives in reverse order of their vote-count scores.

Vote between the top 2 alternatives in the list. The winner then goes
against the next alternative in the list, in another 2-way vote. …etc.
Repeatedly, do a 2-way vote between the current winner and the next
alternative in the list. The winner is the last remaining unbeaten
alternative. (That’s the winner of the vote that includes the alternative at
the bottom of this list).

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 meets the Smith Criterion, defined immediately below:

Smith Criterion:

The Smith set is 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.

[end of Smith Criterion definition]

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
handcount:

For the purpose of the rank methods defined below, X “beats” Y if more
ballots rank X over Y than rank Y over X.

Benham’s method (also called “Benham” or “Condorcet-IRV”):

Do IRV until there is an un-eliminated alternative that beats
each of the other un-eliminated alternatives. Elect hir.

[end of Benham definition]

Definition of IRV (Instant Runoff):

Repeatedly, cross off or delete from the rankings the alternative that
tops the fewest rankings.

Of course (in plain IRV) the winner is the candidate who remains
un-eliminated, when all but one have been eliminated.

[end of IRV definition]

 (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.)

Here is a website that will conduct, for you, a fully-automated poll, using
Benham (also called Condorcet-IRV):

http://www.cs.cornell.edu/andru/civs.html

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, defined immediately below:

Woodall:

Do IRV till only one member of the initial Smith set remains
un-eliminated. Elect hir.

[end of Woodall definition]

For the purpose of this definition, the Smith set is defined in terms
of actual votes:

X beats Y if more ballots rank X over Y than rank Y over X.

The Smith set is the smallest set of alternatives such that all the
set’s alternatives beat everything outside the set.

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.

Schwartz Woodall:

Schwartz Woodall is like Woodall, except that it uses the Schwartz set
(defined below, after Schwartz Woodall) instead of the Smith set.

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.

Schwartz Woodall:

Do IRV till only one member of the initial Schwarz set remains
un-eliminated. Elect hir.

[end of Schwartz Woodall definition]

Let me define the Schwartz set. It has 2 equivalent definitions. Both
definitions define the same set:

Cycle definition of the Schwartz set:

The Schwartz set is the set of alternatives that don’t have a pairwise
defeat that isn’t in a cycle.

A pairwise defeat is what Y has, if X beats Y.

A cycle is a cyclical sequence of defeats, such as X beats Y beats Z beats
X.

Unbeaten set definition of Schwartz set:

1. An unbeaten set is a set of alternatives none of which are beaten
by anything outside the set.

2. An innermost unbeaten set is an unbeaten set that doesn’t contain a
smaller unbeaten set.

3. The Schwartz set is the set of alternatives that are in innermost
unbeaten sets.

[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, at:

http://econ.ucsb.edu/~armytage/hybrids.pdf

*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.

  Michael Ossipoff
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