<p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><b style><span style="font-family:"Arial","sans-serif";font-size:16pt">Recommendations for Voting in
Organizations, Clubs, Committees, Meetings, and Families</span></b></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
<br>
The choice of voting systems (often referred to as "methods") depends<br>
on how similar the alternatives are, how strongly their<br>
merit-differences are felt. That determines whether you insist on<br>
automatic majority rule enforcement, as opposed to just maximizing the<br>
liked-ness of the outcome. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">The
choice is also influenced by how<br>
amicable the organization or voting situation is. That determines how
compromising the<br>
voting system should be..</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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”.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">So,
in any group, there can be situations where voting is the best way to make a
collective choice.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"><span style> </span><br>
So let me suggest voting systems for various conditions:<br>
<br>
</font><font size="3"><b style>1. Maximizing overall satisfaction is
the important thing, more<br>
important than automatic majority rule. ...&/or maximum count-ease<br>
is desired:</b><br>
<br>
Use Approval or Score.<br>
<br>
Approval:<br>
<br>
Each voter can approve one or more alternatives–as many as s/he wants<br>
to approve. To avoid vulnerability to people strategically taking<br>
advantage of previous voting, the ballots shouldn’t be displayed until<br>
they’re all voted.<br>
<br>
A voter approves an alternative by writing its name, or by marking a<br>
box next to its name, on a ballot.<br>
<br>
Score:<br>
<br>
Each voter gives to each alternative a rating from 0 to N, where N can<br>
be any pre-specified number.<br>
<br>
For instance, in 0-10 Score, each voter rates each alternative from 0<br>
to 10. In 0-100 Score, each voter rates each alternative from 0 to<br>
100. Of course Approval amounts to 0-1 Score.<br>
<br>
Approval has the simplest and easiest handcount, but Score adds<br>
flexibility, allowing built in fractional ratings , which are useful<br>
when Approval’s yes/no would be difficult to decide, or when one<br>
desires to strategically give somewhat less than full support to a<br>
potential rival.<br>
.<br>
<b style>2. Automatic majority rule is desired</b></font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><font size="3"><span style="font-family:"Arial","sans-serif"">Automatic
majority rule is achieved by compliance with the Mutual Majority Criterion.
Here is that criterion’s definition:</span><font face="Times New Roman"> </font></font></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><font size="3" face="Times New Roman"> </font></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Mutual
Majority Criterion:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">A
mutual majority (MM) is a set of voters, comprising a majority of</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">the
voters, who all prefer a certain same set of alternatives to all</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">of
the other alternatives. That set of alternatives is their</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">MM-preferred
set.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">If
a MM vote sincerely, then the winner should come from their MM-preferred set.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">[end
of Mutual Majority Criterion definition]</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Definition
of sincere voting:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">A
voter votes sincerely if s/he doesn’t vote an unfelt preference, or</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">fail
to vote a felt preference that the voting system in use would</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">have
allowed hir to vote in addition to the preferences that s/he</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">actually
did vote.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">To
vote a felt preference is to vote X over Y when preferring <span style> </span>X to Y.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">To
vote an unfelt preference is to vote X over Y when not preferring X to Y.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">[end
of sincerity definition]</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">SP
meets the Mutual Majority Criterion (MMC).</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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<span style> </span>the “chicken
dilemma”. MMC compliance has value only with voting systems that don’t have the
chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">The
chicken dilemma:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Say
your faction prefer A, and another faction prefer B. Your 2</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">factions,
combined are a majority, and both detest C, strongly</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">preferring
A and B to C.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">But
if you support B, the B voters can take advantage of your</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">co-operativeness,
by withholding support for A, and thereby winning at</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">your
expense, even if A has more 1st choice support than B. They can</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">do
so because you helped B. You don’t know if they’re going to</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">“defect”
in that way, and that makes you hesitate to help B. But if</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">neither
A not B voters help eachother’s alternative, the detested C</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">will
win.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">That’s
the chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">For
any method more complicated than Approval or Score, there's no</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">excuse
to have the chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">The
choice among the voting systems that give automatic majority rule depends on
certain conditions, listed below:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><b style><span style="font-family:"Arial","sans-serif""><font size="3">1a) Conditions are amicable:<br style>
<br style>
</font></span></b></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Then,
you want a method that elects the Condorcet winner (CW)<br>
compromise (defined below). To not do so would be uncompromising and a bit inimical.
.<br>
I’ll define the CW:<br>
<br>
X is socially preferred to Y if more voters prefer X to Y than prefer Y to X.<br>
<br>
The CW is an alternative that is socially preferred to each one of the<br>
other alternatives.<br>
<br>
The Condorcet Criterion says:<br>
<br>
If there's a CW, and if everyone votes sincerely, then that CW should win.<br>
<br>
[end of Condorcet Criterion definition]<br>
<br>
Definition of sincere voting:<br>
<br>
A voter votes sincerely if s/he doesn’t vote an unfelt preference, or<br>
fail to vote a felt preference that the voting system in use would<br>
have allowed hir to vote in addition to the preferences that s/he<br>
actually did vote.<br>
<br>
To vote a felt preference is to vote X over Y when preferring X to Y.<br>
<br>
To vote an unfelt preference is to vote X over Y when not preferring X to Y.<br>
<br>
[end of sincerity definition]<br>
<br>
Compliance with the Condorcet Criterion guarantees that <i style>all</i> majorities will be satisfied, as opposed to only mutual
majorities. That property is desirable for amicable organizations and amicable
voting situations.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Additionally,
a voting system that dis-satisfies some majority, however constituted, is
vulnerable to replacement, when a majority of the participants demand its
replacement.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Here
are a few suggested Condorcet-Criterion-complying voting systems for amicable
conditions when automatic majority rule is desired:.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
If you want show-of-hands voting (or its Internet equivalent), &/or if<br>
there are many alternatives, no counting software, and little time,<br>
then do Sequential Pairwise Voting:<br style>
<br style>
</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Sequential
Pairwise Voting (SP):</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Arrange the alternatives in a vertical list, in reverse order of their<br>
order of proposal. …or hold a Vote-For-1 balloting, and order the<br>
alternatives in reverse order of their vote-count scores.<br>
<br>
Vote between the top 2 alternatives in the list. The winner then goes<br>
against the next alternative in the list, in another 2-way vote. …etc.<br>
Repeatedly, do a 2-way vote between the current winner and the next<br>
alternative in the list. The winner is the last remaining unbeaten<br>
alternative. (That’s the winner of the vote that includes the alternative at<br>
the bottom of this list).<br>
<br>
SP has a number of important properties:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
SP meets the Condorcet Criterion (defined above).<br>
<br>
It meets the Smith Criterion, defined immediately below:<br>
<br>
Smith Criterion:<br>
<br>
The Smith set is the smallest set of alternatives that all are<br>
socially preferred to everything outside that set. If everyone votes<br>
sincerely, then the winner should come from the Smith set.<br>
<br>
[end of Smith Criterion definition]</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Every
method that meets the Smith Criterion also meets the Mutual Majority Criterion.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">If
you’re interested in an explanation of why SP doesn’t have the chicken dilemma,
then here’s why:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
If the B voters defect against A<br>
before it’s time to vote on B, then you (as an A-preferrer) will<br>
notice that, and you can penalize them by refusing to support B when<br>
it’s time to vote on B. If you’ve already helped B, before it’s time<br>
to vote on A, then the B voters will have no reason to defect against<br>
A, because B must have already been eliminated by losing its 2-way<br>
vote. …unless B's 1st vote, after you've helped B, is between B and A,<br>
in which case it isn’t defection when the B voters sincerely vote B<br>
over A.<br>
<br>
In short, SP has no chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">For
the purpose of the rank methods defined below, X “beats” Y if more ballots rank
X over Y than rank Y over X.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Benham’s
method (also called “Benham” or “Condorcet-IRV”):</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Do IRV until there is an un-eliminated alternative that beats<br>
each of the other un-eliminated alternatives. Elect hir.<br>
<br>
[end of Benham definition]<br>
<br>
Definition of IRV (Instant Runoff):<br>
<br>
Repeatedly, cross off or delete from the rankings the alternative that<br>
tops the fewest rankings.<br>
<br>
Of course (in plain IRV) the winner is the candidate who remains<br>
un-eliminated, when all but one have been eliminated.<br>
<br>
[end of IRV definition]<br style>
<br style>
</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">(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.)</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Here
is a website that will conduct, for you, a fully-automated poll, using Benham
(also called Condorcet-IRV):</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><a href="http://www.cs.cornell.edu/andru/civs.html"><span style="font-family:"Arial","sans-serif""><font color="#0000ff" size="3">http://www.cs.cornell.edu/andru/civs.html</font></span></a><span style="font-family:"Arial","sans-serif""></span></p>
<p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">The
website has complete instructions for setting up a poll. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">I
highly recommend the Condorcet Internet Voting Service, linked to above. It is
operated by a Cornell University professor.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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).</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">In
this article, that voting system is also referred to as “Benham”. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Now, if you want to count the ballots yourself, then actually, SP is as good as
Benham, and a lot easier to count. But<br>
Benham is deluxe, in the sense that it isn’t necessary for voters to<br>
observe and penalize defection, because Benham automatically penalizes<br>
defection. In Benham, it’s simply a matter of sincere ranking. A<br>
mutual majority have no reason to do other than rank sincerely. In<br>
fact no one has need to do other than rank sincerely. That’s also true of
Woodall and Schwartz Woodall, defined immediately below:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Woodall:<br>
<br>
Do IRV till only one member of the initial Smith set remains<br>
un-eliminated. Elect hir.<br>
<br>
[end of Woodall definition]<br>
<br>
For the purpose of this definition, the Smith set is defined in terms<br>
of actual votes:<br>
<br>
X beats Y if more ballots rank X over Y than rank Y over X.<br>
<br>
The Smith set is the smallest set of alternatives such that all the<br>
set’s alternatives beat everything outside the set.<br>
<br>
Though both Benham and Woodall always choose from the Smith set,<br>
Woodall is more particular about which Smith set member it chooses.<br>
For that reason, Woodall achieves slightly better social utility than<br>
does Benham.<br>
<br>
Schwartz Woodall:<br>
<br>
Schwartz Woodall is like Woodall, except that it uses the Schwartz set (defined
below, after Schwartz Woodall) instead of the Smith set. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Those
2 sets are identical if there are no<br>
pairwise ties. But when there aren’t many voters, there can be<br>
pairwise ties. Then, the Schwartz set is a bit more exclusive than the<br>
Smith set. You can get into the Smith set by tying one of its members<br>
and beating all the non-Smith-set alternatives. That won’t get you<br>
into the Schwartz set. So the Schwartz set is more deluxe, for<br>
small-electorate voting.<br>
<br>
Schwartz Woodall:<br>
<br>
Do IRV till only one member of the initial Schwarz set remains<br>
un-eliminated. Elect hir.<br>
<br>
[end of Schwartz Woodall definition]<br>
<br>
Let me define the Schwartz set. It has 2 equivalent definitions. Both<br>
definitions define the same set:<br>
<br>
Cycle definition of the Schwartz set:<br>
<br>
The Schwartz set is the set of alternatives that don’t have a pairwise<br>
defeat that isn’t in a cycle.<br>
<br>
A pairwise defeat is what Y has, if X beats Y.<br>
<br>
A cycle is a cyclical sequence of defeats, such as X beats Y beats Z beats X.<br>
<br>
Unbeaten set definition of Schwartz set:<br>
<br>
1. An unbeaten set is a set of alternatives none of which are beaten<br>
by anything outside the set.<br>
<br>
2. An innermost unbeaten set is an unbeaten set that doesn’t contain a<br>
smaller unbeaten set.<br>
<br>
3. The Schwartz set is the set of alternatives that are in innermost<br>
unbeaten sets.<br>
<br>
[end of Schwartz set definitions]<br>
<br>
I recommend Schwarz Woodall as the deluxe voting system for amicable<br>
conditions. Sequential Pairwise is really just as good, though not as<br>
deluxe. Sequential Pairwise is, of course, much easier to count.<br>
<br>
Benham and Woodall are discussed in a journal article, by James<br>
Green-Armytage, at:<br>
<br>
</font></span><a href="http://econ.ucsb.edu/~armytage/hybrids.pdf" target="_blank"><span style="font-family:"Arial","sans-serif""><font color="#0000ff" size="3">http://econ.ucsb.edu/~armytage/hybrids.pdf</font></span></a><span style="font-family:"Arial","sans-serif""><br>
<font size="3">
<br>
<b style>2b) When conditions are not amicable:</b><br>
<br>
The a) methods (for amicable conditions) are ok under inimical<br>
conditions too. But the methods described below might be preferred:<br>
<br>
Plain IRV, instead of Schwartz Woodall.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Plain
IRV (defined above),<br>
like all of the methods recommended here, other than Approval and<br>
Score, meets the Mutual Majority Criterion and doesn’t have the<br>
chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">IRV
doesn’t always elect the CW compromise (defined<br>
above), making IRV less compromising, and maybe a bit inimical. But<br>
IRV is simpler to count than Schwartz Woodall, or Benham. </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">And,
in<br>
inimical conditions, the CW compromise might even not be desired. It<br>
might be felt that only mutual majorities should be honored, and that<br>
there’s no need to compromise with voters who aren’t in a mutual<br>
majority, and that it isn’t necessary to let voters outside the mutual majority
have a say in which mutual-majority-preferred alternative wins.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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).</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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:</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Exhaustive Balloting, also called “Elimination Voting”:<br>
<br>
Do a Vote-For-1 vote among all the alternatives. Eliminate the<br>
alternative that gets fewest votes. Repeat till only one alternative<br>
remains.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">(actually,
you might as well stop as soon as an alternative gets votes from a majority,
because that alternative will win anyway.)</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><br><font size="3">
Of course this could be done by show-of-hands, or its Internet<br>
equivalent. It’s even easier to count than IRV.<br>
<br>
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.<span style> </span></font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">And,
of course, an inimical organization or voting situation doesn’t need the
compromising-ness of methods that meet the Condorcet Criterion.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">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.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3"> </font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Those
are my recommendations. All of them except for Approval and<br>
Score meet the Mutual Majority Criterion, and have no chicken dilemma.</font></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">
</font><font size="3">
</font></span><span style="font-family:"Arial","sans-serif""></span></p><p><font size="3" face="Times New Roman">
</font></p><p style="margin:0in 0in 0pt;line-height:normal" class="MsoNormal"><span style="font-family:"Arial","sans-serif""><font size="3">Michael
Ossipoff</font></span></p><p><font size="3" face="Times New Roman">
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