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Tom, the "1P-1V" debate raged here a while ago, as you're
probably aware. The bottom line is that it is a fairly meaningless
criteria. Rather than addressing the RESULTS of an election method,
it addresses the MACHINERY of the method. And nearly every method
can be rearranged in a way that respects 1P-1V without changing the
outcome.<br><br>
Tom Ruen wrote:<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>By
definition Plurality is "one person, one vote".</font><br>
<font face="arial" size=2>Runoffs and IRV are also "one person, one
vote" because in any given count every voter can offer at most one
vote and in order for a new count to be made, all previous counts have no
effect on the new count.</font></blockquote><br>
OK, but this justification is going to come back to haunt you.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>In
contrast:</font><br>
<font face="arial" size=2>Approval is definitely NOT "one person,
one vote" since we're electing one candidate and voters can support
as many candidates as they like.</font></blockquote><br>
OK, but we can use the Approval ballots to conduct a sequential count
election where each voter only gets one vote per round - i.e. just like
IRV. See Olli Salmi's excellent message from 12/9/2002 for
details:<br><br>
<a href="http://article.gmane.org/gmane.politics.election-methods/919" eudora="autourl">http://article.gmane.org/gmane.politics.election-methods/919</a><br><br>
Basically, you just eliminate candidates one round at a time, in pairwise
contests, while only allowing those who approve one candidate and not the
other to vote in each round. This produces exactly the same results
as an Approval election, without violating the principles of 1P-1V you
outline above.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Similarly
Borda is definitely NOT "one person, one vote".
</font></blockquote><br>
In this case I agree with you. Borda does seem to violate the
principle of 1P-1V, since it allows some voters more power in certain
contests than other voters - depending on how many candidates they put on
their ballot between the two candidates in question.<br><br>
I can't come up with a sequential variant of Borda that respects 1P-1V in
accordance with your justification above. (This distinguishes it
from approval/Bucklin/Condorcet).<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Similarly
Bucklin is NOT "one person, one vote" because if a second round
is needed, each voter can simultaneously support two
candidates.</font></blockquote><br>
While it would be very cumbersome, for sure, Bucklin CAN be put into a
sequential system that respects your definition of 1P-1V.
Basically, it would go like this:<br><br>
1) Set N=1<br>
2) Go through every candidate and see if that candidate has a
majority of voters ranking him Nth or higher on the ballot. If so,
place him in the winner's circle. (Each such examination of the
ballots with respect to a single candidate is one "round" of
voting. Since those totals are immediately discarded, this still
fits your justification of 1P-1V above.)<br>
3) If the winner's circle is empty, and N is less than the number of
candidates, then add one to N and return to step 2.<br>
4) If the winner's circle has only one candidate, then he/she is the
winner. Otherwise, conduct an approval election as above, with
voting for a candidate in position N or higher constituting
approval.<br><br>
<blockquote type=cite class=cite cite>In the Bucklin vote-counting
system, if no candidate received the majority of first choices, all
second choices were added to the first choices already tallied, and vote
totals were checked to see if any candidate reached the new majority
threshold. Thus, in contrast to Single Transferable Vote, under Bucklin
some voters' votes were counted more than once, </blockquote><br>
But, as I have pointed out in the past, a voter can only cast one vote
for the winning candidate. So your power, just like in Plurality or
IRV, is at most one vote. Your other votes are, in the final
analysis, irrelevant, just as the lower choices or preferences for
eliminated candidates are irrelevant in IRV.<br><br>
Again, the distinction is only in how we look at the ballots, not their
effects. The fact that I can make Bucklin or approval look like an
IRV election just underscores this.<br><br>
<blockquote type=cite class=cite cite>and a second-choice vote for a
candidate could work as a vote against one's first
choice.</blockquote><br>
This is a side criticism that's not really relevant here. Of
course, in IRV, you can fail to cast a crucial vote for your second
choice, and indirectly cause the election of your last choice.
Again, this is an entirely different subject.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Every
method I grouped under "multiple vote" would have the same
constitutional judgment. Granted this case specifically only refers to
Minnesota, but it would appear to be a universal position as well
considering that only "single" vote methods, methods where
voters are only allowed to support a single candidate with a single votes
are used in political elections worldwide.</font></blockquote><br>
That's only one possible conclusion to draw. Since IRV certainly
looks more like plurality to the casual observer than approval or Bucklin
or Condorcet, it should come as no surprise that it has been adopted in
more places. But this may just be more about politics than
criteria.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Does
anyone know a single locale anywhere in the world that has political
elections for single winners that uses a "multiple vote"
method?</font></blockquote><br>
Several online groups of nontrivial size use Condorcet, and Approval is
used by international organizations with tens of thousands of members
(including the IEEE).<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>If this
is true, if "one vote" methods are exclusively used in politics
and "multiple vote" methods exclusively NOT used, why is this
distinction so apparently controversial?</font></blockquote><br>
Because it is meaningless. Because it serves to implicitly divide
the methods into "good and acceptable methods" and "bad
and unacceptable methods". A distinction based on the type of
ballot used is FAR more meaningful. (i.e. yes/no ballot methods vs.
ranked/rated ballot methods). Heck, I would prefer a distinction
based on some arbitrarily picked academic criteria (e.g. "methods
that respect the majority criteria" versus methods that do not) to
what you've put in.<br><br>
<blockquote type=cite class=cite cite> <font face="arial" size=2>Again,
granted that Condorcet I take as a special case, not clearly fitting in
either category.</font></blockquote><br>
First of all, I've already shown that Bucklin and Approval fit into the
category of 1P-1V, provided we decide to work through the ballots in a
particular way. The front end (ballots the voters vote on) and the
back end (the elected candidate) remain unchanged.<br><br>
Now let me show you that even Condorcet can be evaluated in a sequential
fashion that respects your 1P-1V principle. Here's the
method:<br><br>
1) Pick two candidates at random (or the two remaining candidates with
the lowest first-place support, if that makes you happy). Compare
them pairwise - each voter votes for the candidate they rank higher on
their ballot. Eliminate the candidate that loses this
contest.<br>
2) Repeat step 1 until there's only one candidate left.<br><br>
Disturbingly simple, isn't it? And yet, it seems impossible to
argue that this violates the principle of 1P-1V. This method will
always elect the Condorcet winner if one exists, and will always elect a
member of the Smith set regardless.<br><br>
Now, I admit that it is more difficult to define ranked pairs or beatpath
in a way that exactly obeys your principle of 1P-1V above. I can
write out a method that seems to do so by my sensibilities, but it's not
obvious. That said, it's clear that a Condorcet-compliant method
CAN be done using a runoff-based count where each voter only gets one
vote per runoff.<br><br>
<blockquote type=cite class=cite cite> <font face="arial" size=2>Perhaps
I am wrong to make this distinction second most important to (number of
winners). Perhaps the fact that Condorcet methods defy the division, some
other approach is better. I don't know. I judge Condorcet is
fundamentally different and deserves its own classification.</font><br>
<br>
<font face="arial" size=2>If "number of active votes" is
unacceptable criterion, then I can see value in "Ballot type"
and also "Counting type". There are "single vote",
"rank vote", and "rate vote" ballots that are
distinct. </font></blockquote><br>
I think this is a far better and less controversial distinction. In
my opinion, the best divider is the physical type of ballot
required. I see it as three categories:<br><br>
1) Yes/No ballots: ballots where you need only one bit of
information per candidate. Plurality, approval, and any non-instant
runoff method.<br><br>
2) Ranked ballots: ballots where you need at most as many
slots for candidates as there are candidates. Condorcet, instant
runoff, Borda, et cetera.<br><br>
3) Rated ballots: ballots where there are multiple slots per
candidate, and the number is independent of the number of
candidates. Cardinal rankings, majority choice approval.<br><br>
Looking below, I see you agree with this, except you put approval in the
rated section in stead of the single count section. As you can see
above, I disagree with this. The important thing is the type of
ballot required, and approval uses exactly the same ballot as plurality
and runoff.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>There are
also "one count" methods and "multiple count"
methods.</font><br>
<br>
<font face="arial" size=2>Specifically Plurality, Borda and
Approval are all "one count" methods, a single number
applied immediately to each candidate and top number wins. These deserve
some separate recognition from their more complex alternatives in each
ballot category.</font></blockquote><br>
While to some degree that's an artifact of the count, I can see this as a
way of subdividing things.<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>If I were
to group by "ballot type" first and "number of vote
counts" second:</font><br>
<br>
<font face="arial" size=2>1. Single vote ballot</font><br>
<font face="arial" size=2> A.. Single count<br>
* Plurality - count votes, top
wins</font><br>
<font face="arial" size=2> B. Multiple counts<br>
I. Elimination<br>
* Two
round runoff (keep top two)<br>
* Slow
elimination runoff (elimination bottom one)<br>
II. No elimination<br>
*
Exhaustive Runoff (no forced elimination)</font><br>
<font face="arial" size=2>2. Rank preference ballot
(1,2,3,...)</font><br>
<font face="arial" size=2> A.. Single
count</font><br>
<font face="arial" size=2> *
Borda - count votes by ranking value (Value=MAX_RANK-rank)<br>
B. Multiple counts<br>
I. Elimination<br>
* IRV
- bottom elimination runoff<br>
*
Supplementary vote - top two runoff</font><br>
<font face="arial" size=2>
* Coomb - disapproval elimination runoff<br>
II. No elimination<br>
*
Bucklin - approval runoff<br>
*
Condorcet - fixed N*(N-1)/2 pairwise vote counts among N candidates<br>
3. Ratings ballot - assign independent values in range [a,b]</font><br>
<font face="arial" size=2> A.. Single count - count
value votes, top votes win.<br>
* Approval Ratings: No/Yes -
point value 0 or 1.</font><br>
<font face="arial" size=2> *
Cardinal Ratings - assign independent whole numbers a and b.</font><br>
<font face="arial" size=2> *
Generalized Ratings - any finite real number in range [a,b], effectively
equivalent to real range [0,1]</font><br>
<font face="arial" size=2> B. Multiple counts<br>
*
</font><font face="Times New Roman, Times">MCA - like Approval but with
range [0,2] and multiple counting rounds.</font></blockquote><br>
Pretty good, except that Approval should be considered a yes/no ballot
method, and elimination vs. no elimination is only meaningful in the
context of yes/no ballots where the voter actually returns to the polls
to vote again. My version:<br><br>
1. Yes/No ballots <br>
<x-tab> </x-tab>A.. Single
voting round<br>
<x-tab> </x-tab><x-tab> </x-tab>*
Plurality - vote for at most one candidate, count votes, top wins <br>
<x-tab> </x-tab><x-tab> </x-tab>*
Approval - vote yes/no on all candidates, count votes, top wins <br>
<x-tab> </x-tab>B.
Multiple voting rounds <br>
<x-tab> </x-tab><x-tab> </x-tab>I.
Elimination <br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Two round runoff (keep top two) <br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Slow elimination runoff (elimination bottom one) <br>
<x-tab> </x-tab><x-tab> </x-tab>II.
No elimination <br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Exhaustive Runoff (no forced elimination) <br>
2. Rank preference ballot (1,2,3,...) <br>
<x-tab> </x-tab>A.. Single
count<br>
<x-tab> </x-tab><x-tab> </x-tab>*
Borda - count votes by ranking value (Value=MAX_RANK-rank) <br>
<x-tab> </x-tab>B.
Multiple counts <br>
<x-tab> </x-tab><x-tab> </x-tab>I.
Top-preference prioritizing methods<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Hare/IRV - bottom elimination runoff <br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Supplementary vote - top two runoff <br>
<x-tab> </x-tab><x-tab> </x-tab>II.
Condorcet compliant methods<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Ranked Pairs<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Beatpath<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
etc.<br>
<x-tab> </x-tab><x-tab> </x-tab>III.
Other multiple count methods<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Coomb - disapproval elimination runoff <br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>*
Bucklin<br>
3. Ratings ballot - assign independent values in range [a,b] <br>
<x-tab> </x-tab>A.. Single
count - count value votes, top votes win. <br>
<x-tab> </x-tab><x-tab> </x-tab>*
Cardinal Ratings - assign independent whole numbers a and b. <br>
<x-tab> </x-tab><x-tab> </x-tab>*
Generalized Ratings - any finite real number in range [a,b], effectively
equivalent to real range [0,1] <br>
<x-tab> </x-tab>B.
Multiple counts <br>
<x-tab> </x-tab><x-tab> </x-tab>*
MCA - two-round method<br>
<x-tab> </x-tab><x-tab> </x-tab>*
Transformation of rated ballot to ranked ballot (when ranked method
allows equal rankings)<br><br>
My distinctions with in 2B (ranked ballot/multiple count methods) are
admittedly somewhat arbitrary, but I think this approach serves to divide
the category into the two major "camps" of instant runoff and
Condorcet.<br><br>
<blockquote type=cite class=cite cite> <font face="arial" size=2>That
might be more acceptable to members on this list. I added a third level:
Multiple counts whether there is forced elimination involved. (You might
argue single count methods have forced elimination also, but it is
irrelevant since there's no recount after the elimination.)</font><br>
<br>
<font face="arial" size=2>I'd still defend the issue of "number of
active votes", between systems as an important issue worthy to
discuss.</font></blockquote><br>
Again, I think it's important to make the focus on either the ballots the
method uses, or the effects of the method. rather than the (often
non-unique) machinery the method uses to get from one to the
other.<br><br>
-Adam</html>