[EM] Wikipedia

[Adam Tarr]

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.

Tom Ruen wrote:

>By definition Plurality is "one person, one vote".
>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.

OK, but this justification is going to come back to haunt you.

>In contrast:
>Approval is definitely NOT "one person, one vote" since we're electing one 
>candidate and voters can support as many candidates as they like.

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:

http://article.gmane.org/gmane.politics.election-methods/919

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.

>Similarly Borda is definitely NOT "one person, one vote".

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.

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).

>Similarly Bucklin is NOT "one person, one vote" because if a second round 
>is needed, each voter can simultaneously support two candidates.

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:

1)  Set N=1
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.)
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.
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.

>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,

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.

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.

>and a second-choice vote for a candidate could work as a vote against 
>one's first choice.

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.

>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.

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.

>Does anyone know a single locale anywhere in the world that has political 
>elections for single winners that uses a "multiple vote" method?

Several online groups of nontrivial size use Condorcet, and Approval is 
used by international organizations with tens of thousands of members 
(including the IEEE).

>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?

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.

>  Again, granted that Condorcet I take as a special case, not clearly 
> fitting in either category.

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.

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:

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.
2) Repeat step 1 until there's only one candidate left.

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.

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.

>  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.
>
>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.

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:

1)  Yes/No ballots: ballots where you need only one bit of information per 
candidate.  Plurality, approval, and any non-instant runoff method.

2)  Ranked ballots:  ballots where you need at most as many slots for 
candidates as there are candidates.  Condorcet, instant runoff, Borda, et 
cetera.

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.

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.

>There are also "one count" methods and "multiple count" methods.
>
>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.

While to some degree that's an artifact of the count, I can see this as a 
way of subdividing things.

>If I were to group by "ballot type" first and "number of vote counts" second:
>
>1. Single vote ballot
>     A.. Single count
>         * Plurality - count votes, top wins
>     B. Multiple counts
>         I. Elimination
>             * Two round runoff (keep top two)
>             * Slow elimination runoff (elimination bottom one)
>         II. No elimination
>             * Exhaustive Runoff (no forced elimination)
>2. Rank preference ballot (1,2,3,...)
>     A.. Single count
>         * Borda - count votes by ranking value (Value=MAX_RANK-rank)
>     B. Multiple counts
>         I. Elimination
>             * IRV - bottom elimination runoff
>             * Supplementary vote  - top two runoff
>             * Coomb - disapproval elimination runoff
>         II. No elimination
>             * Bucklin - approval runoff
>             * Condorcet - fixed N*(N-1)/2 pairwise vote counts among N 
> candidates
>3. Ratings ballot - assign independent values in range [a,b]
>     A.. Single count - count value votes, top votes win.
>         * Approval Ratings: No/Yes - point value 0 or 1.
>         * Cardinal Ratings - assign independent whole numbers a and b.
>         * Generalized Ratings - any finite real number in range [a,b], 
> effectively equivalent to real range [0,1]
>     B. Multiple counts
>         * MCA - like Approval but with range [0,2] and multiple counting 
> rounds.

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:

1. Yes/No ballots
         A.. Single voting round
                 * Plurality - vote for at most one candidate, count votes, 
top wins
                 * Approval - vote yes/no on all candidates, count votes, 
top wins
         B. Multiple voting rounds
                 I. Elimination
                         * Two round runoff (keep top two)
                         * Slow elimination runoff (elimination bottom one)
                 II. No elimination
                         * Exhaustive Runoff (no forced elimination)
2. Rank preference ballot (1,2,3,...)
         A.. Single count
                 * Borda - count votes by ranking value (Value=MAX_RANK-rank)
         B. Multiple counts
                 I. Top-preference prioritizing methods
                         * Hare/IRV - bottom elimination runoff
                         * Supplementary vote - top two runoff
                 II. Condorcet compliant methods
                         * Ranked Pairs
                         * Beatpath
                         * etc.
                 III. Other multiple count methods
                         * Coomb - disapproval elimination runoff
                         * Bucklin
3. Ratings ballot - assign independent values in range [a,b]
         A.. Single count - count value votes, top votes win.
                 * Cardinal Ratings - assign independent whole numbers a 
and b.
                 * Generalized Ratings - any finite real number in range 
[a,b], effectively equivalent to real range [0,1]
         B. Multiple counts
                 * MCA - two-round method
                 * Transformation of rated ballot to ranked ballot (when 
ranked method allows equal rankings)

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.

>  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.)
>
>I'd still defend the issue of "number of active votes", between systems as 
>an important issue worthy to discuss.

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.

-Adam
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