[EM] Plurality is not a "yes/no voting system"

[Tom Ruen]

Dear Adam,

I back off on calling plurality a "rank system of depth one" for the same
reason you dislike calling Approval a Cardinal Ratings system. However I
still will defend calling plurality a "one vote" system.

Plurality and runoffs (and Random ballot) don't need a checkbox-column style
ballot. They CAN be implemented by voters offering a single name on a
ballot. Similarly they can work without paper by voters using their bodies
as ballots, moving around a room and joining a single group based on their
vote decision. Plurality require voters to make a single choice - one of N
options at a time. There's no multiple votes, no split votes - just one
simple vote.

I define "One vote" methods are methods that allow a single name to be
written on a ballot. That is very well defined I must think. How can anyone
deny this category as unique? Even if the category is limited in possible
methods, it deserves recognition.

In regards to the page:
http://en.wikipedia.org/wiki/Voting_system#Single_Winner_Systems

I believe "Approval" should be moved to "Ratings". I agree it is nice
Approval can fit nicely under existing checkbox ballot format. However I
don't necessarily think Approval is best implemented as a single-column
"checkbox" ballot. I think approval better fits under a "radio-button"
ballot, with your actual 2 column YES/NO ballot and allow explicit marks
under either category. That makes more sense to me to help voters see what
they are doing.

Either of the following ballots can be approval, but the second is more
clearly an approval ballot:

CHECKBOX Ballot:
---------------------------
(Vote for approved candidates, as many as you like)
Vote Candidate
  O   Apple
  O   Banana
  O   Coconut
---------------------------

APPROVAL Ballot:
---------------------------
(Mark one answer per candidate. Mark yes for approved candidates)
(A "No" vote is counted, if candidate is unmarked)
No Yes  Candidate
O   O    Apple
O   O    Banana
O   O    Coconut
---------------------------

Then you can consider 3 catagories with scores {-1,0,+1} equally well.
RATING Ballot:
---------------------------
(Mark one answer per candidate, No for disapproval, Acceptable for
neutrality, and Yes for Approval)
(A "Maybe" vote is counted, if candidate is unmarked)
No Acceptable Yes  Candidate
O         O           O    Apple
O         O           O    Banana
O         O           O    Coconut
---------------------------

Notice that the ballot might have different possible "default" scores if a
candidate is unmarked, "Maybe=0" is default in this case, but not the
minimum possible score.

Alternately a rating ballot might REQUIRE all candidates be marked as a
feedback check to aid votes from accidentally undervoting.

I think ballots that allow one column for every possible mark are more clear
how to vote, and the extra ability to check for under votes can be useful.

My single-winner voting method categories remain:

1. One vote system - vote for one candidate at a time
FORMAT: PREMADE BALLOTS HAVE COLUMN OF CANDIDATES, CHECKBOX BY EACH
VOTE FOR AT MOST ONE
    Plurality count - one vote, add votes for winner
    Random ballot - one vote, pick one ballot randomly for winner
    Runoff - 2 or more rounds with or without elimination

2. Ranking vote systems - rank candidates first, second, third...
FORMAT: PREMADE BALLOTS HAVE N CHECKBOX COLUMNS FOR N RANKS
VOTE FOR ONE CANDIDATE PER RANK COLUMN, NO MORE THAN ONE MARK PER CANDIDATE
    Borda count - assign points on ranking, add for winner
    Sequential rounds - no more than N counting rounds
        IRV - elimination runoff
        Coombs - elimination disapproval runoff
        Bucklin - approval runoff
    Pairwise rounds  - N*(N-1)/2 counting rounds
        Condorcet
            Variations...

3. Rating vote systems - independent points assigned to each candidate
FORMAT: PREMADE BALLOTS HAVE N COLUMNS FOR N RATINGS
VOTE FOR ONE CHOICE FOR EACH CANDIDATE
    Approval count - vote no/yes, assign 0 or 1 points, add for winner
    Cardinal Ratings count - vote whole numbers, example 0,1,2,3,..,10. Add
for winner

All three of these categories are distinct in ballots and voting rules.

You can consider tied-rankings in category two (or split-vote ties) in
category one as well. I wrote the "VOTE" rules to restrict this out of
simplicity and a desire to reduce accidental misvotes. I like the option of
tied votes in many systems, but I don't think it is essential. A system that
can catch bad votes and allow voters to vote again is superior to adding
special counting rules for tied rankings/votes.

Tom Ruen

P.S. I inserted limited comments below...

----- Original Message ----- 
From: "Adam Tarr" <atarr at purdue.edu>
To: <election-methods at electorama.com>
Sent: Sunday, June 06, 2004 10:06 AM
Subject: Re: [EM] Plurality is not a "yes/no voting system"


> Tom Ruen wrote:
>
> >Adam Tarr says Approval voting can fit under "Yes/No voting" or "Ratings
> >voting", however I deny that plurality can be classified as a "yes/no"
> >voting method.
> >
> >Labeling a class of methods as "yes/no" to me implies a series of
> >independent questions where a valid respond can consider independent
> >responses on each question.
>
> This is a reasonable criticism.  However, I once again refer you to the
> first line of the section, which is, "Single Winner systems can be
> classified by ballot type".  I think this is a reasonable approach (in
fact
> it is the best approach I can come up with) and it clearly divides things
> into three categories.
>
> I have struggled (and, in your opinion, failed) to come up with an
adequate
> name for the simplest and most common sort of ballot - namely, the ballot
> where the voter is presented with a list of names with empty boxes next to
> each one.  I am very open to a better suggestion for a name.  Heck,
> "traditional ballot methods" versus "ranked ballot methods" versus "rated
> ballot methods" seems reasonable to me.  Would you consider that an
> improvement?

As I've said, I think Approval is best implemented with a two column ballot.

>
> >A method that allows independent answers is a categorical "ratings
method".
>
> Provided the scale is independent of the number of candidates, I
> agree.  But a method that uses the simplest sort of ballots, is a method
> that uses the simplest sort of ballots.  A tautology, I know, but one that
> apparently needs repeating.
>
> Also, for argument's sake, would this make Condorcet a ratings
> method?  After all, relative ranking is all that matters there.  If I put
> half the candidates in third place, and the other half in fourth place, I
> think my ballot is still valid.

Condorcet could be a pairwise rating ballot. Actually I'd not disagree with
Condorcet implemented as a 3-level rating ballot, one mark per pair row.
Notice each column is no longer a fixed choice.
FOR EACH PAIR, VOTE FOR A, B or Equal.
CANDIDATE-A  EQUAL        CANDIDATE-B
O Apple                  O                O Banana
O Apple                  O                O Coconut
O Banana                O                O Coconut

...
[N*(N-1)/2 pair contests among N candidates]

Again, I'd offer this as a way to "check" ballot is logically coherent. If a
cyclic preference is offered, it can be noted to allow a revote. I also like
the explicit "equal" vote category over tied rankings since tied rankings
might be an accidental vote, while explicitly marking "equal" is a decision.

>
> >A method that has a limitations on answers can only be a "rank" system.
>
> I would define rank systems by systems that ask the voter to submit an
> ordinal ranking.  So here I disagree.
>
> You're trying to make the dichotomy be independent versus dependent
> choices, and I really don't think it fits.  As I have said exhaustively,
> we're basing this on the ballot type.  Basically, it comes down to slots
> per candidate.

I stand by "independent" versus "dependent" categories, with rank systems as
dependent - no more than one mark per column.

>
> Binary choice next to each candidate = traditional ballot, yes/no,
up/down,
> whatever you want to call it
> N slots for candidates (where N is the number of candidates plus or minus
a
> fixed integer factor) = ranked ballot
> N slots per candidate (N is independent of the number of candidates) =
> rated ballot
>
> And yes, when N=2 in the third case, approval fits both the first and
third
> categories.  I do not dispute this.
>
> >It only makes sense to call "plurality" a "rank system". It simply limits
> >the ranking depth to one.
>
> While this can be an academically useful way to look at plurality, I think
> it's a lousy way to classify plurality in an encyclopedia.  It seems
> confusing to the layman.
>

Agreed, but for me that is what puts Plurality back into a separate
category.

> >If people disagree the wikipedia Voting system page should not have a
"one
> >vote" category of single winner systems,
>
> I still think that the ideas of "one vote" and "multiple vote" are poorly
> defined, as they are based on non-unique definitions of how to evaluate
the
> ballots.

"One vote" is well-defined, even if "multiple votes" is not.

>
> -Adam