Attachment CRITTBL1

Mon May 27 00:20:12 PDT 1996

[Mike writes: I have just proposed a vote in which EM members
would rank the proposed methods according to their desirability
as public proposals, for the purpose of presenting those rankings
& their results, by the various count rules, to ER. So why does
Bruce pick this time to post this article about the academic
criteria to this list. He didn't answer my postings, earlier,
when I replied about those criteria. 

We've been discussing the relative merits of methods. I've 
asked Bruce questions on this list, with regard to that issue,
and he hasn't replied to them. Instead he post an article
naming the academic criteria and which methods meet them,
with no reply to my comments about those criteria. Bruce
once objected to people "talking past eachother". But isn't
that what he's doing when his postings don't answer the
questions I've asked him, or comment on the statements I
have made here, regarding Condorcet vs Coplannd? And when
he posts his article on academic criteria, with no comment
about the significance of meeting or not meeting those 
criteria.

He commented on that when he first posted his Condorcet criticisms
article to Steve & Rob L., but I replied to that. I'm not so much
asking Bruce to reply to my comments about the importance of the
academic criteria, or to my comments regarding the relative
merits of Condorcet & Copeland--I'm merely pointing out that

I suggest that we can discuss Bruce's pre-written postings if
we wish, but we shoud NOT let that delay our vote on the
methods now. You might say "Shouldn't discussion precede
voting?" Sure, but if we let anyone persuade us to wade into
the tar-pit that is academic voting systems discussion, I
guarantee that we'll never accomplish our goal. The academics
have been at it for many years, and they're no closer now
to anything that could be called progress than they were
decades ago. Their discussion just isn't oriented toward
practical results. The lesser-of-2-evils standard, so important
to voters, is studiously ignored by the academics. Bruce
said that he doesn't consider it important. If Bruce doesn't
consider important the problem that so many voters are
dominated by, the problem that led us to want single-winner
reform, then should Bruce be able to stop our vote at this
time, with discussion of other criteria. Filibuster?

I realize the importance of politeness, civility, & not criticizing
people on the list. And so I want to emphasize that I'm saying
this in an objective way, not angrily or intending to criticize:

Suppose that someone wanted to prevent progress in EM's goal
of making a recommendation to ER. Suppose one strategem for
that goal was to post academic discussion guaranteed not to lead
to progress toward EM's goals. A strategically advisable time
to post such material would be just when a vote is called for,
to tangle the list into the endless academic discussion. Sure,
maybe it's  just coincidence that that's when Bruce posted
his article. I'm just mentioning that possible explanation.

***

Excuse me if some lines are displaced in this reply. Replying
to some formats, using an edited copy, can do that.

I've just realized that I'm only making a few comments,and that
there are long passages of the copied article that I'm not
replying to, and so I should reply in a separate posting,without
including a copy of the article to which I'm replying.

So no replies have been added to the following part of Bruce's
letter. I included the copy because I thought I'd use the
edited-copy reply format, but I'm going to reply in a separate
posting.

Mike

Buce Anderson writes:
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> Bruce
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> 
> BACKGROUND PAPER
> SOME  RELATIONSHIPS  AMONG  VOTING  
> METHODS  AND  THE  MAJORITY,  CONDORCET,  
> AND  MONOTONICITY  CRITERIA
> 
> Lowell Bruce Anderson
> 
> Voice:  703-845-2148
>   FAX:  703-845-2255
>    e-mail:  landerso at ida.org
> May 2, 1996
> A.	INTRODUCTION
> Each voter casts one ballot by ranking (1st, 2nd, 3rd, etc.) as many 
> of the candidates as the voter wishes, with ties allowed, and with any 
> unranked candidates on a voter's ballot being considered as tied for last 
> by that voter.  Each voter casts only one such ballot, and (with the 
> exception of Approval voting as discussed in Section D), the winners 
> according to each of the voting methods considered below can be 
> determined solely from these ballots.  Each criterion considered below is 
> defined in Section B.  Table 1 then gives relationships involving these 
> criteria and 34 different voting methods.  The voting methods themselves 
> are not defined here, and no proofs or examples are given.  See the 
> publications cited in Reference [1], and their references, for additional 
> information on voting methods.
> B.	DEFINITIONS OF CRITERIA
> To avoid trivialities, assume that two or more alternatives are 
> being considered.
> 1.	Majority Criteria
> a.	The Majority (Winner) Criterion (MW)
> If a strict majority of the voters rank a particular 
> alternative as their unique first choice, then the 
> voting method must select that alternative as the 
> unique winner.
> This criterion is abbreviated by MW below.
> b.	The Majority Loser Criterion (ML)
> If a strict majority of the voters rank a particular 
> alternative as their unique last choice, then the 
> voting method must not select that alternative as a 
> winner.
> This criterion is abbreviated by ML below.
> c.	The Generalized Majority Criterion (MG)
> If there is a nonempty subset of the alternatives, 
> say S, such that, for some strict majority subset of 
> the voters, say M, each voter in M ranks every 
> alternative in S ahead of every alternative not in S, 
> then all of winners selected by the voting method 
> must be in S.
> This criterion is abbreviated by MG below.  Note that if a voting 
> method satisfies MG then it must satisfy both MW and ML, but not vice 
> versa.
> 2.	Condorcet Criteria
> The criteria in this section involve an alternative "winning or 
> losing the pairing" between it and individual other alternatives.  These 
> terms are defined as follows.  Given the voters ballots (as described 
> above), all possible distinct pairings of the candidates are considered.  
> For any two candidates, say A and B:
> A wins (and B loses) their pairing if more voters rank A ahead of B than 
> rank B ahead of A,
> B wins (and A loses) their pairing if more voters rank B ahead of A than 
> rank A ahead of B,
> and the pairing is a tie if the same number of voters rank A ahead of B as 
> rank B ahead of A.
> Accordingly, a "pairing" between two alternatives can be viewed as a 
> "head-to-head matchup" between them, which necessarily results in one 
> (and only one) of the three outcomes just described.
> a.	The Condorcet (Winner) Criterion (CW)
> If a particular alternative would win all of the 
> pairings between it and each other alternative, then 
> the voting method must select that alternative as 
> the unique winner.
> This criterion is abbreviated by CW below.
> b.	The Condorcet Loser Criterion (CL)
> If a particular alternative would lose all of the 
> pairings between it and each other alternative, then 
> the voting method must not select that alternative 
> as a winner.
> This criterion is abbreviated by CL below.
> c.	The Generalized Condorcet Criterion (CG)
> If there is a nonempty subset of the alternatives, 
> say S, such that every alternative in S would win 
> all of the pairings between it and each of the 
> alternatives not in S, then all of winners selected 
> by the voting method must be in S.
> This criterion is also known as Smith's generalized Condorcet 
> criterion.  It is abbreviated by CG below.  Note that if a voting method 
> satisfies CG then it must satisfy both CW and CL, but not vice versa.  
> Also note that if a voting method satisfies CG then it must satisfy MG 
> (and, hence, MW and ML), but not vice versa.
> 3.	The Monotonicity Criterion (Mono.)
> If an alternative would be a winner according to 
> the voting method with some particular set of 
> voter's rankings, and then one or more voters 
> change their rankings in a way favorable to that 
> alternative (without changing the relative order in 
> which they rank any other alternatives), then that 
> alternative must still be a winner.
> A completely equivalent way of stating this criterion is as 
> follows:
> If an alternative would not be a winner according 
> to the voting method with some particular set of 
> voter's rankings, and then one or more voters 
> change their rankings in a way unfavorable to that 
> alternative (without changing the relative order in 
> which they rank any other alternatives), then that 
> alternative must still not be a winner.
> To see that these two ways of stating the monotonicity criterion 
> are equivalent, note that if a voting method fails either one then it 
> necessarily must fail the other.  This criterion is abbreviated by Mono. 
> below.
> C.	RELATIONSHIPS AMONG THESE CRITERIA AND 
> SELECTED VOTING METHODS
> Whether or not Dodgson's voting method satisfies ML or MG 
> remains an open question here.  Except for these two cases, Table 1 on 
> page 4 states which of the listed voting methods satisfy which of these 
> seven criteria.  Those that satisfy all seven are listed in bold italics.
> D.	APPROVAL  VOTING
> Approval voting requires an additional input beyond just a 
> ranking from each voter.  That is, a valid Approval ballot is a valid 
> (ranked) ballot, as defined here, because ties are allowed in voter's 
> rankings.  Thus, any voter who believes that the alternatives can be put 
> into one of two categories (either approved or non-approved) can always 
> cast a valid ranked ballot as well as a valid Approval ballot.  Conversely, 
> though, a valid ranked ballot does not generally correspond to a valid 
> Approval ballot because it contains insufficient information_the 
> additional input of where in a voter's ranking that voter separates his or 
> her approved alternatives from the non-approved ones is also needed 
> from each voter.  Table 1 assumes that both the voter's rankings and this 
> additional input are on the voter's ballot under Approval voting.
> 
> REFERENCE
> 
> 1.	Anderson, L.B., An Introductory Bibliography on Single-Winner 
> Voting Methods, Background Paper, March 1996.
> 
> 
> Table 1.   Voting Methods vs. the Majority, Condorcet, and 
> Monotonicity Criteria
> 
> Criteria
> 
> Voting Method
> MW
> ML
> MG
> CW
> CL
> CG
> Mono.
> All
> 
> Anderson
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Approval
> no
> no
> no
> no
> no
> no
> yes
> no
> 
> Arrow-Raynaud
> no
> yes
> no
> no
> yes
> no
> no
> no
> 
> Black 
> yes
> no
> no
> yes
> yes
> no
> yes
> no
> 
> Borda
> no
> no
> no
> no
> yes
> no
> yes
> no
> 
> Bucklin
> yes
> yes
> yes
> no
> no
> no
> yes
> no
> 
> Complete-Champion
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Condorcet
> yes
> no
> no
> yes
> no
> no
> yes
> no
> 
> /Condorcet/1a/
> yes
> yes
> yes
> yes
> yes
> yes
> no
> no
> 
> Consensus-
> Champion
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Coombs
> yes
> yes
> no
> no
> yes
> no
> no
> no
> 
> Copeland
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> /Copeland/2a/
> yes
> yes
> yes
> yes
> yes
> yes
> no
> no
> 
> Copeland-mod
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Dodgson
> yes
> ?
> ?
> yes
> no
> no
> no
> no
> 
> Fishburn
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Hare
> yes
> yes
> yes
> no
> yes
> no
> no
> no
> 
> Kemeny
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Max-Tourneys
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Nanson
> yes
> yes
> yes
> yes
> yes
> yes
> no
> no
> 
> Niemi-Riker
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Plurality
> yes
> no
> no
> no
> no
> no
> yes
> no
> 
> Plurality-w/runoff
> yes
> yes
> no
> no
> yes
> no
> no
> no
> 
> Regular-Champion
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Schwartz
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Sister
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Smith
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Smith//Borda
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Smith//Bucklin
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Smith//Condorcet
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Smith//Plurality
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Qualified-Champion
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Qualified-Kemeny
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> yes
> 
> Young
> yes
> no
> no
> yes
> no
> no
> yes
> no
> 
> 
> 5
> 
> 
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