[EM] (P1) tweak up ... Québec Ombudsman, "rank"

Craig Carey research at ijs.co.nz
Tue Feb 1 13:55:56 PST 2000

At 15:04 01.02.00 , Blake Cretney wrote:
>Craig Carey wrote:
>> >1.  Check to see if any candidates get more than 1/3 of the 1st
>> >preferences.  If not, the winner is the candidate with the most 1st
>> >preferences (like FPP).  Otherwise, go to step 2.

(s1) If all candidates 1st pref counts were <1/3 then pick the FPP winner;
(s2) If any candidate 1st preferences were >1/3 then:

>> >2.  Eliminate all candidates with 1/3 or under of the 1st
>> >preferences.  These candidates are eliminated from ballots in the same
>> >way candidates are eliminated in AV.
>> >3.  Hold an AV election between the remaining candidates.
>> > 
>> >Is there any part of that procedure that you do not view as
>> >sufficiently defined?
>> Suppose there are 20,000 candidates. It is highly unlikely that any
>>  would get more than 1/3 of the vote. Very unlikely. Rather than the
>>  method becoming incomprehensibly adequate at recovering support
>>  at deep preference levels, it just pick the FPP winner, i.e. it
>>  ignores all preferences after the 1st.
>I never said that AVQ was better than AV, or than I advocate AVQ. 
>However, it is true that AVQ passes P1, while AV does not.

I can't believe that it passes P1. But the method is resisting my
 analysis and eally, it can't be overstated just how little an
 improvement this is, over First Past the Post.

However lower down, it is said that it just an example devised to
 show that a method can pass P1. I was losing time on attempting to
 prove it was actually failed by P1, and nothing to show.

>> ...
>> >> Ideally the 100th preference should if possible,
>> >> have the same power and influence as a first preference, contrary
>> >> to the nature of STV.
>> >
>> >Methods that consider candidates two-by-two (pairwise) have this
>> >property.  I'm going to describe such a method further down.
>> Condercet has that other problem of not finding enough winners.
>I didn't even say "Condorcet".  I just said pairwise methods.
>> >> Condorcet is a method that returns the wrong
>> >>  number of winners. As far as it goes (which isn't far) , it satisfies
>> >>  (P1).
>> >
>> >When I said Condorcet-type methods, I meant methods that meet the
>> >Condorcet criterion.  There are lots of suggested methods along these
>> >lines, however, I am going to describe one of the better ones,
>> >Tideman's method.
>> >
>> Now that AVQ was lost into history as a failed method ...
>AVQ was designed to answer the question, "Are there any methods other
>than FPP that pass P1?"  It serves this purpose very well.  I also
>think it compares well with FPP and AV.

I am onto this now: AVQ is not suitable for use in reality. It is my job
 to attempt to prove it is failed by P1.

I have no doubt that a fully defined method for every number of candidates,
 that satisfies P1, exists.

AVQ puts a slice based on 1st preference counts and it may fail
 alterations where the 1st 1-2 preferences are unchanged.


I was on the wrong track: Blake wasn't defining a method.

>> >Compare every candidate to every other to get one-on-one (pairwise)

That is n*(n-1) (or n**2) comparisons, (n = number of candidates).

>> >majority decisions.  That is, if there are candidates X and Y, you
>> >would find out how many people rank X over Y, and how many rank Y over

Then there would be n*(n-1) Boolean values (or [from coments below]
 maybe n**2  3-valued values).

>> >X.  Then, the candidate with more votes is said to have a majority
>> >over the other, with a margin of whatever the difference is.

A list of Booleans was constructed and then we need to find some
 "more votes".

>> >
>> >For example, if 30 people vote X over Y, and 20 vote Y over X, I will
>> >say that X has a majority over Y with a margin of 10.  
>> >
>> There are 5 cases. You actually ignored two cases:
>> .......
>> ...X...
>> ...Y...
>> ..X..Y..
>> ..Y..X..
>> I do not know what is to be done with papers marked (...X...).
>I don't understand.  What do you mean by a paper marked "(...X...)". 

There are 5 possibilities. Any one of those possibilities can occur,
 so unless you rule some out, they can all occur.

>Has Y somehow been omitted from the paper?  If the voter has left Y
>unranked, then that is usually interpreted to mean that the voter has
>implicitly ranked it under all the explicitly ranked candidates.

You have the word rank both (1) limit possibilities, and (2) it is
 also a Boolean applied to the list held on a single paper.

 If this is to become a method or a rule then there is an existential
 logic "for all"  or "there exists" operator. That could be a method
 of actually adding votes. We are going to need an i<>j term?. A
 function ("rank") should not limit the possible values its argument
 can take, unless formula returns an undefined result or whatever and
 absolutely no progress can be made until that is spotted.

The definition of the word "rank" seems flawed.

I regard your statement "usually interpreted ..." as extremely
 controversial if it means that point need not be noted. For example,
 if a paper is altered from (ACB {DE) to (AC {BDE), then B can win
 the first and lose the 2nd. I presume a new method is being built
 on the foundation well understood but still missing definition of
 the term rank. The Blake-C "rank" of B with respect to all other
 candidates if totally invariant under that alteration just above,
 yet presumably in a best possible method, the win lose state of B
 can alter. 

The idea of rank (copied from Condorcet theory, is it?) is not friendly
 with rules such as (3:AB) = (1:ABC,1:ABD,1:ABE) if the candidates are
 {A,B,C,D,E}. That is in my opinion, easily enough to allow a rejection
 of summing ideas borrowed from Condorcet. 

Instead of Blake writing "usually interpreted", i.e. usually assumed,
 it might be truer to write "usually not assumed" (lots pof people
 use STV and when a subsequent preference names B, then that can
 improve B's chance of winning.

Who would agree that there need not be clear 'explicitness' about
 a "usually" present assumption when that assumption will rule out a
 set of best or near best methods.

Condorcet style assumptions should not be implicit. Mr Catchpole and
 I have sent a large quantity of words into this mailing list that
 were over nothing but a refusal to define ideas because they were
 similar to ideas taken from Condorcet styles methods. A perfect method
 seems to not ever follow if they get assumed. The problem has nothing
 to do with Condorcet but more to do with the dislike of mathematics
 that upholders of the Condorcet idea tend to have.


The author wrote:

>Has Y somehow been omitted from the paper?  If the voter has left Y
>unranked, then that is usually interpreted to mean that the voter has
>implicitly ranked it under all the explicitly ranked candidates.

Here are all the 205 possible papers in a 5 candidate election (with
 the last preference being omitted). There clearly observable instances
 where a candidate able to be represented by a variable named Y, is
 indeed missing. So Y can somehow be omitted from a paper.

{{A}, {A,B}, {A,B,C}, {A,B,C,D}, {A,B,C,E}, {A,B,D}, {A,B,D,C},
{A,B,D,E}, {A,B,E}, {A,B,E,C}, {A,B,E,D}, {A,C}, {A,C,B}, {A,C,B,D},
{A,C,B,E}, {A,C,D}, {A,C,D,B}, {A,C,D,E}, {A,C,E}, {A,C,E,B},
{A,C,E,D}, {A,D}, {A,D,B}, {A,D,B,C}, {A,D,B,E}, {A,D,C}, {A,D,C,B},
{A,D,C,E}, {A,D,E}, {A,D,E,B}, {A,D,E,C}, {A,E}, {A,E,B}, {A,E,B,C},
{A,E,B,D}, {A,E,C}, {A,E,C,B}, {A,E,C,D}, {A,E,D}, {A,E,D,B},
{A,E,D,C}, {B}, {B,A}, {B,A,C}, {B,A,C,D}, {B,A,C,E}, {B,A,D},
{B,A,D,C}, {B,A,D,E}, {B,A,E}, {B,A,E,C}, {B,A,E,D}, {B,C}, {B,C,A},
{B,C,A,D}, {B,C,A,E}, {B,C,D}, {B,C,D,A}, {B,C,D,E}, {B,C,E},
{B,C,E,A}, {B,C,E,D}, {B,D}, {B,D,A}, {B,D,A,C}, {B,D,A,E}, {B,D,C},
{B,D,C,A}, {B,D,C,E}, {B,D,E}, {B,D,E,A}, {B,D,E,C}, {B,E}, {B,E,A},
{B,E,A,C}, {B,E,A,D}, {B,E,C}, {B,E,C,A}, {B,E,C,D}, {B,E,D},
{B,E,D,A}, {B,E,D,C}, {C}, {C,A}, {C,A,B}, {C,A,B,D}, {C,A,B,E},
{C,A,D}, {C,A,D,B}, {C,A,D,E}, {C,A,E}, {C,A,E,B}, {C,A,E,D}, {C,B},
{C,B,A}, {C,B,A,D}, {C,B,A,E}, {C,B,D}, {C,B,D,A}, {C,B,D,E}, {C,B,E},
{C,B,E,A}, {C,B,E,D}, {C,D}, {C,D,A}, {C,D,A,B}, {C,D,A,E}, {C,D,B},
{C,D,B,A}, {C,D,B,E}, {C,D,E}, {C,D,E,A}, {C,D,E,B}, {C,E}, {C,E,A},
{C,E,A,B}, {C,E,A,D}, {C,E,B}, {C,E,B,A}, {C,E,B,D}, {C,E,D},
{C,E,D,A}, {C,E,D,B}, {D}, {D,A}, {D,A,B}, {D,A,B,C}, {D,A,B,E},
{D,A,C}, {D,A,C,B}, {D,A,C,E}, {D,A,E}, {D,A,E,B}, {D,A,E,C}, {D,B},
{D,B,A}, {D,B,A,C}, {D,B,A,E}, {D,B,C}, {D,B,C,A}, {D,B,C,E}, {D,B,E},
{D,B,E,A}, {D,B,E,C}, {D,C}, {D,C,A}, {D,C,A,B}, {D,C,A,E}, {D,C,B},
{D,C,B,A}, {D,C,B,E}, {D,C,E}, {D,C,E,A}, {D,C,E,B}, {D,E}, {D,E,A},
{D,E,A,B}, {D,E,A,C}, {D,E,B}, {D,E,B,A}, {D,E,B,C}, {D,E,C},
{D,E,C,A}, {D,E,C,B}, {E}, {E,A}, {E,A,B}, {E,A,B,C}, {E,A,B,D},
{E,A,C}, {E,A,C,B}, {E,A,C,D}, {E,A,D}, {E,A,D,B}, {E,A,D,C}, {E,B},
{E,B,A}, {E,B,A,C}, {E,B,A,D}, {E,B,C}, {E,B,C,A}, {E,B,C,D}, {E,B,D},
{E,B,D,A}, {E,B,D,C}, {E,C}, {E,C,A}, {E,C,A,B}, {E,C,A,D}, {E,C,B},
{E,C,B,A}, {E,C,B,D}, {E,C,D}, {E,C,D,A}, {E,C,D,B}, {E,D}, {E,D,A},
{E,D,A,B}, {E,D,A,C}, {E,D,B}, {E,D,B,A}, {E,D,B,C}, {E,D,C},
{E,D,C,A}, {E,D,C,B}} 

Nothing new in the listing above. It was produced by a REDUCE program.

>It is quite possible that the paper ranks X and Y as equal, either
>explicitly (if this is allowed), or by leaving them both unranked (if
>this is allowed).  In that case, the vote is not counted either as
>ranking X over Y, or Y over X, since it doesn't do either.
>> Also, until you add the word "Condorcet" (or whatever), there is no
>>  summation of counts on papers. 
>Is this a complaint?  You'll have to rephrase this, because I have no
>idea what you mean.

It seems to me that I am in error because you have not yet got to
 introduce any summing. However that is done immediately below, where
 you write:
  << I also use the word "rank" to apply to the final result. >>

>> The word "rank" can only apply to a single paper (since it is
>> defined for [3 of the 5 cases for] a single paper). 
>I also use the word "rank" to apply to the final result.  As in, the
>method ranks candidate A over candidate B.  Often it is desirable to

The "final result" is a set of winners (or a Boolean value for each
 candidate). Now there are 4 cases (for each pair is distinct
 candidates) and 2 of them are undefined and the other two are probably
 obvious. There is a problem with the definition, and yet another
 problem if meaning of the word "ranking" which is used in deriving a
 set of winners, is dependent on the set of winners not yet found.

There is just an overloading of meaning onto the single word, "rank".

>get a complete ranking of the candidates by the method.  This complete
>ranking is essentially a bi-product of Tideman's method.
>> Your definition above seems to not contain the
>>  idea of adding counts of papers.
>I really think you must be reading too much into this.  Let's say I
>have the following votes
>40 A>B>C, meaning 40 ballots rank A over B over C
>35 B>A>C
>25 C>B>A
>40 voters rank A over B.  35+25=60 rank B over A.  So, I say that B
>has a majority over A with a margin of 20.

Z(x,y) = (Sum p) . Z(p)*(if (x<>y) & (x in tr(p,y)) then 1 else 0);
M(x,y) = Z(x,y) - Z(y,x).               [ p is a paper. x,y are candidates
Notation: "tr(p,x)" means truncate list p just x (or else including x),
  if x is in p, otherwise don't truncate. "in" autoconverts lists to sets.

Blake: you could have made less mistakes and reduced controversy and
 defined the matter a lot better in 4 lines.

I shall leave Tideman theory up to others and just not reply because
 because I suspect the other members of the list are going into the
 cave after a total dead end (or loser).

I see you noted that ties are comparisons of real numbers and not
 a comparing of sums of Booleans (once represented as either 0 or
 1). So ties are a rather trivial subject during the derivation of
 a final method (unles someone says only smallish integers are allowed).


>> Here's another argument for STV and all similar methods (i.e. about
>>  STV) (any number of winners).
>> * * *
>> It seems to me that proportionality mops up degrees of freedom, and the
>>  only other important reality is what a voter can detect when in the
>>  voting booth. They don't understand that LIIAC is important. That is
>>  a sort of rule that a method designer might (falsely) allege important.
>Just because voters don't understand a criterion doesn't mean it
>isn't important.  Voters have never heard of GITC, but they are

I would suggest that if a restriction is not proportionality and a voter
 doesn't understand it, then it is not actually going to be allowed to be
 an axiom (in any theory of mine). Like open government, marking a paper
 in a voting booth ought be as transparent as is possible. The last 5
 words rule out LIIAC. That is the much-missing IFPP theory.

>There are three major kinds of strategic voting (as far as I know).
>Burying-  Lower a candidate (with respect to sincere placement) in
>the hopes of defeating it.  This is what SPC prevents.

>Compromising- Raise a candidate in the hopes of electing it.  This is
>impossible to eradicate in a non-random method, but some methods are
>more affected than others.

These two seem to be wrongly defined. Compromising is defined twice
 with different definitions. I read and deleted the following.

>Of course, we should also question whether strategy should be our
>only consideration, or whether a method might be less strategically
>influenced, but still be rejected on the grounds that its decisions
>are poor when people vote sincerely.
>> However, one can get an invariance of the winner set on altering
>>  trailing preferences. So that (named "SPC" in this list) may as well
>>  be done. SPC is an easy constraint to meet, and a major method (STV)
>>  satisfies it.
>First, you keep mentioning STV.  Can't we restrict the discussion to
>single-winner methods, like AV and Tideman?  Second, I see no evidence
>that SPC is easy to meet.  It's certainly easy to find methods that
>meet it, FPP comes to mind, but it seems to conflict with other
>criteria, which may be more important.  In general, I think it is wise
>to be slow to accept a criterion as necessary.  

SPC is easy to meet.


You don't know what is important?. Perhaps rules could be questioned and
 criticised by non-experts on the grounds of their absence of presence of
 "transparency of decision making (by the formula)".

What getting the axioms devised in such a way that a voting paper
 could have, on the back of the sheet, a statement saying what the
 axioms are. It could say that proportionality is maximised but subject
 to these rules; then list the axioms.

What axioms do voters want to have on the back of the sheet(s)?.

The AV axioms that haphazardness is pretty random?.

The last thing on their mind is getting a good electoram method that
 elects other people's choices.

What voters would want and ought get is rules excluding stupid changes
 in the outcome when they alter their paper.

Blake, PR consultant: suppose you were being paid to develop a method
 and you were told that you had to explain your method on the back of
 every single voting paper.

(Proportionality can be difficult to explain: There has to be some
 method doing something like pairwise comparing with actually doing
 that. In IFPP it would be done by using results from embedded
 subproblems. That is going to be more proportional than Condorcet
 syle summing would get, since the latter conceals constraints....)

If a voter happens to peep at the back of a voting paper, would
 they want to want to see a dinosaur dog dinner of LIIAC global
 outcome theory; or Condorcet "BC ranking" theory substituting for
 where an idea of proportionality should be.

My suggestion is: only what interests voters, and politicians get
 nothing but proportionality.  (except for (2:A)=(1:AB,1:AC), and
 possibly anything else)

Lack of openness about every axiom on which a method electing a
 goverment is based is not suitable for a democratic society.

For the many others that write to the list, I have quoted a
 paragraph on FOGBOUND thinking

- - - - - -


"When it comes to government affairs, citizens want OPENNESS.
 They want to know the motivations for the decisions affecting them
 directly, the criteria guiding government policy making, the
 guidelines for the awarding of contracts, etc."

- - - - - -



 Each year, thousands of people call on the Québec Ombudsman because
 they find the government impenetrable. Openness in dealings between
 public authorities and the people is nothing less than one of the
 main pillars of life in a democracy.


With nearly 30,000 complaints received each year by the Québec
 Ombudsman, the reasons people are dissatisfied with government
 are -- obviously enough --wide and varied, if not always
 justified. The variety of complaints does not, however, imply a
 variety of causes -- often, the root cause is a government
 department blinkered to the needs of its client groups.
 Unintelligible or incomplete information delivered hastily,
 impenetrable voice mail, overloaded telephone lines -- in short,
 explanations that just aren't available. In my opinion, if
 government makes itself unapproachable, it will exist only for
 itself, and citizens will be the last thing taken into

This is the case when a public agency writes to inform people
 they are eligible for financial assistance, telling them the
 amount granted but without providing the criteria and figures
 that would enable them to verify the calculations. The murkiness
 of such a response is compounded by the difficulty of obtaining
 further information since the departments involved are almost
 impossible to reach by phone. And perish the thought that someone
 might want to speak directly with the civil servant in charge!


What is an "open" department or agency?

It is a department or agency that:

 * Facilitates citizen access to public information and services 
 * Makes every effort to provide timely, accurate information that
    is easy to understand 
 * Clearly explains to citizens any decisions affecting them 
 * Says what it will do and does what it says 
 * Freely accounts for its acts or omissions 

- - - - - -

(The Québec Ombudsman Daniel Jacoby)


"3. Explains decisions clearly to citizens
   The Régie des marchés agricoles didn't sufficiently explain its
   decisions about setting milk prices (p. 12)."


How do we get Tideman onto the back of a voting paper?.

The topic of the mailing list is algorithms for making
 decisions about individuals, and it must be entirely
 appropriate for any such algorithm that would decide a national
 election, to come under the consideration of an Ombudsman.

Methods do not make decisions national election outcomes only,
 some methods eill turn a vote for candidate A into a vote
 against candidate A. Monotonicity and similar is not really an

(I usually have problems with merely the definitions given).

Mr G. A. Craig Carey,  research at ijs.co.nz,   Auckland, New Zealand
Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
Multithreaded URL Submit: http://www.ijs.co.nz/submit/submit.htm
MEDLINE search: http://www.ijs.co.nz/med/medline.htm

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