[EM] Droop fails the Markus Schulze Rule

[Craig Carey]

At 22:57 19.10.99 , Markus Schulze wrote:
>Dear Craig,
>
>you wrote (19 Oct 1999):
>> At 21:16 18.10.99 , Markus Schulze wrote:
>> > I want to add that (in so far as most election methods don't
>> > guarantee that a voter cannot be punished for going to the polls
>> > and voting sincerely) the concept of wasted votes cannot really
>> > be used as a criterion. It is only a heuristic like Blake
>> > Cretney's aim to find the "best guess for the best candidate."
>> > The reason: The concept of wasted votes implicitly presumes that
>> > every voter wants to be counted; but a voter who worsens the
>> > election result (by going to the polls and voting sincerely)
>> > rather wants to be ignored than counted. This is also the reason
>> > why Michael Dummett rejects the concept of wasted votes.
>>
>> When a voter casts a vote, that vote shifts the point
>> representing the election outcome by some amount towards the
>> point representing the voter's vote. Given that the point of
>> the election outcome exists if the voter does vote, then if the
>> voter doesn't turn up and vote, the voter is effectively casting
>> a negative vote and the election's point goes back to where it
>> was. So not voting is little different from voting, in that the
>> point representing the election outcome is moved by some distance.
>>
>> Mr Schulze may be wrong when saying voters want to be ignored:
>> That seems to presume that the voter has not got a full knowledge
>> of the method and the paper counts. Some of the persons advocating
>> their positions had a knowledge of an instance where number made
>> their stance correct.
>
>Do you question that some election methods sometimes punish voters
>for going to the polls and voting sincerely? Or do you question that
>a voter rather wants to have no influence on the election result than
>to worsen the election result?
>
>Markus Schulze

---------

There are two questions. To the first I reply: no, election methods
 can punish voters for voting. A proof could involve an analysis of
 voting method devised to allow the proof to proceed easily, e.g.
 a method too defective to be used in practice.

To the second question, I'd reply:
 The topic is about individual humans (unless programs in some
 electoral methods contest with strategic voting done by programs),
 and what they want. They have not got a perfect knowledge of the
 paper counts or ratios, during a actual vote. Either they'll
 risk doing the wrong thing, or there is no risk, or an analysis
 of the election has been made. What happens in practice is that
 voters cast votes in a way they themselves could say not optimal
 if later given all the facts. But the more that get the facts
 after the election, the less accurate the election outcome data
 would be.

I am one of those that write to this list that take the opinion
 that the intent and wishes and hopes and concerns of voters,
 and their individual and collective will, their futures, their
 disliking for rain, and ultimately, their humanity in crises like
 the Labrador dog being profoundly sick, should be absolutely
 and totally ignored. Is that how it is in your region of the
 world Mr Schulze?.

I have yet to find a method or formula that actually contains a
 'term' representing voters wishes. The Borda method doesn't have
 such a term, and some of these STV experts could give an opinion
 about that method.

You wrote "do you question that a voter rather wants...".
 Why use the word "wants" ?.
 How is that idea used twice so that it becomes more than an idle
 and fruitless definition?. 
The estimation of the quantity of wants not only creates a basis
 asking for involvement of statisticians, but psychologists too.

Mr Schulze most definitely did use the word wants, and maybe it
 had a special meaning that did not include the usual English
 meaning of the word "want".

It is simple to replace it: For example, if the set of winners in
 an election are {B, E, G}, and if a preferential voting paper
 under consideration is (A B C D E F), then the election outcome
 satisfies the paper by this amount given by this number:

(A wins)+(B wins)/2+(C wins)/4+(D wins)/8+(E wins)/16+(F wins)/32
= 0 + 1/2 + 0/4 + 0/8 + 1/16 + 0/32
= 9/16.

For a single paper only, different outcomes (sets of winners)
 could be compared.

(Replacing a "voter" with the competing concept: "voting paper",
 has a problem quite fixable in the construction of rules, which
 is that more than one voter may have contributed to a single
 paper's count.)

To reply (by commenting) to two messages at once, I note that
 Mr Catchpole had written:

>
>Let Pi(A,B:V) represent the truth of whether voter i prefers candidate A
>over B in voting schema V.
>
>Let W(V) represent the set of winners of voting schema V
>
>For all V, all V', W(V)<>W(V') implies-
>
>there exists i, A, B such that A is an element of W(V), A is not an
>element of W(V'), B is an element of W(V'), B is not an element of W(V),
>not Pi(B,A,V),not Pi(A,B,V')


Quite apart from which of those commas are logical conjunctions and
 which are implication operators, and the seeming excessive weakness
 of the statement, and the pairwise formulation which is best avoided
 since it makes a rule less useful in mathematics, I note the words:

        "...the truth of whether voter i prefers...".

Could "truth" mean an approximation made by Condorcet pairwise comparing?,
 rather than what people tend to understand by that word. A precise
 definition of the use of something that is never known or properly
 defined. That would be OK if the aim was to prevent all progress
 and obscure the cause for that. 

>> let p:A be the list truncated at the preference for candidate A.
>> B beats A in a Condorcet sense if (B in p:A), and 'in' treats the
>>  RHS list as if a set. Whether it is better to have (A in p:A)
>>  or not is not obvious.
>
>This itself is unclear. What do you mean? Does (B in p:A) represent the
>number of voters who favour B over A? Clearly there's a cultural
>difference here which can only be resolved through beginning again from
>first principles and _not_ attempting to express principles solely through
>a quasi set algebra.

Since Mr Catchpole recently sought to minimise the truth that
 "set" theory had a place in preferential voting theory.

Ms Nadine Strossen, president of the US ACLU (American Civil Liberties
 Union) was criticised by Senator Alston in August 1999 for stating that
 Australia was the (or, a) "global village idiot". (I wrote to the
 EFA (Electronic Frontiers Australia) "Stop-Censorship mailing list
 asking for a more believable defence, than the "cultural differences"
 defence made out by the Senator. No one replied.

Set theory in prefeential voting theory:

-----------------------------------------------------------------------
Loading image file :R:\REDUCE\ZIB\fix95\bin\win95\reduce.img
REDUCE 3.6, 15-Jul-95 ...

1: forall w,p let want(w,p)=for k:=1:length(p) sum if member(part(p,k),w) then 2**(-k) else 0;

Declare want operator ?  (Y or N)
?y

2: want({b,e,g},{a,b,c,d,e,f});

 9
----
 32

-----------------------------------------------------------------------
"member(A,S)" = (A in S); "part(p,k)" = p[k].

When people talk about wishes of voters but not numbers like 9/32
 or anythig at all that has to do with ballots, how is that
 compatible with an idea like : 'the counts of the papers decide
 the winners' ?.

Errata:

I had written this:

:If the rule applies to a single paper, then the weight of the
: paper is the distance of the point representing the election
: to the face opposing the paper's vertex. The rule defines a
: region around the election point that extends outwards by that
: distance. (Q1) says that that region shall not intersect a
: win-lose boundary.

That is wrong in that one papers for voters can shift the election
 outcome by the distance allowed by the paper's voting weight, but
 the (Q1) violation does not occur at all win-lose surfaces
 intersecting the region around the outcome's point, but only
 at those win-lose surfaces where the outcome on the far side
 would give a larger (binary) paper-satisfaction (Q1) number.

I note that some countries have privacy laws, and the wishes of
 voters can't be obtained all that easily. There seems to be
 more than enough information about how politicians complain
 about faults in STV of AV. That information does not vary from
 election to election.

I disagree with Mr Donaldson & Mr Round and some others, who
 have been aiming to make arguments by using some process of
 'understanding'. A problem with that particular method of
 reasoning (or thinking), in the case of issues about STV's
 properties, is that STV is complex and a rigourous or adequate
 treatment of how that complexity does not invalidate the
 plausible (or not plausible) understanding-based argument,
 hasn't been occurring. Probably there should be a particular
 reference to all paragraphs in documents that define STV.


__________________________________________________________________
Mr G. A. Craig Carey                   E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
MEDLINE (PubMed), Public Proxies, Multithreaded Add-URL DNSLookup
__________________________________________________________________