Reply to Bruce re: Report

[Mike Ossipoff]

Lowell Bruce Anderson writes:
> 
> Steve:
> 
> I think you made wise decisions concerning what to include in (and what to 
> leave out of) the election-methods-list report.  Congratulations.
> 
> For whatever they're worth, I have a few minor suggestions.

Discusion & debate are of much worth, and I would like to say why
I disagree with Bruce's suggestions.

Briefly, it's that I want to remind Bruce that we aren't writing
to a mathematical journal. We're writing to a list that kicked us
off the list because our discussion was too technical. We're
writing to a list that is specifically discussing _public_ voting
methods. Our report to them is specifically about what to propose
to the public for public political elections.

Therefore, we _don't_ want or need to confuse the language by
calling the Smith set a nonempty set. Sure, to a nitpicking
mathematician, the Smith set might not be the smallest set
of alternatives, if the empty set is (questionably) regarded
as a set of alternatives (it isn't a set of anything, is it).

And it would make no sense, given the purpose of our report, to
horribly confuse the subject by talking, in that report, about
pairwise ties. Bruce told me much about small elections, with few
voters, a topic that I hadn't found out anything about till 
corresponding with Bruce. I hadn't, for instance, heard of
the Schwartz set, and it was Bruce who informed me about it.

Yes, I agree that it would be a good idea to also inform ER about
methods for small elections, and about the special aspects &
problems of small elections, since, as Bruce pointed out, electoral
reformers, including the ones on ER, are often holding single-
winner elections in small committees. Absolutely. But it should
be a different report, _after_ our current report on the recomendation
for public proposals for public elections.

I'm not trying to make up a new rule at this point. I'm merely
pointing out what the expressed & agreed-upon purpose of the
Single-Winner Committee has always been, and what our report to
ER has been agreed-on & understood to e about.

Now, in case I've missed something, I'll specifically reply to
statements in Bruce's letter:

> 
> First, in the general discussion of Pairwise Methods, I think that you 
> should explicitly define and briefly discuss "pairwise ties."

As I said, pairwise ties are so unlikely in public political
elections, which is what this report is about, and which is what
ER is about, that I claim that we shouldn't bring that up in the
report.

 
> Second, in the discussion of Smith, you should add the word "non-empty" to 
> change:  "(To be more precise, the "best" group is the smallest group which 
> can be found such that..." into:  "(To be more precise, the "best" group is 
> the smallest non-empty group which can be found such that...".

As I said, that's necessary & desirable only if we were writing to
a mathematicians' journal. Everyone knows that the smallest of
set of alternatives such that each alternative in the set beats 
every alternative outside of the set refers to a set that contains
at least one alternative, and is not the empty set. It's questionable
whether it's correct to call the empty set a set of alternatives, but
in any case, there's no need to lay that issue on ER.

> 
> Third, you should change:  "...the winner is the candidate..." to:  "...the 
> winner(s) is/are the candidate(s)...", and change "elects the candidate 
> whose largest pairing-loss is..." to:  "selects the candidate(s) whose 
> largest pairing-loss is...", and so on, everywhere that a tie is possible.  
> I agree that such ties will be rare in large public elections.  However, I 
> think that the use of "good" single-winner voting methods is quite important 
> in many different voting situations, not just in large public elections.  
> For example, many votes are taken in governmental and quasi-governmental 
> voting situations by:  legislatures, councils, committees, subcommittees, 
> boards, panels, commissions, juries, delegations, etc.  Many of these 
> "smaller" voting situations could easily result in ties.  Though perhaps not 
> as important, similar comments can be made about votes taken in private 
> voting situations.  Moreover, in some private voting situations, the entire 
> electorate could be relatively small, which, of course, increases the 
> likelihood of ties.  Finally, I think that people will generally want to 
> examine small examples and run small test cases before they adopt a new 
> voting method for large public elections.  Again, ties may be likely.  Note 
> that by "ties" here I do NOT just mean cases in which exactly 1/N of the 
> voters rank each of N candidates as being their unique ith choice for all i 
> from i=1 to i=N, and N > 1.  I also mean, for example, cases in which 
> Smith//Condorcet would result in a tie, but Smith//Condorcet//Plurality 
> would not, and cases in which
> Smith//Condorcet//Plurality would result in a tie, but 
> Smith//Condorcet//Plurality-ext would not.

No! For the reasons I've given. What we could do is, mention,
offhand, that, as a matter of formality, an electoral law could
specify that, as highly improbable as a tie is, it shall be solved
by Plurality. But our current voting rules don't specify a different
method or count rule to solve ties, so why should we?? No, we shouldn't
even bring it up. 

Remember that we're only talking about which method is better; we're
not writing the electoral law! And even if we were, it would be
doubtful whether there needs to be a rule for ties, since, as I
said, there now isn't a rule for using a different method if there's
a tie. I don't know--maybe there's an obscure, never-used, rule
to draw lots in the event of a tie. Fine, when writing an electoral
law we could simply leave that part in. So I oppose even adding
Plurality, or (especially) Plurality.ext to an electoral law
proposal.

> 
> Finally, I think that names like Condorcet are in the public domain, and so 
> it's quite reasonable for you to define "Condorcet's method" one way and for 
> Hugh or me to define it slightly differently (e.g., differently only when 
> ties or truncations occur on voter's ballots), just as long as we always 
> clearly state the definitions we are using.  However, I think that when 

As long as you call it "Condorcet(Tobin)" or "Condorcet(Anderson)"
in cases where you've proposed something that conflicts with Condorcet's
own proposal, or differs from it in a way that adds something that
makes a quite different method, as opposed to merely an interpretation
of what "least beaten" means, or other wording in Condorcet's 
definition. When you propose adding a rule to count un-voted
preferences, you're crossing the line in the sense of adding
something completely external to Condorcet's proposal, which didn't
provide for inventing un-expressed preferences.

"Condorcet's method" is not in the public domain to that extent,
though there's nothing wrong (probably) with naming a method
"Condorcet (Anderson)" to denote that it's Condorcet's method
plus something entirely different. So I don't object to the
name Condorcet(Tobin).


> someone makes up a name that is clearly "brand new" in voting parlance, then 
> others ought to either ignore that name or to use it has its originator 
> defined it.  In particular, I made up the name "Regular Champion," and I 
> defined it to be:  [Copeland]//[Plurality-ext]//Random, not 
> Copeland//Plurality.  If you want, you can ignore Regular Champion, and 
> (say) discuss Copeland-Plurality instead.  Alternatively, if you want, you 
> could declare that every voting method you discuss is to automatically be 
> read as ending in "//Random", in which case you could say that Regular 
> Champion is [Copeland]//[Plurality-ext].  But Regular Champion is not 
> Copeland//Plurality.  My objection here is purely definitional, it does not 
> affect the recommendations.

Steve, we have no choice but to comply with that request, because
Bruce has a right to insist that a metahod that he's named be defined
only as he's requested. I suggest that follow his suggestion to
replace "Regular Champion" with "Copeland//Plurality". We can say,
if desired, that Copeland//Plurality is a version or interpretation
relevant to the purpose of our report, a version of a more
complicated & general method propsed by a mathematician. Or we
could just change "Regular Champion" to "Copeland//Plurality",
wherever that name occurs in our report. There's no democratic problem
about that, because when we discussed & voted on what we were calling
"Regular Champion", we all understood that we were talking about
Copeland with its (frequent) ties solved by Plurality. We could,
then, merely change the name in the report, without having to
talk about a more complicated version that isn't really what we
discussed & voted on, and which isn't necessary in regards to
public elections. So I'm claiming that Copeland//Plurality & not
Regular Champion, as Bruce defines it, is what we've been talking
about & voting on.


> 
> Bruce
> 
> .-
> 
Mike


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