[EM] Plurality (aka FPP) meets "minimal defense" criterion??

[Chris Benham]

  Mike,
On  Mon.Feb.2,04,  you wrote to Marcus Schulze:

"You said:

I would call

   "If more than half of the voters prefer alternative y over
   alternative x, then that majority must have some way of voting
   that ensures x will not be elected and does not require any of
   them to rank y equal to or over any alternatives preferred over y."

the "motivation" of this criterion and

    "Any ordering of the alternatives must be an admissible vote,
    and if more than half of the voters rank y over x and x no higher
    than tied for bottom, then x must not be elected."

the "definition" of this criterion.

I reply:

You said  "...rank y over x". What if the method isn't a rank method? Or 
does your criterion apply only to rank methods? If so, then it isn't 
equivalent to SDSC.

Or maybe when you said "rank y over x", you meant "vote y over X". Of 
course, when writing a criterion, it's better if you say what you mean. If 
you mean for "rank" to mean "vote", then you've got to tell us what you want 
"rank" to mean.

And you haven't stated a definition for voting y over x anyway.

Maybe you have a definiiton, special for Plurality, that says that if you 
vote for y, then you're "ranking" y over everyone else. But you didn't tell 
us that, and so, again, your definition isn't complete. Additionally, if 
that's what you were trying to say, your definitions require a special 
definition for Pluralilty. None of my definitions require a special 
definition for a particular method. They all apply to all proposed methods, 
without method-specific definitions."

As I understand it, there are only three basic types of voting methods: 
(1)ranking methods (like IRV, Borda, and First Preference Plurality)
(2)rating methods (like Approval)
(3)hybrids of 1 and 2 (like Approval Elimination Runoff, and Condorcet completed by Approval).

Since giving a higher rating to A than to B in a rating method implies that the voter ranks A over B, 
and ranking A over B in a ranking method implies that the voter rates A higher than B, I don't see
any real point in your disinction between "rank over" and "vote over".

Later in the same message you wrote:

"Let me copy your criterion definition here:


    "Any ordering of the alternatives must be an admissible vote,
    and if more than half of the voters rank y over x and x no higher
    than tied for bottom, then x must not be elected."

Say the method is Plurality, and that more than half of the voters vote for 
y. Then x won't win.

Therefore Plurality meets your criterion."

In the first place Plurality doesn't normally allow equal first preferences (the version that does I
have seen referred to as "Single-seat Cumulative Voting"), so therfore it doesn't strictly meet 
"Any ordering of the alternatives must be an admissable vote". 
(BTW,"admissable" means "capable of being allowed;permissible", in other words eligible to be counted 
according to the rules of the method.)
In the second place,in ranked methods such as First Preference Plurality,to "vote for y" means to rank
y first and is not the only way to "rank y over x". Take this example:

40:x>y=z
25:y>z>x
35:z>y>x

"More than half the voters rank y over x, and x no higher than tied bottom" and yet x is elected.
Therfore "Plurality" fails this criterion.

It is true that the lower prefences are ignored by the method and so as a convenience to all concerned
they are not entered on the ballots, but that is not relavent to our analysis. If the rules stated
"voters rank the candidates, no equal first preferences allowed, and the winner is the candidate with
the most first preferences", wouldn't that be a "rank method"? A method that is exactly equivalent to
a rank method, in my book *is* a rank method.

As Alex Small put it (Tue.Jul.15,03):
"Plurality does not _need_ preferential ballots, but the results of a
plurality election could be inferred from preferential ballots:  Count the
number of voters who ranked each candidate first.  If the results of an
election method can always be uniquely determined from preferential
ballots, then the method is equivalent to a preferential method, even if
some clever implementation avoids using preferential ballots."

http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-July/010166.html


The thread was "Arrow's Theorem". 

Chris Benham 





  





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