[EM] In effect and in voting theory, Plurality is a rankings method.

[Chris Benham]

Mike,
This is the full text of  Steve Eppley's  discussion/definition of   his 
 "Minimal  Defense" criterion from which  Marcus Schulze copied:

minimal defense 
<http://www.alumni.caltech.edu/%7Eseppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm>:  
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. (Another 
        wording is nearly equivalent: 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.  
        This criterion, in particular the first wording, is promoted by 
Mike 
        Ossipoff under the name Strong Defensive Strategy Criterion.  
        Satisfaction means a majority can defeat "greater evil" 
alternatives 
        without having to pretend to prefer some compromise alternative 
        as much as or more than favored alternatives.  Since voters in 
public 
        elections cannot be relied upon to misrepresent their preferences 
        in this way, non-satisfaction means that elites will sharply 
limit the 
        set of nominees that voters are asked to vote on, by offering a 
system 
        in which there are only two viable parties, each of which nominates 
        only one alternative.)

CB: I must say I greatly prefer the "nearly equivalent" wording as being 
much more concise, simple and reasonable-sounding.

Earlier  (Fri.Feb.6) I wrote:

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.

To which you replied (Fri.Feb.6):

""Equivalent to [in some particular specified regard]"  most definitely does 
not mean "is"."

"First Preference Plurality" (as Woodall calls it, a name I prefer to "ranked Plurality")  is not just
 equivalent to Plurality "in some particular specified regard". It is equivalent in EVERY regard that
is of interest to voting theorists. It transmits voted preferences into a result identically, and is 
therefore of course strategically equivalent. 
This (Tue.Jul.15,03) quote from Alex Small in the "Arrow's Theorem" thread is of some relavence/interest:

"In the formal derivations of Arrow's Theorem that I've seen, an election
method is defined as a mapping from the set of voter preferences to the
set of candidates.  Show me the preference order of each individual voter,
and (barring the case of ties) I'll show you who the winner is.  No
ambiguity."

You wrote:
"Your unproposable method is "equivalent" to Plurality in the sense that both 
only count indicated favorites. But because different voting is admissible 
in the 2 methods, they are not the same method, in keeping with your own 
definition of "admissible"."

For the purpose of rationally analysing voting methods, the fact that "different voting is admissable" 
is only relavent if that can possibly give a different result. (And then it is only interesting if it
makes a different viable strategy available,like equal ranking in RP versus equal ranking not allowed
in RP.)
In FPP, the only restriction on vote admissabilty that is relavent is that the voter can mark as 
favourite one candidate only. Obviously it makes no difference whether voters are not allowed to enter
lower rankings or are compelled to enter lower rankings or anything in between.

By way of a contrasting example,there is a horrible method called "the Supplementary Vote" (is or was
used to elect the Lord Mayor of London in the UK), which is a version of IRV that restricts voters to
voting a single first and a single second preference. Obviously, with four or more candidates, this is 
not equivalent to IRV because it can give a different result.

Chris Benham







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