[EM] strong defensive strategy criterion
Steve Eppley
seppley at alumni.caltech.edu
Mon Oct 18 09:18:08 PDT 2004
Hi,
James G-A wrote:
> I suggest that ordinary winning votes methods (beatpath,
> ranked pairs, river, etc.) fails Mike Ossipoff's "strong
> defensive strategy criterion", according to what I think
> is the most reasonable interpretation of that criterion,
> whereas cardinal pairwise passes the criterion.
-snip-
To conclude that James' interpretation is most reasonable,
I think one must take Mike's words out of context, since
elsewhere Mike wrote that truncating a preference shall
_not_ be considered falsely voting two candidates equal.
But I'm just nitpicking, since there's a legitimate
question as to which version is the better criterion.
James' version appears to me to be equivalent to my
"sincere defense" criterion, which can only be satisfied
if the voting method is more complex for the voter than
merely expressing an order of preference. The added
complexity means it may not be a better criterion.
It depends on what the voters can handle and will
tolerate...
The cardinal pairwise strategy James suggested for the
majority trying to ensure x cannot win, which involves
giving a rating of 100 to some compromise y they all
prefer over x, raises the question whether voters can
be relied on to carry it out. Giving a maximal rating to
a compromise candidate is similar to ranking a compromise
equal to one's favorite--the "nondrastic defense strategy"
--and voters may be similarly reluctant to do it. It
might be inconsistent with the spirit of SDSC to rely
on voters to misrepresent upward their rating of the
compromise candidate.
Long ago when I wrote about the sincere defense criterion
and several families of voting methods that satisfy it,
all of which allow the voter to optionally insert a
dividing line somewhere in her order of preference,
I stressed that the dividing line should NOT be interpreted
as an approval/disapproval line; it should be publicized
as a strategic device that does not correspond to any
sincere preferences. Some voters (e.g., supporters of
Ralph Nader) may be reluctant to use it appropriately
if they believe its strategically optimal usage would
be interpreted as an expression of "approval" of a
"lesser of evils." If the dividing line is entirely
strategic, then no matter where the voter places it
it will not be considered a misrepresentation of
preferences.
> According to Steve Eppley's wording of the criterion,
> under the name "minimal defense", winning votes Condorcet
> does indeed pass. This is because Steve's definition says
> that the majority can't falsify a preference regarding
> the higher-ranked candidate, but it doesn't say that
> you can't manipulate other preferences.
>
> Steve's minimal defense criterion:
> "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.)"
>
> Steve's definition is a weaker criterion. Winning
> votes meets Steve's criterion but not my interpretation
> of Mike's criterion; cardinal pairwise meets both.
> Other anti-strategy add-ons to the pairwise method,
> such as Mike's AERLO and ATLO, will probably also
> meet the stricter definition of the criterion.
The second wording of minimal defense (which I described
as "nearly equivalent") is not strictly weaker than sincere
defense; it's different. It specifies a particular simple
voting strategy that must be effective and does not mention
any input beyond orders of preference. I don't recall the
definition of James' cardinal pairwise method, so I cannot
say whether it satisfies the second wording.
--Steve
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