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Russ,<br>
In my last post in this thread, I wrote:<br>
<blockquote type="cite">"A more useful criterion is the normal (as
opposed to Mike-style)
<br>
criterion taken from Blake Cretney's website:
<br>
<br>
Name: Secret Preferences Criterion: SPC
<br>
Application: Ranked ballots
<br>
Definition:
<br>
If alternative X wins, and some of the ballots are modified in their
<br>
rankings below X, X must still win.
<br>
<br>
Condorcet does not pass this criterion, which tells us that voters have
<br>
incentive to truncate in some cases if not routinely."
<br>
<br>
Woodall splits this somewhat oddly-named criterion into two fairly
self-explanatory others:
<br>
<br>
"Later-no-Harm: adding a later preference to a ballot should not harm
any candidate already listed", and
<br>
"Later-no-Help: adding a later preference to a ballot should not help
any candidate already listed".
<br>
<br>
Condorcet passes neither of these, but your conclusion only applies to
Later-no-Harm.
<br>
In WV Condorcet (BP/RP/MM/River), the two LNHs are not in balance
(adding a later preference is more likely
<br>
to help than harm an already listed candidate) so that in the
zero-information case there is a random-fill incentive.
<br>
<br>
As Kevin Venzke just more-or-less pointed out, the right
zero-information strategy in WV is to equal-rank the candidates
<br>
above some ("the") approval cutoff point and to strictly rank
(random-filling if necessary) all the candidates below it.
</blockquote>
You responded:<br>
<blockquote type="cite">Interesting. Your telling me that adding a
preference is more likely to help than harm a higher-ranked candidate? <br>
</blockquote>
Yes.<br>
<br>
<blockquote type="cite">Can you prove that or point me to a proof?
<br>
<br>
<br>
</blockquote>
In the great EM Margins versus Winning Votes (formerly called
"Votes-Against") debate (mainly between Blake Cretney<br>
and Mike O.) it was an undisputed point on the Margins side that in
WV in general adding more votes to the winning side <br>
of a pairwise comparison harms the loser more than it helps the winner.<br>
Suppose there are 3 candidates and the voting method is MinMax (WV) or
one of the equivalent methods. If the voter's<br>
favourite has a pairwise loss, then that candidate can only win if each
of the other candidates also have a pairwise loss and<br>
if the pairwise comparison lost by the voter's favourite is the one
with the fewest votes on the winning side. So in that case<br>
a faction of voters that is indifferent between their two
non-favourites does better to not truncate because by increasing<br>
the "strengths" of the non-favourites' defeats they might cause their
favourite's defeat to be the weakest.<br>
<br>
This scenario is more likely than the one in which with truncation
there is a cycle that is won by the faction's favourite, but<br>
random filling causes the candidate that pairwise beats the faction's
favourite to also beat the other candidate and so become<br>
the voted CW.<br>
<br>
Methods that have the two LNHs probabilistically out of balance will
either have a 0-info. random-fill incentive or else <br>
(say for voters with a big enough gap in their sincere ratings of the
candidates) a 0-info. truncation incentive.<br>
One of Woodall's criteria/"properties" is "Symmetric-Completion". <br>
<br>
"Symmetric-Completion: a truncated ballot should be treated in the
same way as its symmetric completion.<br>
(The symmetric completion of a ballot is obtained by replacing it by
all possible completions of it with equal weight, chosen so<br>
that the total weight is 1. For example, if there are five candidates
a,b,c,d,e, then the symmetric completion of a ballot marked<br>
ab consists of six ballots, each with a weight of 1/6, marked abcde,
abced, abdce, abdec, abecd, abedc.)"<br>
<br>
IMO this isn't really a big deal in itself, but it seems easy to check
and it implies No Zero-Information Strategy (NZIS), without<br>
being a prerequisite for it. It is met by Margins and IRV, as well as
my two current favourite Condorcet plain ranked-ballot methods:<br>
SCRIRVE and Woodall's CNTT,AV.<br>
<br>
<blockquote type="cite">And what if equal rankings are not allowed?
</blockquote>
Then WV Condorcet couldn't meet Steve Eppley's "Non-Drastic Defense"
criterion (and probably a similar one of Mike O.'s).<br>
<br>
<p style="margin-left: 30px;"><b><i>Non-Drastic Defense</i>:</b> Each
voter must be allowed to vote as many <br>
alternatives as s/he wishes tied for top, and if more than half of the
voters <br>
vote some alternative <i>y</i> (tied for) top, then no alternative
voted below <i>y</i> <br>
by more than half of the voters may be chosen.<br>
<br>
<a class="moz-txt-link-freetext" href="http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm">http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm</a><br>
</p>
I'm not sure that would be a huge loss.<br>
<br>
<br>
Chris Benham<br>
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