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Participants,<br>
James G-A and I have have been discussing his "Voting
Methods:definitions and criteria" page off-list, but James now thinks
it would be a good idea if we took it on to the list,<br>
starting with this my most recent message to him. The quotes are all
of James G-A or myself.<br>
<br>
<br>
<div class="moz-text-html" lang="x-western"> James,<br>
<blockquote type="cite">
<pre wrap="">The plurality criterion might be a good one to add. Should I cite
Woodall for that? If so, which paper of his?</pre>
</blockquote>
Probably this one:<br>
<a class="moz-txt-link-freetext"
href="http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf">http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf</a><br>
<br>
In my message I deliberately referred to a "version" of the Plurality
criterion, because as I recently pointed out in an EM message addressed
to Russ,<br>
Woodall likes to economise on axioms and so doesn't include the
common-sense axiom that two ballots that differ only in that one
doesn't rank the one<br>
candidate the other specifically ranks last should be
treated/interpreted as identical. <br>
<br>
<a class="moz-txt-link-freetext"
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/014958.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/014958.html</a><br>
<br>
["Plurality: if some candidate x has more first-preference votes than <br>
some other candidate y has votes in total, then x's probability<br>
of election must be greater than y's."<br>
<br>
In his papers, Woodall likes to economise on axioms; so doesn't include
<br>
the common-sense axiom that a ballot that leaves one candidate<br>
unranked should be treated/regarded the same as a ballot that ranks <br>
this candidate last and all the other candidates the same.<br>
His "votes in total" refers to explicit rankings in any position.<br>
<br>
Incorporating this axiom, a "version" of the Plurality criterion I
like is<br>
<br>
"If some candidate x is ranked in first-place on more ballots than <br>
candidate y is ranked above equal-last, then y can't win".]<br>
<br>
For me, Plurality and Minimal Defense are the real clinching arguments
that WV is better than Margins (defeat-droppers).<br>
But there are three plain rankings methods that I prefer to
Defeat-Dropper (WV); and they are CDTT,IRV and SCRIRVE and CNTT,IRV.<br>
<br>
<blockquote type="cite">
<pre wrap="">Frankly, I'm not sure if I fully understand LNH and LNH. "Adding a
preference to a ballot must not decrease the probability of election of
any candidate ranked above the new preference." Does that mean adding a
candidate who was previously not listed on the ballot?</pre>
</blockquote>
If by "listed" you mean "ranked", then yes. Sometimes Woodall's
language seems to assume that the candidates' names are displayed
somewhere,<br>
and that voters vote on blank sheets of paper by writing down the names
of candidates the voter wishes to "vote for" in order of preference
with the<br>
highest-ranked at the "top" of the "list", and the most-preferred
also written down "first" (in time). (That explains the "later" in
LNHarm.)<br>
I think at one point Kevin Venzke came up with a "pairwise" version
that is maybe a bit stronger:<br>
"Adding a vote to A's pairwise tally versus B must not reduce the
chance of any candidate winning except B" (my paraphrasing)<br>
<br>
<blockquote type="cite">
<pre wrap=""> So my
LPC is based on Blake's "secret preferences criterion". It seems that LPC
is a good indicator of burying vulnerability, no?</pre>
</blockquote>
In the sense that it is equivalent to complete invulnerability to
Burying, yes But that is a very expensive property that is
incompatible even with Condorcet(Gross).<br>
<br>
<blockquote type="cite">
<pre wrap="">IMO, two "consistency" criteria that are of greater practical importance
<span class="moz-txt-citetags">></span>than the ones you list are "Mono-add-plump"
<span class="moz-txt-citetags">></span>and "Mono-append".
</pre>
<pre wrap=""><!---->
Maybe, I don't know. Again, these criteria are not as widely accepted as
monotonicity, participation, and consistency. They might have some merit,
but I haven't personally discovered it yet.
</pre>
</blockquote>
I don't know how anyone can think that "monotonicity" (aka Woodall's
Mono-raise) is worth mentioning (and/or worrying about) and at the same
time wonder if<br>
these two "have any merit". I personally think that Mono-raise is
nice, but too expensive because its incompatible with Weak Burial
Resistance.<br>
Most of the criteria are "nice" and have at least some strong aesthetic
appeal, and the reason why we don't have a method that meets them all
is that some are<br>
incompatible with others. They all have some "price". Some we insist on
at any price because they are about the fundamental aim of the method.
One of these <br>
for me is (Mutual ) Majority. Others are always on our shopping list
mainly because they are so "cheap", like Mono-add-plump and
Mono-append!.<br>
<br>
<blockquote type="cite">
<pre wrap="">In any case they both should definitely have a higher number than does
<span class="moz-txt-citetags">></span>plain IRV in the "paradoxical" row, and the
<span class="moz-txt-citetags">></span>number for ER-IRV(whole) should be 4 or 5.
</pre>
<pre wrap=""><!---->
Why is that? You may have to refresh my memory since our discussion of
ER-IRV(whole) was quite some time ago. I believe that I had a good
conceptual reply to your last message on the topic, but I never got around
to writing it.
</pre>
</blockquote>
There was a blunder in some of my posts on this topic regarding
ER-IRV(fractional). It is not easy to come up with a three candidate
scenario in which the Pushover-compressionists<br>
can succeed with all their supporters carrying out the strategy, but
the strategy is still more tempting than in plain IRV.<br>
But there was nothing wrong with my example regarding ER-IRV(whole).<br>
<blockquote type="cite"> 45:Right=Left>CentreRight<br>
35:CentreRight>Right>Left<br>
20:Left>CentreRight>Right<br>
<p>First-preference tallies<br>
Right:45 CentreRight:35 Left:65<br>
</p>
CentreRight has the lowest tally, and so is eliminated then Right wins.
<br>
This time no coordination was needed. As long as the Right suporters
knew that Right had more first-prefernces than CentreRight, and a<br>
pairwise win against Left, then each individual Right supporter got an
increased expectation by insincerely upranking Left from last to<br>
equal-first with no risk.</blockquote>
This would also work if the numbers 45/35/20 were replaced with
49/48/3. I suggest the right numbers in your "paradoxical" row should
be IRV1, ER-IRV(fractional)2,<br>
ER-IRV(whole) 5!<br>
<br>
<blockquote type="cite">
<pre wrap="">Probably WV should have a lower number than Margins in the
<span class="moz-txt-citetags">></span>"compromising-reversal" row, because sometimes
<span class="moz-txt-citetags">></span>in WV compromising-compression can be an effective "defensive strategy"
<span class="moz-txt-citetags">></span>but to achieve the same effect those voters
<span class="moz-txt-citetags">></span>in Margins have to compromise-reverse.
</pre>
<pre wrap=""><!---->
That's interesting. Would you mind showing me an example? It sounds
familiar, but I don't have anything like that on the surface (of my mind,
or of my voting files).
</pre>
</blockquote>
This is classic Ossipoff/Eppley/Tarr stuff from the Jurassic period
of WV versus Margins. This is from Steve Eppley's site:<br>
<br>
<a class="moz-txt-link-freetext"
href="http://alumnus.caltech.edu/%7Eseppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm">http://alumnus.caltech.edu/~seppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm</a><br>
<br>
<p><u>Example 2</u>: The non-drastic defense voting strategy.</p>
<p style="margin-top: -10px; margin-left: 30px;">Suppose there are 3
alternatives <i>x</i>, <i>y</i> and <i>z</i>. Suppose the voters' <br>
preferences regarding the alternatives are as follows:</p>
<div align="center">
<center>
<table bgcolor="#ffffff" border="1" bordercolor="#ffffff" width="38%">
<tbody>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><u>46%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>10%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>10%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>34%</u></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z</i></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>y</i></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
</tr>
</tbody>
</table>
</center>
</div>
<p style="margin-left: 30px;">That is, 46% of the voters sincerely
prefer <i>x</i> over <i>y</i> and <i>y</i> over <i>z</i>, 10%
prefer <i>y</i> <br>
over <i>x</i> and <i>x</i> over <i>z</i>, etc. Suppose the
voters vote the following rankings:</p>
<div align="center">
<center>
<table bgcolor="#ffffff" border="1" bordercolor="#ffffff" width="40%">
<tbody>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><u>46%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>10%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>10%</u></td>
<td bordercolor="#ffffff" align="center" width="24%"><u>34%</u></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z,y</i></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
</tr>
<tr>
<td bordercolor="#ffffff" align="center" width="25%"><i>y</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>z</i></td>
<td bordercolor="#ffffff" align="center" width="24%"><i>x</i></td>
<td bordercolor="#ffffff" align="center" width="24%"> </td>
</tr>
</tbody>
</table>
</center>
</div>
<p style="margin-left: 30px;">The votes of the 46% who voted <i>x</i>
over <i>z</i> over <i>y</i> misrepresent their preferences <br>
since they prefer <i>y</i> over <i>z</i>. (As above, this is the
classic "reversal" strategy.) <br>
The 34% who ranked both <i>z</i> and <i>y</i> tied for best are part
of a 54% coalition <br>
who voted <i>y</i> over <i>x</i> and no worse than tied for best.
Satisfaction of <i>non-drastic <br>
defense</i> requires that <i>x</i> must not be elected given these
votes. Note that the <br>
34% who prefer <i>z</i> over <i>y</i> do not need to "drastically"
rank <i>y</i> over <i>z</i> to ensure <br>
that <i>x</i> is not elected, assuming satisfaction of <i>non-drastic
defense</i>.</p>
<br>
<blockquote type="cite">
<pre wrap="">I had a look
at the weak burial resistance criterion, but I unfortunately found it
somewhat confusing.</pre>
</blockquote>
I'm sorry to hear that. Here it is:<br>
<blockquote type="cite">"If x is the CW (and wins), and on more than
1/3 of
the ballots ranked above y and z; and afterwards on
some of the ballots that rank y above x and x not
below z, z's ranking relative to x is raised while
keeping y ranked above them both, then if there is a
new winner it cannot be y."
</blockquote>
<br>
<blockquote type="cite">
<pre wrap="">As far as I understand CDTT-IRV, the basic strategic vulnerability is
that if the sincere IRV winner X differs from the sincere Condorcet winner
Y, X>Y voters will have an incentive to bury-reverse Y. </pre>
</blockquote>
CNTT,IRV has that problem, but CDTT,IRV is less vulnerable to Burial
than Defeat-Dropper(Winning Votes) or any other plain rankings method
that meets<br>
Mutual Majority, Smith(Gross) and Clone Independence.<br>
Take this classic example:<br>
49: A (sincere is A>B)<br>
24: B<br>
27: C>B<br>
<br>
The CNTT is the normal Smith set, that on these votes includes all the
candidates. CNTT,IRV elects A.<br>
One of the definitions of the CDTT is "the set of candidates that all
have a majority strength beat-path to the candidates that have one to
them."<br>
The CDTT here is BC. In the IRV count, B is first eliminated and so C
wins (an example of failing the Plurality criterion).<br>
The A supporters can do nothing to get A into the CDTT, but they can
gain a result they prefer by voting sincerely.<br>
The B supporters can do theselves no harm by voting B>A if they
want to. <br>
Of course, unlike plain IRV, it fails Later-no-Help. The C supporters
help C by ranking B.<br>
<br>
The horror possible real-world scenario with this method is that a
lot of voters are advised to truncate, producing the above election, by
those whose<br>
agenda is to bring the method into disrepute so that they can get rid
of it. But if the participants accept that the system is fair and
permanently in place,<br>
and just try to get their preferred candidates elected, then it should
work well.<br>
One possible political advantage of CDTT,IRV is that it can be sold
as an improved form of IRV. I think that is better than jumping in
front of the IRV<br>
movement and shouting "Go Back! IRV is evil!".<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
</div>
<br>
<br>
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