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<p>Ted,<br>
<br>
I don't see the two methods (VIASME and Smith/IBIFA ) as being
in competition with each other because they use<br>
two very different types of ballot and and VIASME is probably
much harder to explain and sell.<br>
<br>
</p>
<blockquote type="cite">Smith/<something IBI> at least has
the benefit of satisfying later-no-help ...</blockquote>
<br>
I'm afraid not. IBIFA fails Later-No-Help because adding a lower
(or "later") preference (i.e. rating another candidate X<br>
above Bottom) can trigger another (say a second) round that is won
by a candidate (not X) you prefer to the one (also not X) <br>
who would have otherwise won (say in the first round). <br>
<br>
I thought of a possible kludge to try and fix that but it makes
the method much more complicated and and less Condorcet<br>
efficient.<br>
<br>
*(Say we are using 3-slot IBIFA.) We consider the IBIFA winner A
to be provisional. Then we truncate all the ballots below A<br>
and if A is still the IBIFA winner we elect A. <br>
<br>
But if instead there is a new IBIFA winner B, we un-truncate the
ballots below A and truncate below B and if B is still the<br>
IBIFA winner then we elect B.<br>
<br>
But if instead there is a new IBIFA winner C then repeat the
process. If we run out of candidates or a previous provisional<br>
winner appears, then we simply elect the most approved candidate.*<br>
<br>
A very ugly answer to a question no-one was asking, and I'm not
even completely sure it works. Median Ratings methods<br>
(such as Bucklin and MJ) do meet Later-no-Help. Arguably it is
desirable that Later-no-Help and Later-no-Harm should<br>
either both be met (like IRV) or both failed (like IBIFA and
Condorcet methods). Otherwise you either get a random-fill<br>
incentive (yuck) or a very strong truncation (or only use the top
and bottom rating slots) incentive.<br>
<br>
And complying with Later-no-Help is one of the properties that
Woodall has proved is incompatible with Condorcet, so<br>
"Smith/ anything" can't meet it. The other criterion compliances
in the same boat are Later-no-Harm, Particpation,<br>
Mono-raise-random, Mono-raise-delete, Mono-sub-plump,
Mono-sub-top.<br>
<br>
<pre><a class="moz-txt-link-freetext" href="http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf" moz-do-not-send="true">http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf</a>
</pre>
<blockquote type="cite">
<p>Election 6: <br>
bca 3 <br>
bac 2 <br>
cab 3 <br>
cba 2<br>
abc 3 <br>
acb 2<br>
</p>
<p>Theorem 2 says that if an election rule satisfies Condorcet's
principle, then it cannot possess any of the seven properties
that are crossed in the column headed 2 in Table 1. <br>
This is a lot to prove. Fortunately most of it can be proved
by considering variants of Election 6 above. The only bit that
cannot is the incompatibility of Condorcet with <br>
participation; this is proved by Moulin2, and I shall not
attempt to reproduce his proof here. The following proof of
the rest of Theorem 2 invokes the axioms of symmetry <br>
and discrimination, for a precise statement of which see
Woodall4.<br>
<br>
So suppose we have an election rule that satisfies Condorcet.
By symmetry, the result of this rule applied to Election 6
above must be a 3-way tie. But by the axiom of <br>
discrimination, there must be a profile P very close to the
one in Election 6 (in terms of the proportions of ballots of
each type) that does not yield a tie. So our election rule,<br>
applied to profile P, elects one candidate unambiguously; and
there is no loss of generality in supposing that this
candidate is a. However, there are ways of modifying the <br>
profile P so that c becomes the Condorcet winner, so that our
election rule must then elect c instead of a. This happens,
for example, if all the bac ballots are replaced by a; <br>
and the fact that this causes c to be elected instead of a
means that our election rule does not satisfy
mono-raise-random, mono-raise-delete, mono-sub-top or
mono-sub-plump. <br>
It also happens if all the abc ballots are replaced by a, and
this shows that our election rule does not satisfy
later-no-help.<br>
<br>
To prove that our election rule does not satisfy
later-no-harm, it is necessary to consider a slight
modification of the profile in Election 6, in which the second
and third choices <br>
are deleted from all the abc, bca and cab ballots. Again, our
election rule, applied to this profile, must result in a 3-way
tie. But again, there must be a profile P' very close to this
<br>
(in terms of the proportions of ballots of each type) that
does not give rise to a tie, and we may suppose that our
election rule elects a when applied to profile P'. But if we
replace <br>
the a ballots in P' by abc, then b becomes the Condorcet
winner, and so must be elected by Condorcet's principle; and
this shows that our election rule does not satisfy
later-no-harm.<br>
Together with the result of Moulin2 already mentioned, this
completes the proof of Theorem 2, that an election rule that
satisfies Condorcet cannot satisfy any of the seven properties
<br>
crossed in the column headed 2 in Table 1.<br>
</p>
</blockquote>
<br>
<p>Chris Benham<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 20/06/2019 5:20 am, Ted Stern
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAHGFzOStRvonBPtg04b9V9fNptUNuyb3r-9pXJnfjKQem+dD8g@mail.gmail.com">
<meta http-equiv="content-type" content="text/html;
charset=UTF-8">
<div dir="ltr">Just as I'm warming up to Smith/Relevant-Ratings
(or Smith/IBIFA), you introduce another method. :-)
<div><br>
</div>
<div>This seems to be in the same vein as MinLV(erw)SME.</div>
<div><br>
</div>
<div>I like the general idea, but would prefer to avoid doing
multiple tabulations as that makes the method not precinct
summable.</div>
<div><br>
</div>
<div>Smith/<something IBI> at least has the benefit of
satisfying later-no-help and mono-raise without requiring
multiple passes through the ballots. </div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Jun 19, 2019 at
10:59 AM C.Benham <<a href="mailto:cbenham@adam.com.au"
moz-do-not-send="true">cbenham@adam.com.au</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<p>This is my favourite Condorcet method that uses
high-intensity Score ballots (say 0-100):<br>
<br>
*Voters fill out high-intensity Score ballots (say
0-100) with many more available distinct scores<br>
(or rating slots) than there are candidates. Default
score is zero.<br>
<br>
1. Inferring ranking from scores, if there is a pairwise
beats-all candidate that candidate wins.<br>
<br>
2. Otherwise infer approval from score by interpreting
each ballot as showing approval for the<br>
candidates it scores above the average (mean) of the
scores it gives.<br>
Then use Approval Sorted Margins to order the candidates
and eliminate the lowest-ordered<br>
candidate.<br>
</p>
<p>3. Among remaining candidates, ignoring eliminated
candidates, repeat steps 1 and 2 until <br>
there is a winner.*<br>
<br>
To save time we can start by eliminating all the
non-members of the Smith set and stop when<br>
we have ordered the last 3 candidates and then elect the
highest-ordered one.<br>
<br>
<a
class="gmail-m_6983318839793776997moz-txt-link-freetext"
href="https://electowiki.org/wiki/Approval_Sorted_Margins"
target="_blank" moz-do-not-send="true">https://electowiki.org/wiki/Approval_Sorted_Margins</a><br>
</p>
<p>In simple 3-candidate case this is the same as Approval
Sorted Margins where the voters signal<br>
their approval cut-offs just by having a large gap in
the scores they give.<br>
<br>
That method fulfils Forest's recent 3-candidate,
3-groups of voters scenarios requirements, resists
Burial <br>
relatively well and meets mono-raise. The motivation
behind this version is to minimise any disadvantage <br>
held by naive (and/or uninformed) sincere voters.<br>
<br>
Chris Benham<br>
<br>
</p>
<p><b>Forest Simmons</b> <a title="[EM] What are some
simple methods that accomplish the following
conditions?"
href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3CCAP29onet%2BO9hCZJ6hvNnnpUWNyrDkKa9xFXrX5P-RPoF6ndtfw%40mail.gmail.com%3E"
target="_blank" moz-do-not-send="true">fsimmons at
pcc.edu </a><br>
<i>Thu May 30 </i></p>
<p> </p>
<blockquote type="cite">In the example profiles below 100
= P+Q+R, and 50>P>Q>R>0. <br>
<br>
I am interested in simple methods that always ...<br>
<br>
(1) elect candidate A given the following profile:<br>
P: A<br>
Q: B>>C<br>
R: C,<br>
<br>
and<br>
(2) elect candidate C given<br>
P: A<br>
Q: B>C>><br>
R: C,<br>
<br>
and<br>
(3) elect candidate B given<br>
P: A<br>
Q: B>>C (or B>C)<br>
R: C>>B. (or C>B)<br>
<br>
</blockquote>
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