<div dir="ltr">I've modified my electowiki page to include a simpler calculation of Relevant Rating:<div><br></div><div><ol style="margin:0.3em 0px 0px 3.2em;padding:0px;font-family:sans-serif;font-size:14px"><li style="margin-bottom:0.1em">Initialize the rating level R to MAXRATING</li><li style="margin-bottom:0.1em">Initialize candidate totals, <b>T(X)</b>, to zero</li><li style="margin-bottom:0.1em">Initialize <b>TCA(X,C)</b> to the highest approval for any candidate on ballots that rate X below R</li><li style="margin-bottom:0.1em">Repeat until a winner is found:<ol style="margin:0.3em 0px 0px 3.2em;padding:0px"><li style="margin-bottom:0.1em">For each candidate X, add ballots rating X at level R to T(X)</li><li style="margin-bottom:0.1em">Is <b>T(X) > TCA(X,C)</b>? If so X is a member of the current qualifying set</li><li style="margin-bottom:0.1em">If the current qualifying set has at least one member Q, the candidate with the highest T(Q) is the winner</li><li style="margin-bottom:0.1em">Otherwise, decrement R by one</li><li style="margin-bottom:0.1em">For each candidate X, set <b>TCA(X,C)</b> to the highest approval for any candidate on ballots that rate X below the new R rating level</li><li style="margin-bottom:0.1em">For each candidate X, is <b>T(X) > TCA(X,C)</b> (using new TCA(X,C))? If so, then X is a member of a new qualifying set.</li><li style="margin-bottom:0.1em">If the new qualifying set has at least one member Q', then the candidate with the highest T(Q') is the winner.</li></ol></li></ol></div><div><br></div><div>You could easily augment this algorithm with your Condercet modification.</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jun 14, 2019 at 11:12 AM C.Benham <<a href="mailto:cbenham@adam.com.au">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>IBIFA very naturally meets Plurality, Minimal Defense and
Non-Drastic Defense so it occurred to <br>
me to use it as a "Condorcet-completion" method thus:<br>
<br>
*Voters fill out out either unlimited rankings ballots or
multi-slot ratings ballots. <br>
<br>
A pairwise-beats-all candidate wins. Otherwise carry on the IBIFA
process until a <br>
Smith-set member qualifies. If only one does that candidate is
elected.<br>
</p>
<p>If more than one does in the same round, then simplest and
probably good enough<br>
is just to elect the one with highest score in that round.*<br>
<br>
(That last provision is Bucklin-like as in original IBIFA. Using
the Smith set the more<br>
complex Relevant Ratings and the possibly a bit arbitrary-looking
"revised IBIFA"<br>
I think would be very unlikely to give different winners.)<br>
<br>
I think this is my favourite method that meets both Condorcet and
Minimal Defense.<br>
<br>
Also it can be used with an approval cutoff to meet what Forest
was asking for on 30 May 2019.<br>
<br>
All rankings/ratings would be used to identify the Smith set, but
for the IBIFA stage ballots would<br>
be treated as if they truncate all their unapproved candidates.
The default should be approval of<br>
all candidates voted above at least one candidate.<br>
<br>
Chris Benham<br>
</p>
<p><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">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>
<br>
<p></p>
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