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<font face="Helvetica, Arial, sans-serif">It's interesting that
there was mandatory truncation in the election: voters were asked
to rank "up to three candidates". That is something i hadn't
considered in another thread. <br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 15/09/2022 12:05, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite"
cite="mid:21dc4ec4-1193-1a79-7c58-dcdc11269e79@t-online.de">On
9/14/22 23:28, Andy Dienes wrote:
<br>
<blockquote type="cite">CVR available here
<a class="moz-txt-link-freetext" href="https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/">https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/</a>
<a class="moz-txt-link-rfc2396E" href="https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/"><https://vote.minneapolismn.gov/results-data/election-results/2021/council-ward-2/></a>
<br>
</blockquote>
<br>
Looks right! Nice! I've attached the ballots in the more familiar
EM format.
<br>
<br>
If we eliminate everybody but the Smith set, the ballots become:
<br>
<br>
1572: Arab
<br>
775: Arab>Gordon
<br>
133: Arab>Gordon>Worlobah
<br>
592: Arab>Worlobah
<br>
164: Arab>Worlobah>Gordon
<br>
822: Gordon
<br>
596: Gordon>Arab
<br>
205: Gordon>Arab>Worlobah
<br>
843: Gordon>Worlobah
<br>
334: Gordon>Worlobah>Arab
<br>
492: Worlobah
<br>
750: Worlobah>Arab
<br>
338: Worlobah>Arab>Gordon
<br>
852: Worlobah>Gordon
<br>
447: Worlobah>Gordon>Arab
<br>
<br>
There's an Arab>Gordon>Worlobah>Arab cycle. Schulze and
Minmax-type methods elect Arab (whether restricted to the Smith
set or not). fpA-fpC restricted to the Smith set would give:
<br>
<br>
fpArab = 3236
<br>
fpGordon = 2800
<br>
fpWorlobah = 2879
<br>
<br>
score(Arab) = 3236 - 2879 = 357
<br>
score(Gordon) = 2800 - 3236 = -436
<br>
score(Worlobah) = 2879 - 2800 = 79
<br>
<br>
and thus elect Arab. Smith//IRV would eliminate Gordon and then
Worlobah beats Arab pairwise.
<br>
<br>
At least plain IRV chose a Smith set member here! But most of the
actual Condorcet methods prefer Arab.
<br>
<br>
The first preferences before elimination are:
<br>
fpAnderson = 982
<br>
fpArab = 2719
<br>
fpGaskin = 546
<br>
fpGordon = 2508
<br>
fpUWI = 9
<br>
fpWorlobah = 2763
<br>
<br>
So Friendly Cover would go: all Smith set members cover all the
non-Smith members, so everybody has {Anderson, Gaskin, UWI} as
friends, with a first preference sum of 1537. Then
<br>
Arab has himself as friend and Worlobah as defeater.
<br>
Score = 2719 + 1537 - 2763 = 1493
<br>
Gordon has himself as friend and Arab as defeater.
<br>
Score = 2508 + 1537 - 2719 = 1326
<br>
Worlobah has himself as friend and Gordon as defeater.
<br>
Score = 2763 + 1537 - 2508 = 1792,
<br>
<br>
and Worlobah wins.
<br>
<br>
So it agrees with Smith//IRV but not with itself restricted to the
Smith set, hence failing ISDA. I'm inclined to believe that Arab
is the right choice since so many other methods agree.
<br>
<br>
-km<br>
<br>
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