<div dir="auto">Yeah, MAMPO seems like it might behave more sensibly there.</div><div dir="auto"><br></div><div dir="auto">IIB doesn’t make sense to me outside of positional voting systems (which trivially satisfy it). If an empty ballot was genuinely intended to be irrelevant, the voter wouldn’t have cast it in the first place. An equal-ranking isn’t a way to express indifference (or else equal-ranks would never happen); it’s a way of pleading the fifth. Learning that a voter refuses to say whether they prefer Bob or Bill provides an important piece of information.</div><div dir="auto"><br></div><div dir="auto">Learning a voter has cast a completely blank ballot is an extreme case, where the ballot provides a very important piece of information: it means the voter expects a participation failure, because <span>a</span> nonempty ballot will hurt them.</div><div dir="auto"><br></div><div dir="auto">A rational response to this is to raise the threshold for a defeat, because setting the bar for a defeat closer to 50% prevents cycles (and therefore participation failures). In other words, these ballots are <i>very</i> relevant.</div><div dir="auto"><br></div><div><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jun 6, 2024 at 7:40 AM Chris Benham <<a href="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><u></u>
<div>
<p>Kevin,<br>
<br>
</p><blockquote type="cite">
<pre style="font-family:monospace">I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)</pre>
</blockquote>
<br>
Inventing those methods was some achievement as a thought
experiment to demonstrate that certain criteria are mutually
compatible. <br>
<br>
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on
its electowiki page.<br>
<br>
<a href="https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval" target="_blank">https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval</a><br>
<blockquote type="cite">
<h2 style="margin:1em 0px 0.25em;padding:0px;overflow:hidden;border-bottom-width:1px;border-bottom-style:solid;font-size:1.5em;font-weight:normal;font-family:"Linux Libertine",Georgia,Times,serif;line-height:1.375;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);border-bottom-color:rgb(162,169,177);color:rgb(0,0,0)"><span id="m_7234359816249269230Procedure" style="font-family:"Linux Libertine",Georgia,Times,serif">Procedure</span></h2>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">The
voter submits a ranking of the candidates. The candidates
explicitly ranked are considered<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">approved</i><span style="font-family:sans-serif"> </span>by
that voter.</p>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">A
candidate is<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">dominated</i><span style="font-family:sans-serif"> </span>if
more than half of the voters rank some other candidate
strictly above him.</p>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">All
dominated candidates are eliminated, unless this would
eliminate all the candidates.</p>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">Of
remaining candidates, the one approved by the most voters is
elected.</p>
<h2 style="margin:1em 0px 0.25em;padding:0px;overflow:hidden;border-bottom-width:1px;border-bottom-style:solid;font-size:1.5em;font-weight:normal;font-family:"Linux Libertine",Georgia,Times,serif;line-height:1.375;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);border-bottom-color:rgb(162,169,177);color:rgb(0,0,0)"><span id="m_7234359816249269230Criteria" style="font-family:"Linux Libertine",Georgia,Times,serif">Criteria</span></h2>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)"><b style="font-family:sans-serif">MDDA</b><span style="font-family:sans-serif"> </span>satisfies
the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Favorite_Betrayal_criterion" title="Favorite Betrayal criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Favorite
Betrayal criterion</a>,<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Strategy-Free_criterion" title="Strategy-Free criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Strategy-Free
criterion</a>, the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion" title="Strong Defensive Strategy criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Strong
Defensive Strategy criterion</a><span style="font-family:sans-serif"> </span>(and<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Minimal_Defense_criterion" title="Minimal Defense criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Minimal
Defense criterion</a>), and<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Monotonicity_criterion" title="Monotonicity criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">monotonicity</a>.</p>
<p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">It
fails<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Strategic_nomination" title="Strategic nomination" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Clone-Winner</a>,
the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Plurality_criterion" title="Plurality criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Plurality
criterion</a>, the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Generalized_Strategy-Free_criterion" title="Generalized Strategy-Free criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Generalized
Strategy-Free criterion</a>, the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Condorcet_criterion" title="Condorcet criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Condorcet
criterion</a>, the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Smith_set" title="Smith set" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Smith
criterion</a>,<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Participation_criterion" title="Participation criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Participation</a>,
the<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Majority_criterion" title="Majority criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Majority
criterion for solid coalitions</a>, and<span style="font-family:sans-serif"> </span><a href="https://electowiki.org/wiki/Later-no-harm_criterion" title="Later-no-harm criterion" style="text-decoration:none;background:repeat;font-family:sans-serif;color:rgb(51,102,204)" target="_blank">Later-no-harm</a>.</p>
<br>
</blockquote>
<br>
<p></p>
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;font-family:monospace;color:rgb(0,0,0)">25: A>B
26: B>C
23: C>A
04: C
78 ballots (majority threshold = 40)
B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
Now only B is without a "majority-strength defeat", so the winner changes from C to B.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method would also fail Irrelevant Ballots Independence. It may be far less bad.
<a href="https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition" target="_blank" style="font-family:monospace">https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition</a>
<blockquote type="cite" style="font-family:monospace"><h2 style="margin:1em 0px 0.25em;padding:0px;overflow:hidden;border-bottom-width:1px;border-bottom-style:solid;font-size:1.5em;font-weight:normal;font-family:"Linux Libertine",Georgia,Times,serif;line-height:1.375;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);border-bottom-color:rgb(162,169,177);color:rgb(0,0,0)"><span id="m_7234359816249269230Procedure" style="font-family:"Linux Libertine",Georgia,Times,serif">Procedure</span></h2><p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">The voter submits a ranking of the candidates. The candidates explicitly ranked are considered<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">approved</i><span style="font-family:sans-serif"> </span>by that voter.</p><p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">The<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">score</i><span style="font-family:sans-serif"> </span>for candidate<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">X</i><span style="font-family:sans-serif"> </span>against candidate<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">Y</i><span style="font-family:sans-serif"> </span>is equal to the number of voters ranking<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">X</i><span style="font-family:sans-serif"> </span>above<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">Y</i>. The<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">max score</i><span style="font-family:sans-serif"> </span>of candidate<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">X</i><span style="font-family:sans-serif"> </span>is the largest score of any other candidate against<span style="font-family:sans-serif"> </span><i style="font-family:sans-serif">X</i>.</p><p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">If nobody is approved by more than half of the voters, then the candidate approved by the most voters is elected.</p><p style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);color:rgb(32,33,34)">Otherwise, the candidate with the lowest max score, who is approved by more than half of the voters, is elected.</p></blockquote>
Chris B.
</pre></div><div>
<br>
<br>
<div>On 2/06/2024 7:23 am, Kevin Venzke
wrote:<br>
</div>
<blockquote type="cite">
<pre style="font-family:monospace">Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevin
<a href="http://votingmethods.net" target="_blank" style="font-family:monospace">votingmethods.net</a>
</pre>
</blockquote>
</div>
</blockquote></div></div>