<div dir="auto">Here's another hint.<div dir="auto"><br><div dir="auto">Which of the listed methods elect the approval winner A for the following ballot profile?</div><div dir="auto"><br></div><div dir="auto">46 A</div><div dir="auto">5 A=C</div><div dir="auto">5 B=C</div><div dir="auto">44 B</div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Dec 7, 2022, 4:43 PM Forest Simmons <<a href="mailto:forest.simmons21@gmail.com">forest.simmons21@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">Toby,<div dir="auto"><br></div><div dir="auto">You are very close ... only one of these fails to elect the approval winner when fed approval ballots.</div><div dir="auto"><br></div><div dir="auto">I'm going to give everybody one more day to figure out which one, and what about it makes the difference.</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Dec 7, 2022, 1:42 AM Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk" target="_blank" rel="noreferrer">tdp201b@yahoo.co.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:Helvetica Neue,Helvetica,Arial,sans-serif;font-size:13px"><div></div>
<div dir="ltr">Presumably ranking top means the highest possible score in the cardinal methods. Intuitively it seems that pretty much all of these methods should elect the approval winner. The Condorcet ones surely. I'm not sure what justification there would be for not doing so, so it sounds like the birth of a new criterion.</div><div dir="ltr"><br></div><div dir="ltr">Toby</div><div><br></div>
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On Wednesday, 7 December 2022 at 02:15:19 GMT, Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" rel="noreferrer noreferrer" target="_blank">forest.simmons21@gmail.com</a>> wrote:
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<div><div id="m_7141312669196067761m_3613828217827657596ydpddb3ea40yiv9506911147"><div>Suppose that for some ballot B, the only candidates ranked on B are the ones ranked Top or Equal Top. In that case we say that B has been voted "approval style". <div><br></div><div>Suppose that every ballot in the entire ballot set is voted approval style. Which of the following methods will elect the approval winner (the one voted Top or Equal Top on the most ballots)?</div><div><br></div><div>Range/Score, Bucklin, Ranked Pairs, Copeland, Majority Judgment, Kemeny-Young, STAR, Approval Sorted Margins, DMC, IRV, DAC, DSC, MMPO, River, Schulze CSSD, Baldwin, Nanson, Black, MinMax(margins), SPE, Gross Loser Elimination, BTR-IRV, Score Chain Climbing, List Based Banks, Benham?</div><div><br></div><div>I won't give away the answers until tomorrow ... so you can think about it.</div><div><br></div><div>Then, after some additional questions to explore, a new method ... a natural outgrowth of our new understanding!</div><div><br></div><div>-Forest</div><div><br></div><div><br></div><div>6</div></div>
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