<div dir="ltr">I've been mulling over ways to get a Smith/Approval method into a somewhat practical form, and have taken some cues from Jameson Quinn's Vote-321.<br><br>Vote-321 is a pretty method, with a lot of strategy resistance, and if it were among the options for a new voting system (with no Condorcet method available), I would choose it immediately.<div><br></div><div>However, I have a few issues with it: vulnerability to cloning; lack of expression; and what I consider a too-small provisional subset. The latter is more of a psychological / media problem, and what I mean by "too-small" is that if only the top three first-place candidates make it past the first pass, public attention could be excessively focused on the front-runners at the cost of addressing issues raised by less popular candidates. But the too-small subset is also what enables Vote-321's vulnerability to cloning. By including at least one or two more candidates in the first pass of candidate reduction, cloning risk is reduced.<br><br>Following is what I call the <b>High 5 </b>method for three or more candidates:<br><br><b>Ballot Expression:</b><div>I prefer a 6 slot ranked ballot, equal-ranking and gaps allowed, with the rank/tiers named as follows:<br> <span id="gmail-docs-internal-guid-2c7b416e-7fff-ce8f-2372-8a9c3f86ab9b"><div dir="ltr" style="margin-left:0pt" align="left"><table style="border:none;border-collapse:collapse"><colgroup><col width="128"><col width="288"><col width="208"></colgroup><tbody><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Tier Name</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Approval Status</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Description</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">A</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Approved</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Most Preferred / Best / Favorite</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">B</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Approved </span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Good</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">C</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Approved</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">OK / Acceptable</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">D</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Disapproved</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Not Preferred, but would be in their coalition (i.e. Compromise)</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">E</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Disapproved</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Mostly Unacceptable but Lesser Evil</span></p></td></tr><tr style="height:0pt"><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Reject</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Dispapproved</span></p></td><td style="border-width:1pt;border-style:solid;border-color:rgb(0,0,0);vertical-align:top;padding:5pt;overflow:hidden"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:11pt;font-family:Arial,sans-serif;color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline">Completely unacceptable</span></p></td></tr></tbody></table><br></div><div style="margin-left:0pt" align="left">Summarized, there are 3 approved ranks (Most Preferred, Good, OK), 2 disapproved ranks (compromise, lesser of two evils), and Reject. Blank ballots are counted as rejection.<br><br><b>Tabulation:</b></div><div style="margin-left:0pt" align="left"><ul><li>Total most-preferred votes per candidate (i.e. "A" votes).</li><li>Approval / Disapproval totals per candidate<br></li><li>Pairwise preference array</li><li>Optional:</li><ul><li>Tied-Approval pairwise</li><li>Tied-Disapproval (above reject) pairwise</li><li>Approved vs Disapproved/Reject pairwise</li></ul></ul><b>First-pass subset:</b></div><div style="margin-left:0pt" align="left"><ul><li><b>Top 5 candidates by most-preferred votes</b></li></ul><b>Procedure:</b></div><div style="margin-left:0pt" align="left"><ul><li>Of the top 5 most-preferred candidates are found, drop the least-approved candidate.</li><li>Among the remaining candidates, use the pairwise preference array to find the Smith Set</li><li>If more than one candidate is in the Smith Set, pick the most approved member of the set as the winner.</li></ul></div><div style="margin-left:0pt" align="left">If you start with 3 candidates, this method reduces to top-two approval.<br><br>Starting with 4 candidates, this method reduces to sorting the candidates by Approval and doing a top-three tournament: the winner is the pairwise winner of A1 versus (the pairwise winner of A2 versus A3).</div><div style="margin-left:0pt" align="left"><br></div><div style="margin-left:0pt" align="left">For 5 or more candidates, the method has a very high probability of finding the CW (if one exists) among the top five favorites, while falling back to approval in the event of a cycle among the four most-approved of those top five.<br><br>In a "jungle-primary" type of situation (though no primary is necessary), media attention would be given to at least the top 5 candidates instead of just the top two, ensuring attention to a range of viewpoints. And in the event of a large number of candidates, it would not be necessary to tabulate pairwise preferences for more than 7 or 8 top-first-ranked candidates as determined by pre-election polling, reducing tabulation complexity while retaining summability.</div><div style="margin-left:0pt" align="left"><br></div><div style="margin-left:0pt" align="left">Using most-preferred votes for the first pass has a slight anti-cloning effect, as a preference ballot would lead to a tendency toward vote splitting if one faction has too many candidates. The anti-cloning pressure is greater than in Vote-321 because of the larger range of expression.<br><br>Finally, the Smith//Approval method, when combined with the explicit approval cutoff ballot, allows enough strategy to reduce burial incentive.<br><br>I'm calling this "High 5" voting because it's descriptive of both the ranking method and the top-five most preferred first-level truncation, and it's easier to remember than Smith//Approval.<br><br>Thoughts?</div><div style="margin-left:0pt" align="left"><br></div></span></div></div></div>