<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div>I propose the following as a reasonably practical, "summable", Condorcet method:</div><div><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">*Voters rank from the top however many candidates they wish. Equal-ranking is allowed.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom</div><div style="color: rgb(0, 0, 0); font-size: 16px;
font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">any X=Y contribute one whole vote to X>Y and another to Y>X.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">Ballots that truncate both X and Y have no effect on the X>Y and Y>X entries in the pairwise</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">matrix.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style:
normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).*</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">It isn't a big deal if Ranked Pairs or River are used instead of Schulze. "Losing Votes" means </div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">that the pairwise results are weighed purely by the number of votes on the losing
side. The "weakest</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">defeats" are those with the most votes on the losing side, and of course conversely the "strongest</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">victories" are those with the fewest votes on the losing side.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">This has these advantages over Winning Votes: it appears to meet the "Approval Bad Example" </div><div style="color:
rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">defection-related criterion, it can't fail to elect a positionally dominant Smith-set member, and it</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">doesn't have any zero-info random-fill incentive.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">Instead, in the "acceptables versus unacceptables" situation it has the more natural zero-info </div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times
new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">strategy of just equal-top ranking the acceptables and truncating the unacceptables.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">It doesn't share Winning Votes' compliance with Minimal Defense (incompatible, or effectively so,</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">with ABE compliance).</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style:
normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">It has these advantages over Margins: it meets the Plurality criterion and it meets Steve Eppley's old</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">"Non-Drastic Defense" criterion.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">That says that if more than half the voters rank X above Y and X no lower than equal top, then Y</div><div style="color: rgb(0, 0, 0);
font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">can't win.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">46: A>C ("sincere" may be A>B)</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">10: B>A</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">10: B>C</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times,
serif; background-color: transparent; font-style: normal;">34: C=B ("sincere" may be C>B)</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">More than half the voters rank B above A and B no lower than equal-top, but Margins elects A.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">If the method were Bucklin, B would be the only candidate with a majority score in the first round.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div
style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">Using the rules of my suggested method, the pairwise comparisons go:</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"> B>A 54>46, A>C 56-44, <span style="font-size: 12pt;">C>B 80-54 (the 34 C=B have been added to both sides).</span></div><div style="color: rgb(0, 0, 0); font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><span style="font-size: 12pt;"><br></span></div><div style="color: rgb(0, 0,
0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><span style="font-size: 12pt;">The weakest defeat (as measured by Losing Votes) is B's, so B wins. Or in terms of Ranked Pairs,</span></div><div style="color: rgb(0, 0, 0); font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><span style="font-size: 12pt;">the strongest pairwise result is A>C so that is locked and the next strongest is B>A so that is locked</span></div><div style="color: rgb(0, 0, 0); font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><span style="font-size: 12pt;">and then C>B is skipped because it's incompatible with an already locked result; so the final order is</span></div><div style="color: rgb(0, 0, 0); font-size: 12pt; font-family: 'times new
roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><span style="font-size: 12pt; background-color: transparent;">B>A>C.</span><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">Enough for the time being.</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;">Chris Benham</div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new
roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: 'times new roman', 'new york', times, serif; background-color: transparent; font-style: normal;"><br></div></div></body></html>