Looks good. Similar to ICT, I think, and simpler (from my perspective). What does "ERABW" stand for? This should have a good name; "Least Disappontment Condorcef" or something of the kind.<br><br><div class="gmail_quote">
2012/11/16 Chris Benham <span dir="ltr"><<a href="mailto:cbenhamau@yahoo.com.au" target="_blank">cbenhamau@yahoo.com.au</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div style="font-size:12pt;font-family:times new roman,new york,times,serif"><div>I propose the following as a reasonably practical, "summable", Condorcet method:</div><div><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
*Voters rank from the top however many candidates they wish. Equal-ranking is allowed.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">any X=Y contribute one whole vote to X>Y and another to Y>X.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">Ballots that truncate both X and Y have no effect on the X>Y and Y>X entries in the pairwise</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">matrix.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).*</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif"><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
It isn't a big deal if Ranked Pairs or River are used instead of Schulze. "Losing Votes" means </div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
that the pairwise results are weighed purely by the number of votes on the losing
side. The "weakest</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">defeats" are those with the most votes on the losing side, and of course conversely the "strongest</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">victories" are those with the fewest votes on the losing side.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">This has these advantages over Winning Votes: it appears to meet the "Approval Bad Example" </div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">defection-related criterion, it can't fail to elect a positionally dominant Smith-set member, and it</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">doesn't have any zero-info random-fill incentive.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">Instead, in the "acceptables versus unacceptables" situation it has the more natural zero-info </div>
<div>strategy of just equal-top ranking the acceptables and truncating the unacceptables.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">It doesn't share Winning Votes' compliance with Minimal Defense (incompatible, or effectively so,</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">with ABE compliance).</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">It has these advantages over Margins: it meets the Plurality criterion and it meets Steve Eppley's old</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">"Non-Drastic Defense" criterion.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">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="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">can't win.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">46: A>C ("sincere" may be A>B)</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
10: B>A</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">10: B>C</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
34: C=B ("sincere" may be C>B)</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif"><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
More than half the voters rank B above A and B no lower than equal-top, but Margins elects A.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
If the method were Bucklin, B would be the only candidate with a majority score in the first round.</div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">Using the rules of my suggested method, the pairwise comparisons go:</div>
<div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif"><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
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="font-style:normal;font-size:12pt;background-color:transparent;font-family:'times new roman','new york',times,serif">
<span style="font-size:12pt"><br></span></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif"><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="font-style:normal;font-size:12pt;background-color:transparent;font-family:'times new roman','new york',times,serif"><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="font-style:normal;font-size:12pt;background-color:transparent;font-family:'times new roman','new york',times,serif"><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><span style="font-size:12pt;background-color:transparent">B>A>C.</span><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">Enough for the time being.</div><span class="HOEnZb"><font color="#888888"><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">Chris Benham</div><div><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif"><br></div><div style="font-style:normal;font-size:16px;background-color:transparent;font-family:'times new roman','new york',times,serif">
<br></div></font></span></div></div><br>----<br>
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