<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>On Dec 5, 2009, at 7:41 PM, Dave Ketchum wrote on: Election Goals & Methods - a review:</div><div><br></div><div>Here I explore some possibilities based on using margins. Assuming polling has given perfect knowledge as to the voting without strategy, what change might a strategist propose for the one group of voters that hears strategy gimmicks.</div><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;"><br></span></div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">100 votes:</span></div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">45A</span></div></div></blockquote> 5A,B - these 5 voters add in B as second choice. Effect is 31B to 29 C and B winning.<br><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">11B</span></div></div></blockquote> 3B,A - effect is 48A to 44C and B winning (3 vote margin is less than this 4 vote margin).</div><div><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">15B,C</span></div></div></blockquote> 3B - effect is 45A to 41C and B winning. <br><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">29C,B</span></div></div></blockquote> 6C,A - effect is 51A to 49B and A winning (hard to sell, since C wins without strategy).<br><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;"><br></span></div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;"><span class="Apple-style-span" style="font-family: -webkit-sans-serif; font-size: 13px; line-height: 19px; -webkit-text-stroke-width: 0; "><div style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">The pairwise defeats are as follows:</div><ul style="line-height: 1.5em; list-style-type: square; margin-top: 0.3em; margin-right: 0px; margin-left: 1.5em; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-image: url(http://en.wikipedia.org/skins-1.5/monobook/bullet.gif); margin-bottom: 0.5em; "><li style="margin-bottom: 0.1em; ">B beats A, 55 to 45 (55 winning votes, a margin of 10 votes)</li><li style="margin-bottom: 0.1em; ">A beats C, 45 to 44 (45 winning votes, a margin of 1 vote)</li><li style="margin-bottom: 0.1em; ">C beats B, 29 to 26 (29 winning votes, a margin of 3 votes)</li><div><br></div></ul></span></span></div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;"><span class="Apple-style-span" style="font-family: -webkit-sans-serif; font-size: 13px; line-height: 19px; -webkit-text-stroke-width: 0; "><div style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">Using the winning votes definition of defeat strength, the defeat of B by C is the weakest, and the defeat of A by B is the strongest. Using the margins definition of defeat strength, the defeat of C by A is the weakest, and the defeat of A by B is the strongest.</div><div style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">Using winning votes as the definition of defeat strength, candidate B would win under minimax, Ranked Pairs and the Schulze method, but, using margins as the definition of defeat strength, candidate C would win in the same methods.</div><div style="margin-top: 0.4em; margin-right: 0px; margin-bottom: 0.5em; margin-left: 0px; line-height: 1.5em; ">If all voters give complete rankings of the candidates, then winning votes and margins will always produce the same result. The difference between them can only come into play when some voters declare equal preferences amongst candidates, as occurs implicitly if they do not rank all candidates, as in the example above.</div></span></span></div><div><br></div><div><span class="Apple-style-span" style="-webkit-text-stroke-width: -1;">Dave Ketchum</span></div></div></blockquote></div></body></html>