<div>Dear all,</div>
<div> </div>
<div>Please let me return to an older discussion (see emails below).</div>
<div>The issue of the hybrid ballot A>B=C>D.</div>
<div>
<div>Just an idea on this topic, which might be worth mentioning.</div>
<div>It could be a way to handle the problem of bullet voting.</div>
<div>Ant it could be a way to disband the dichotomy between different criterias of winning in condorcet elections (margins, winning votes, quotas losing votes).</div>
<div> </div>
<div>1] IRV-based elections:</div>
<div>Basically in IRV-based STV, when arriving at an equal sign in the ballot, the ballot could simply be split into the number of candidates with equal preferences and re-weighted accordingly (i.e. for instance A=B=C would give three ballots, A>B=C, B>A=C, C>A=B, each with weight 1/3 of the original weight).</div>
<div> </div>
<div>Example:</div>
<div> </div>
<div>Say we have an STV election with 20 ballots on the form
<div>A>B=C=D>E</div>A is elected, and we need to transfer, say 9 surplus votes.</div>
<div>Normally in STV (say scottish STV) with fractional transfers, each of the 20 votes would have the weight 9/20. </div>
<div> </div>
<div>When allowing equal signs we will instead create three new ballots for each ballot as seen below.</div>
<div>Thus the ballot B=C=D>E is split into the following three ballots</div>
<div>B>C=D>E</div>
<div>C>B=D>E</div>
<div>D>B=C>E</div>Each of the ballots above would have 1/3 of the weight of the original ballot
<div> </div>
<div>Thus when transferring the surplus votes using weight 9/20 in the example above.</div>
<div>We would use the weights 9/20/3=3/20 for each of the three created ballots above.</div>
<div> </div>
<div>
<div>The idea is to give the first preference to each one of the equally ranked candidates and leave the others with the equal sign as second preferences.</div>
<div>This method would work for STV elections, which only look at the first preferences.</div>
<div>
<div>Might the method above be a good one to use when equal-ranking ballots, in STV elections which only look at first preferences?</div>
<div>Has the method above been used yet in any implementations?</div>
<div> </div></div>
<div>Condorcet-based elections:</div>
<div>In Condorcet elections (including STV) then A=B would simply mean 0.5 wins for A>B and 0.5 wins for B>A.</div>
<div> </div>
<div>Kevin Venzke wrote in his mail below (May 9th 2010):</div>
<div>35 A>B<br>25 B<br>40 C</div>
<div>A will win. This is only acceptable when you assume that the B and C<br>voters meant to say that A is just as good as the other candidate that<br>they didn't rank. I don't think this is likely to be what voters expect.<br>
It seems misleading to even allow truncation as an option if it's treated<br>like this.</div>
<div>End of quote</div>
<div> </div>
<div>Well I think think that as a voter I would indeed be pleased if A would win and not C.</div>
<div>If the completion system above would be used (i.e. A=B would be counted as 0.5 win for A vs B and 0.5 win for B vs A), then there the winner would always be the same disregarding which of the following winning criteria was used: winning votes, losing votes, margins or quotas. </div>
<div> </div>
<div>Let us analyse the example in your mail below. We apply the Schulze beatpath with different criteria (biggest win, margins and ratios):</div>
<div>35 A>B>C<br>25 B>A=C<br>40 C>A=B</div>
<div> </div>
<div>Pairwise wins -<br>X A B C<br>A X 55 47.5<br>B 45 X 60<br>C 52.5 40 X</div>
<div> </div>
<div>Path strenghts - Method 1: Biggest win</div>
<div>A vs B: 55</div>
<div>A vs C: 55</div>
<div>B vs A: 52.5<br>B vs C: 60</div>
<div>C vs A: 52.5</div>
<div>C vs B: 52.5</div>
<div> </div>
<div>Beat-paths:</div>
<div>A beats B</div>
<div>B beats C </div>
<div>A beats C </div>
<div> </div></div>
<div>A wins</div>
<div>(I hope the calculation is correct)</div>
<div> </div>
<div>
<div>
<div>
<div>Path strenghts - Method 2: Margins</div>
<div>A vs B: 10</div>
<div>A vs C: 10</div>
<div>B vs A: 5</div>
<div>B vs C: 20</div>
<div>C vs A: 5</div>
<div>C vs B: 5</div>
<div> </div>
<div>
<div>Beat-paths </div>
<div>A beats B </div>
<div>B beats C </div>
<div>A beats C </div>
<div> </div></div>
<div>A wins</div>
<div> </div>
<div>Truncated ballots:</div>
<div>
<div>Using this system, optionally, all candidates not ranked would get equal rank.</div>
<div>I.e. in the election of candidates A, B, C, the ballot A would be counted as A>B=C.</div>
<div>A blank ballot would be counted as A=B=C.</div>
<div>An abstention could theoretically also be counted as A=B=C.</div>
<div> </div>Discussion:
<div>What are the pros and cons of the approach above?</div>
<div>Prima facie it seems that the treatment of hybrid ballots above could solve the problem of bullet voting, but I am far from sure.</div></div></div></div></div>
<div> </div>
<div>Best regards</div>
<div>Peter Zborník</div><br><br></div>
<div class="gmail_quote">On Sun, May 9, 2010 at 7:14 PM, Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Hi Peter,<br> <br>We consider rank ballots that allow equality of ranking and truncation all<br>the time.<br>
<br>For Condorcet methods the question of how to treat equality of ranking is<br>what Juho and I usually talk about.<br><br>If Markus prefers not to use the split vote treatment it is probably<br>because it violates CDTT (it doesn't respect voted majorities) and<br>
the Plurality criterion:<br><br>35 A>B<br>25 B<br>40 C<br><br>A will win. This is only acceptable when you assume that the B and C<br>voters meant to say that A is just as good as the other candidate that<br>they didn't rank. I don't think this is likely to be what voters expect.<br>
It seems misleading to even allow truncation as an option if it's treated<br>like this.<br><br>There's also a strategy issue. When truncation is counted as zero votes,<br>then you have three options when you decide how to rank the worse of<br>
two frontrunners (who is really better than all the other unimportant<br>candidates):<br>1. sincerely support the worse frontrunner<br>2. insincerely bury the worse frontrunner (which can steal the election<br>if the other faction does #1, or else elect a completely terrible<br>
candidate if the other faction does #2 or #3)<br>3. truncate. That protects the better frontrunner and it is not trying<br>to steal the election.<br><br>When you can't meaningfully truncate, you don't have #3. So #2 is both<br>
your offensive and your defensive strategy. That seems like a problem to<br>me.<br><br>Kevin Venzke<br><br><br><br><br>----<br>Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em</a> for list info<br>
</blockquote></div><br>