<div>Hi Kevin,</div>
<div> </div>
<div>I think an additional rule, "the absolute majority rule" is needed in Condorcet elections in order to preserve the power of a blank vote to block the election of a candidate and force new elections.</div>
<div> </div>
<div>This rule might be used "on top" of the winning votes rule and would require a candidate to get that more than 50% of the votes cast in order to get a win in a pairwise comparison in a Condorcet election.</div>
<div> </div>
<div>This extra rule, if combined with winning votes, would not violate Woodal's plurality criterion furthermore it would obey what I call the </div>
<div> </div>
<div>I think that the discussion so far was confounded by requiring equal treatment to two different "phenonema": (i) incomplete ballots (or partially blank votes as I would like to call them) and (ii) equally ranked candidates, where the ranking is explicitly made on the ballots.</div>
<div> </div>
<div>This leads to equal treatment between unranked candidates and explicitly ranked candidates with equal ranking.</div>
<div> </div>
<div>I propose different rules for:</div>
<div>(i) unranked candidates on partially blank votes (incomplete ballots).</div>
<div>(ii) equally ranked candidates, where the ranking is explicitly made on the ballot</div>
<div> </div>
<div>Rule (i) above applies for candidates not given any ranking on the ballot.</div>
<div> </div>
<div>Rule (ii), gives two explicitly equally ranked candidates 0.5 points each in a pairwise comparison.</div>
<div>Rule (i) however a new winning rule (or maybe it has been proposed before) in order to preserve the majority criterion in condorcet elections with partially blank votes (incomplete ballots).</div>
<div> </div>
<div>
<div>If we have the election</div>
<div>30 A>B</div>
<div>40 B>A</div>
<div>30 Blank,</div>
<div>then in a condorcet election (<a href="http://en.wikipedia.org/wiki/Schulze_method#Ballot" target="_blank">Schulze</a>) B is elected, while in a majority election requiring 50 percent of the votes cast, no candidate is elected.</div>
<div> </div>
<div>Thus Schulze elections</div>
<div> </div>
<div>We can compare this situation with voting, where you can vote "yes", "no" and "abstain", in order to get the vote passed 50% of the votes cast are required to be "yes" votes.</div>
<div>It might thus be appropriate to retain this blocking property of the abstention (or blank) vote for Condorcet elections.</div>
<div> </div>
<div>I think that the so far proposed winning criteria do not allow for abstention voting in condorcet elections.</div>
<div> </div>
<div>I guess that the only way to retain the expressive power of the blank vote, is through adding an additional rule for when a pairwise comparison to qualifies as a win.</div>
<div> </div>
<div>This rule would state that a pairwise comparison results in a win only if the candidate gets more than 50% of all votes cast in the election.</div>
<div> </div>
<div>Thus in the election </div>
<div>
<div>40 A>B</div>
<div>30 B>A</div>
<div>40 Blank</div></div>
<div>A vs B would end 30% vs 40%.</div>
<div>No candiate would win.</div>
<div>New elections would be held.</div>
<div>Maybe this rule could be called the "absolute majority" rule for instance (or whatever).</div>
<div> </div>
<div>
<div>I.e. winning votes, losing votes, ratio and margins do not respect the something we might call the "blank vote criterion" or the "static quota criterion", which for single winner elections states that: a candidate can win a two-candidate election only if he/she is preferred by a majority of the voters". </div>
<div> </div>
<div>The general case of the "blank vote criterion" or the "static quota criterion" would read: a candidate can win a multiple member election only if he/she is preferred by a static quota number of the voters" (the quota used can be Droop, Hare, etc.).</div>
<div> </div>
<div>However, in order not to penalize explicit equal rankings on the ballot by giving both equally ranked candidates 0 wins thus making it more difficult for these candidates to meet the "static quota criterion", separate treatment is needed for explicit equal rankings and for candidates left out of the ballot, in the same way as I propose these two cases to be separately treated in an IRV-STV election.</div>
<div> </div>
<div>Thus we need to add two new rules to a Condorcet election.</div>
<div> </div></div>
<div><strong>The generalized symmetric completion rule for condorcet elections:</strong></div>
<div><strong>Equal rankings explicitly made on the ballot are counted as 0.5 win for each candidate.</strong></div>
<div> </div>
<div>
<div>Any candidate left out from the ballot is counted as ranked lower than all candidates explicitly ranked on the ballot. This rule is currently implemented for Schulze, so I just state it for completenes.</div>
<div> </div>
<div><strong>Absolute majority rule: a pairwise comparison between two candidates results in a win only if more than 50% of the total votes cast are in favour of any candidate.</strong></div>
<div><strong></strong> </div>
<div>The absolute majority rule might thus lead to the case where there is no winner of the election.</div>
<div> </div>
<div>In that case a new election might be held, or the voters can go home.</div>
<div> </div>
<div>It seems most natural to combine the absolute majority rule with winning votes, but in theory it might maybe be combined with any other rule (margins, ratios, losing votes). I have no firm oppinion on this.</div>
<div> </div></div>
<div>Turning to your example to apply these new rules:</div>
<div>35 A>B<br>25 B<br>40 C</div>
<div> </div>
<div>Let us first count the votes cast.</div>
<div>
<div>Total votes cast are 100 with the following matrix:<br>X A B C<br>A X 35 35</div></div>
<div>B 25 X 60<br>C 40 40 X<br></div>
<div>We only count as a win >50% of the votes casts.</div>
<div>Thus the election results in no candidate being elected as no candidate scores a win against both the other candidates.</div>
<div> </div>
<div>To see the similarity with the blank vote cast, let us imagine, that a second round of the election is held.</div>
<div>C has no chance of winning, as B beats C with more than 50% of the votes.</div>
<div>Thus let's assume that only A and B go through to the second round and that the voters keep their preferences from the first election intact.</div>
<div> </div>
<div>Then we get the following result.</div>
<div>35 A>B<br>25 B, which is completed to B>A using the current rules of Schulze.</div>
<div>40 Blank votes (these voted for C before)</div>
<div> </div>
<div>Thus we get A vs B: 35% vs 25%.</div>
<div>No candidate is elected, as no one got more than 50% of the votes.</div>
<div>Thus the blank vote criterion is not violated.</div>
<div> </div>
<div>This procedure allows the voters to find a candidate, who has better support in the electorate.</div>
<div>Of course it also allows for "sabotaging" elections. <br>In the example above C's voters can prevent any candidate from being elected. </div>
<div>However, that is exactly how elections are done in our party today, and the blank votes are thus respected.</div>
<div> </div>
<div>I guess that the extention of the approach above to Condorcet-STV is a rather trivial excersise (static quotas used), but I haven't looked at that case.</div>
<div> </div>
<div>
<div>Maybe the "blank vote" criterion above somehow "crashes" the Condorcet method, I don't know, even though I hope it doesn't.</div></div>
<div> </div>
<div>Woodalls plurality criterion (a retraction):</div>
<div>The criterion reads: <em>If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.</em></div>
<div>
<dd><a href="http://en.wikipedia.org/wiki/Plurality_criterion" target="_blank">http://en.wikipedia.org/wiki/Plurality_criterion</a></dd></div>
<div><br>If the the method described above (the generalized symmetric completion rule for condorcet elections and the absolute majority rule) is used together with the winning votes rule, then Woodal's plurality criterion is not violated.</div>
<div> </div>
<div>Thus I have to retract my statement "that Plurality is "a rather arbitary property that surely mustn't hold in any real election", which I wrote in my email to Kristofer today (Fri, May 27, 2011 at 12:28 PM).</div>
<div>That bold statement did not last a day even.</div>
<div> </div>
<div>A more correct statement is that "Plurality is a property that might not lead to proportional representation in multiple-winner elections"</div>
<div> </div>
<div>
<div>A short disambiguation:</div>
<div>With "biggest win", I meant "winning votes".</div>
<div>I think my calculation of the method "winning votes" using symmetrical completion with 0.5 wins to each candidates in case of equal ranking was correct, as I controlled it with the calculations on </div>
<div><a href="http://www1.cse.wustl.edu/~legrand/rbvote/calc.html" target="_blank">http://www1.cse.wustl.edu/~legrand/rbvote/calc.html</a></div>
<div>I entered:</div>
<div>35:A>B>C<br>25:B<br>40:C<br>and pressed the button "Schulze".</div>
<div> </div>
<div>
<div>
<div>To sum up my argument so far:</div>
<div>1] symmetrical completion is not a good way to process <em>incomplete ballots (or partially blank votes)</em>, as it removes the possibility to "protest" in the election.</div>
<div> </div></div>
<div>2] Generalized symmetrical completion is a good way to process <em>equally and explicitly ranked candidates</em> in an IRV-STV election, if the algorithm is modified to "dissolve" only one equal sign at a time (i.e. A=B=C is broken up to three ballots A>B=C, B>A=C, C>A=B).</div>
<div> </div>
<div>3] Generalized symmetrical completion for Condorcet elections would give each candidate 0.5 points in a Condorcet election only if both candidates explicitly were equally ranked on the ballot.</div>
<div> </div>
<div>4] My preferred way to handle incomplete ballots in IRV-STV for now, is through using static quotas and no ballot completion as it retains the power of the blank vote to block elections.</div>
<div> </div>
<div>5] Absolute majority is proposed as an additional winning rule for Condorcet elections which retains the power of the blank vote to block elections. The rule requires the candidate to get more than 50% of the votes cast in order to get a win in a pairwise comparison. Thus a plurality of the votes is not enough to qualify for a win. This rule does not violate something I call the "blank vote criterion", i.e. partially blank votes have the power to block the election of a candidate.</div>
<div> </div>
<div>6] The extention of the absolute majority rule to Condorcet-STV elections seems to be trivial if static quotas are used.</div></div></div>
<div> </div>
<div>Best regards</div></div>
<div>Peter Zborník</div>
<div> </div>
<div class="gmail_quote">On Fri, May 27, 2011 at 4:59 PM, Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr" target="_blank">stepjak@yahoo.fr</a>></span> wrote:<br>
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<div>Hi Peter,</div>
<div> </div>
<div>Let me say first of all that proportional representation isn't my area of interest, so you</div>
<div>shouldn't take anything I say to apply also to a PR situation.</div>
<div> </div>
<div>And although STV has a single-winner case, my thoughts on equal ranking don't apply</div>
<p dir="ltr" style="MARGIN-RIGHT: 0px">there either.
<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">
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<p dir="ltr" style="MARGIN-RIGHT: 0px"><br><br>--- En date de : <b>Ven 27.5.11, Peter Zbornik <i><<a href="mailto:pzbornik@gmail.com" target="_blank">pzbornik@gmail.com</a>></i></b> a écrit :
<div><br><br>[end quote]<br><br>I think you forgot Schulze as it is usually done: Weakest biggest loss.<br></div>
<p></p>
<p></p>
<p></p>
<p></p></p></p></blockquote>
<div>
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<div> </div>
<div>With "weakest biggest loss", do you mean losing votes (<a href="http://m-schulze.webhop.net/" target="_blank" rel="nofollow">http://m-schulze.webhop.net/</a>, page 7)?</div>
<div> </div>
<div> </div></blockquote></div>
<div>No I mean "winning votes" on that page. Is that what you meant by "biggest win"?</div>
<div>I can't really see how those could be the same thing.</div>
<div>
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<div> </div>
<blockquote style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid"><br>Experimentally, in simulations: When you treat equal-ranking as split<br>votes, voters will have to compromise more often, instead of just<br>
compressing the top ranks. This suggests weaker, non-frontrunner<br>candidates are more likely to be best advised to drop out of the race,<br>because their presence is more likely to harm the voters that support<br>them.<br>
</blockquote>
<div> </div>
<div>Could you please send me a link to these simulations?</div>
<div> </div>
<div> </div></blockquote></div>
<div>There is no complete set of simulations currently/yet. If you want to get a sense of</div>
<div>what I was doing, you can go to the archives:</div>
<div><a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/" target="_blank">http://lists.electorama.com/pipermail/election-methods-electorama.com/</a></div>
<div>and read my March 2011 posts in particular. My simulations involve voters who do not</div>
<div>initially know anything about the method except the valid ballot types, but try to </div>
<div>determine their ideal vote in a given situation via repeated and hypothetical polling.</div>
<div> </div>
<div>I have explained (probably five years ago) why we should expect margins to have more</div>
<div>favorite betrayal incentive than WV though. Suppose that you want to vote A>B, but</div>
<div>so doing causes C to win instead of B, because A defeats B pairwise. In WV both</div>
<div>reversing the order to be B>A or compressing the top to be A=B have the same effect</div>
<div>in reducing the magnitude of B's loss to A. But in margins reversal is twice as effective</div>
<div>as compression.</div>
<div> </div><font color="#888888">
<div>Kevin Venzke</div>
<div> </div></font>
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