Hi Kevin, I am sending you a small hopefully clarifying P.S. to my email below. 1] My appologies for some unfinished sentences, please disregard them
2] In my email below I state three things: a] Giving explicitly equally ranked candidates 0.5 votes each in their pairwise comparison, but not for unranked candidates does not violate Woodalls's plurality criterion in a condorcet election where winning votes are used. Woodall's plurality criterion is only violated if symetrical completion is used and the previously unranked candidates are given 0.5 votes each. b] In order to preserve the power of the blank vote to prevent a candidate from being elected in a Condorcet election, it is necessary to introduce a blank vote criterion (static quota or absolute majority criterion), which entails the following rule: in a Condorcet single winner election a candidate wins a pairwise comparison only if he/she gets a majority of the total votes cast (including blank votes). c] combinations of the rules (i) Rule b] can be combined with rule a] (winning votes) without violating Woodall's plurality criterion. (ii) Rule b] can be applied for winning rules: margins and quotas similarly as for case (i) above (iii) With losing votes I am not sure (haven't studied this criterion), but I guess there should be a natural extension along the principles in (i) above. I hope this makes the email below somewhat clearer. Best regards Peter Zbornik On Fri, May 27, 2011 at 7:35 PM, Peter Zbornik <[email protected]> wrote: > Hi Kevin, > > 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. > > 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. > > This extra rule, if combined with winning votes, would not violate Woodal's > plurality criterion furthermore it would obey what I call the > > 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. > > This leads to equal treatment between unranked candidates and explicitly > ranked candidates with equal ranking. > > I propose different rules for: > (i) unranked candidates on partially blank votes (incomplete ballots). > (ii) equally ranked candidates, where the ranking is explicitly made on the > ballot > > Rule (i) above applies for candidates not given any ranking on the ballot. > > Rule (ii), gives two explicitly equally ranked candidates 0.5 points each > in a pairwise comparison. > 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). > > If we have the election > 30 A>B > 40 B>A > 30 Blank, > then in a condorcet election > (Schulze<http://en.wikipedia.org/wiki/Schulze_method#Ballot>) B > is elected, while in a majority election requiring 50 percent of the votes > cast, no candidate is elected. > > Thus Schulze elections > > 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. > It might thus be appropriate to retain this blocking property of the > abstention (or blank) vote for Condorcet elections. > > I think that the so far proposed winning criteria do not allow for > abstention voting in condorcet elections. > > 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. > > 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. > > Thus in the election > 40 A>B > 30 B>A > 40 Blank > A vs B would end 30% vs 40%. > No candiate would win. > New elections would be held. > Maybe this rule could be called the "absolute majority" rule for instance > (or whatever). > > 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". > > 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.). > > 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. > > Thus we need to add two new rules to a Condorcet election. > > *The generalized symmetric completion rule for condorcet elections:* > *Equal rankings explicitly made on the ballot are counted as 0.5 win for > each candidate.* > > 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. > > *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.* > ** > The absolute majority rule might thus lead to the case where there is no > winner of the election. > > In that case a new election might be held, or the voters can go home. > > 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. > > Turning to your example to apply these new rules: > 35 A>B > 25 B > 40 C > > Let us first count the votes cast. > Total votes cast are 100 with the following matrix: > X A B C > A X 35 35 > B 25 X 60 > C 40 40 X > We only count as a win >50% of the votes casts. > Thus the election results in no candidate being elected as no candidate > scores a win against both the other candidates. > > To see the similarity with the blank vote cast, let us imagine, that a > second round of the election is held. > C has no chance of winning, as B beats C with more than 50% of the votes. > 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. > > Then we get the following result. > 35 A>B > 25 B, which is completed to B>A using the current rules of Schulze. > 40 Blank votes (these voted for C before) > > Thus we get A vs B: 35% vs 25%. > No candidate is elected, as no one got more than 50% of the votes. > Thus the blank vote criterion is not violated. > > This procedure allows the voters to find a candidate, who has better > support in the electorate. > Of course it also allows for "sabotaging" elections. > In the example above C's voters can prevent any candidate from being > elected. > However, that is exactly how elections are done in our party today, and the > blank votes are thus respected. > > 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. > > Maybe the "blank vote" criterion above somehow "crashes" the > Condorcet method, I don't know, even though I hope it doesn't. > > Woodalls plurality criterion (a retraction): > The criterion reads: *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.* > http://en.wikipedia.org/wiki/Plurality_criterion > > 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. > > 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). > That bold statement did not last a day even. > > A more correct statement is that "Plurality is a property that might not > lead to proportional representation in multiple-winner elections" > > A short disambiguation: > With "biggest win", I meant "winning votes". > 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 > http://www1.cse.wustl.edu/~legrand/rbvote/calc.html > I entered: > 35:A>B>C > 25:B > 40:C > and pressed the button "Schulze". > > To sum up my argument so far: > 1] symmetrical completion is not a good way to process *incomplete ballots > (or partially blank votes)*, as it removes the possibility to "protest" in > the election. > > 2] Generalized symmetrical completion is a good way to process *equally > and explicitly ranked candidates* 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). > > 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. > > 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. > > 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. > > 6] The extention of the absolute majority rule to Condorcet-STV elections > seems to be trivial if static quotas are used. > > Best regards > Peter Zborník > > On Fri, May 27, 2011 at 4:59 PM, Kevin Venzke <[email protected]> wrote: > >> Hi Peter, >> >> Let me say first of all that proportional representation isn't my area of >> interest, so you >> shouldn't take anything I say to apply also to a PR situation. >> >> And although STV has a single-winner case, my thoughts on equal ranking >> don't apply >> >> there either. >> >> >> >> >> >> --- En date de : *Ven 27.5.11, Peter Zbornik <[email protected]>* a >> écrit : >> >> >> [end quote] >> >> I think you forgot Schulze as it is usually done: Weakest biggest loss. >> >> >> With "weakest biggest loss", do you mean losing votes ( >> http://m-schulze.webhop.net/, page 7)? >> >> >> >> No I mean "winning votes" on that page. Is that what you meant by "biggest >> win"? >> I can't really see how those could be the same thing. >> >> >> >> >> Experimentally, in simulations: When you treat equal-ranking as split >> votes, voters will have to compromise more often, instead of just >> compressing the top ranks. This suggests weaker, non-frontrunner >> candidates are more likely to be best advised to drop out of the race, >> because their presence is more likely to harm the voters that support >> them. >> >> >> Could you please send me a link to these simulations? >> >> >> >> There is no complete set of simulations currently/yet. If you want to get >> a sense of >> what I was doing, you can go to the archives: >> http://lists.electorama.com/pipermail/election-methods-electorama.com/ >> and read my March 2011 posts in particular. My simulations involve >> voters who do not >> initially know anything about the method except the valid ballot >> types, but try to >> determine their ideal vote in a given situation via repeated and >> hypothetical polling. >> >> I have explained (probably five years ago) why we should expect margins to >> have more >> favorite betrayal incentive than WV though. Suppose that you want to vote >> A>B, but >> so doing causes C to win instead of B, because A defeats B pairwise. In WV >> both >> reversing the order to be B>A or compressing the top to be A=B have the >> same effect >> in reducing the magnitude of B's loss to A. But in margins reversal is >> twice as effective >> as compression. >> >> Kevin Venzke >> >> >> >
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