[EM] Hybrid/generalized ranked/approval ballots

Fri May 27 11:49:57 PDT 2011

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 <pzbornik at gmail.com> 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 <stepjak at yahoo.fr> 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 <pzbornik at gmail.com>* 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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