[EM] Hybrid/generalized ranked/approval ballots

Fri May 27 10:35:07 PDT 2011

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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