[EM] Generalized symmetric ballot completion

Tue May 31 09:52:38 PDT 2011

Juho,

a correction:
I wrote: "If a candidate is ranked on >50% of the ballots, then this method
will always produce a winner"

That is not correct. Say we have 4 A>B, 3 B>A, 3 blank.
Noone wins that election in the modified IRV election I proposed, neither
candidate has 50% of the total vote in the first and final round, but both
candidates are explicitly ranked on >50% of the ballots.

The example above illustrates the difference between the two rules I
proposed for blank voting in Condorcet elections in my previous emails. I
restate the rules again:

Rule 1 (proposed above):
 In a pairwise comparison of a Condorcet election (or in the final round of
an IRV election), a winning candidate needs to get >50% of the total votes
(including blank votes). This rule amounts to: "A majority of all voters
support A before B". Technically this is a three part election with A vs B+X
and B vs A+X. Thus we can have elections with no winner.

Rule 2 (from the generalized ballot):
A winning candidate needs to be explicitly ranked on >50% of the ballots.
This rule amounts to "A majority of all voters support the election of A
rather than having no election winner". Technically this rule means that any
candidate A has to win the election of A vs X in order to have a chance of
winning the election.

If the proposed method (call it Static-IRV) fails to produce a winner (i.e.
all IRV winners, who don't satisfy Rule 1 above are deleted), then the IRV
election would be repeated only for candidates having least 50% of explicit
ballot rankings (applying rule 2 instead of rule 1). If no candidate has at
least 50% of explicit ballot rankings, then the IRV winner would be elected.

The same heuristic could be applied for Condorcet elections.

Heuristics are frowned upon, I know, but even Schulze uses heuristics, and a
lot of them.

The benefits of the proposed Static-IRV election method is
1] to keep the LNH property as long as possible and
2] respect the blank vote and get a winner with 50% of all votes in the last
round (the run-off), if possible
3] to generate candidates with strong support for the runoff

IRV can be seen as a heuristic to generate two good candidates for a
head-to-head election.

If the blank vote is not respected and the winner is not required to have
50% of the vote, then we have a plurality voting system.

 In the Czech senatorial elections, it is not possible to vote blank in the
second round and some senators are elected with less than 50% support of the
voters, counting "invalid" votes and abstentions.
If blank votes were allowed in the second round of run-off elections, then
double-voting could be allowed too (A=B, half a vote to each) and possible
allowing for ranking of the candidates (A>B) in order to allow the voters to
compensate the blank votes.

In the Czech parliament, >50% of the votes (including abstentions) is
required for a decision.
A good argument for the blank vote and for the 50% requirement in elections
is to refer to the voting in parliament.

Do you know of any nice paper or post on this list, which discusses possible
significant modifications/improvement of the general mechanics of Condorcet
elections (apart from the debate on ranked-pairs, maximin, minimax, Schulze,
Beatpath, Copeland etc.)?

Best regards
Peter Zborník

On Tue, May 31, 2011 at 11:58 AM, Peter Zbornik <pzbornik at gmail.com> wrote:

> Juho,
>
> comments in the text below.
> Mostly details.
>
> Below I propose a new election method using IRV, which is closer to
> Condorcet than regular IRV and would have elected Montroll in Burlington.
>
> Method:
> If the IRV winner doesn't get >50% of the votes (including blank ballots or
> "write-in candidates") then he/she is deleted and the IRV election is re-run
> on the same ballots without the candidate.
> Repeat until we have a winner with >50%.
> If no candidate is ranked on >50% of the ballots, then a new election is
> called.
> If a candidate is ranked on >50% of the ballots, then this method will
> always produce a winner
>
> That would be, I think the smallest improvement on IRV, which could make a
> positive change in real life and would support centrist candidates.
>
> The generalized ballot completion procedure will not work in an IRV-STV
> election, I think, but adding null-candidates at the end of the empty
> ballot will work, if the null-candidate cannot be deleted. However static
> quotas is easier to understand in IRV-STV, than null candidates, I think. I
> cannot see how to integrate negative rankings in STV elections.
>
> The rest in the text below
>
> Best regards
> Peter Zborník
>
>   On Tue, May 31, 2011 at 12:19 AM, Juho Laatu <juho4880 at yahoo.co.uk>wrote:
>
>>   On 30.5.2011, at 18.41, Peter Zbornik wrote:
>>
>>  Juho,
>>
>> summarize my argument concerning generalized ballot and generalized ballot
>> completion and in the end of this email I suggest a new single-member
>> Condorcet election system.
>>
>>  Nomenclature: I think that "null-candidate" (marked "X") is a fitting
>> name for voting for not filling a seat. The other names given do not have
>> that chique mathematical sound: "White", "None of the Above", "Re-open
>> nominations", "Ficus (the plant)", etc.
>>
>> In the discussion, I think I showed the following
>>  If blank voting ("null candidates") is not allowed, then
>> truncated/incomplete ballots give different election results for winning
>> votes and for margins.
>> Compare Kevin Venzke's example:
>> 35:A>B
>> 25:B
>> 40:C
>> If we complete this election (Woodall's original proposal) to
>> 35:A>B>C
>> 25:B>A=C
>> 40:C>A=B,
>> then the election gives different results whether the candidates in the
>> ties are resolved as 0.5 vs 0.5 (margins - A winner) or 0 vs 0 (winning
>> votes - B winner)
>> (compare the results of the election at  http://condorcet.ericgorr.net/ and
>> http://www1.cse.wustl.edu/~legrand/rbvote/calc.html)
>>
>> For margins, Woodall's plurality criterion is violated.
>>
>> If the same election is completed to allow for blank voting:
>>  35:A>B>X>C
>> 25:B>X>A=C
>> 40:C>X>A=B,
>> then the election gives same result (B - winner) both for margins and for
>> winning votes and the parwise comparison matrix will be identical for both
>> methods if a an equality  awarded 0.5 votes for both candidates.
>>
>>
>> To summarize my thoughts...
>> - I think explicit cutoffs work fine when the cutoff carries some agreed
>> message (e.g. approved vs. not approved)
>> - Using explicit cutoff just as an extra candidate that voters can use as
>> a strategic tool to generate big defeats to some candidates is more
>> problematic (you can try to bury someone under X without any risk of
>> electing X)
>>
> You can try to bury someone under all other candidates anyway. Introducing
> a null-candidate as a "cuttoff" does not change that.
>
>
>>  - Implicit cutoff is problematic since it may encourage truncation
>> - Woodall's plurality criterion assumes an implicit cutoff (i.e. voters
>> are expected to vote so that unlisted candidates are considered "bad" and
>> listed candidates "good"; unlisted candidates are thus not just purely "tied
>> last")
>> - In elections where unlisted candidates should be considered purely "tied
>> last" Woodall's criterion is not relevant (i.e. when one wants "B" to mean
>> "B>A=C" and nothing more than that)
>>
> Well, I guess the relevance of any criterion depends on what the method is
> supposed to achieve.
>
>
>>  - There are many alternative rules for cutoffs (one could e.g. not use
>> the cutoff as a regular candidate that can win and lose to others but
>> require that n% of the votes must approve the winner)
>>
> Yes, I think the rule in the parentesis is the same as having a
> null-candidate, if approval is defined as explicitly ranking the cadidate on
> the ballot. As I wrote below I cannot show it though.
>
>
>>
>>
>>  Thus, truncated/incomplete ballots can be completed using the
>> following generalized symmetric ballot completion algorithm, in order to
>> give same election results for margins and winning votes and to not violate
>> Woodall's plurality criterion for margins:
>> 1.  add s "null candidates" under the ranked candidates, where s is the
>> number of seats
>> 2.  rank the unranked candidates equally and under the "null candidate".
>> 3.  equalities are resolved by giving each candidate 0.5 votes in the
>> pairwise comparison.
>>
>> If margins are used in Condorcet elections with generalized symmetric
>> ballot completion, then Woodall's plurality criterion is not violated, since
>> the "blank votes" are actually represented and the ballot is complete.
>>
>> Maybe the entry in Wikipedia could be updated, where we read "Only methods
>> employing winning votes satisfy Woodall's plurality criterion<https://mail.google.com/wiki/Plurality_criterion>
>> ."
>> http://en.wikipedia.org/wiki/Condorcet_method#Defeat_strength
>>
>>  I think an equality on the ballot between two candidates A=B should
>> intuitively mean nothing else than giving half a vote to A>B and B>A, i.e.
>> the pairwise comparison matrix should not change and Woodall's plurality
>> criterion should be kept at the same time. This is only possible if the
>> generalized symmetric ballot completion algorithm is used.
>>
>>
>> I think the original margins style of simply completing the ballots as
>> "tied last" without any implicit cutoff is ok and from that point of view it
>> is not a problem that it does not meet Woodall's plurality criterion (since
>> no implicit cutoff (meaning "approval" of the candidates) was intended). So
>> maybe the new method should not be considered an improved margins method but
>> as one of the approaches that have an implicit cutoff and that also meet
>> Woodall's plurality criterion.
>>
>
>>
>> The rule of requiring the candidate to score more than 50% in a pairwise
>> comparison which I proposed in a previous email is enforced if generalized
>> symmetric completion is used.
>>
>> Furthermore, the Wikipedia entry could also mention the inclusion of
>> "null-candidates" as the natural way to enable blank voting and avoid
>> elections of candidates, where the voters would rather like to see an empty
>> seat.
>>
>>
>> Note that Wikipedia does not want to have original research. So the
>> correct approach would be to first publish the new approach somewhere and
>> only then refer to it. (Note that the electorama web site contains many new
>> proposed methods, so it can also serve as a storage place for new methods.
>> Not a wikipedia though.)
>>
>>  I.e., A wins the following election with current Condorcet
>> implementations (disregarding if we use margins or winning votes):
>> 45:A
>> 40:B
>> 15:Blank
>>
>> If we use generalized ballot completion, then the null-candidate wins in a
>> Condorcet election (but not in an IRV election):
>> 45:A>X>B
>> 40:B>X>A
>> 15:X>A=B
>> Woodall's plurality criterion is not violated because X is not a candidate
>> to win a seat.
>>
>> Introducing a cutoff, like saying that "a winning candidate needs to be
>> explicitly ranked on 50% of the ballots" maybe is equivalent to the
>> generalized ballot completion algorithm (I don't know). However such a
>> cutoff doesn't allow for ranking between disfavoured alternatives, which the
>> generalized ballot does.
>>
>> I aggree that it is better to require the voter to rank all candidates, as
>> an incomplete ballot is completed in any case and the voter might not
>> know the ballot completion algorithm.
>>
>>
>> Having complete rankings is good but it may be ok to accept also ballots
>> that have accidentally failed to rank some of the candidates. This depends
>> also on the number of candidates (ranking 100 of them could be too much for
>> most voters).
>>
>
> Well, a truncated ballot is a shorthand for a specific type of ballot. Of
> course it could be used, but the voter should know the algoritm to translate
> the shorthand to a complete ballot. But this is essentially only technical
> details. In essence, I aggree.
>
>
>>
>>
>> I don't think that introducing a null candidate in a Condorcet election
>> has any impact on its violation of Later-no-harm, i.e..the incentive of the
>> voter to bullet-vote to maximize the success of "His" candidate. Even if the
>> equalities and null candidates would be disallowed on the ballot,
>> later-no-harm would still not hold for Condorcet elections and burying would
>> still be an efficient strategy (slightly OT: the claim that Condorcet
>> methods elect centrist canidates is questionable, since the centrist
>> candidate will be the prime target for burying attempts, since he/she has
>> the highest chance of winning, thus losing his "centricity" even before it
>> is measurable in a election).
>>
>>
>> My approach to the various criteria is that one should take into account
>> also how much some method violates some criterion. No proper method meets
>> them all. Condorcet methods are very good from this point of view in the
>> sense that although they fail Later-no-harm there is "usually and by
>> default" no harm ranking also "later" candidates. Same with burial. They are
>> vulnerable to burial but "usually and by default" one need not worry about
>> burial (=not a practical strategy in typical large public elections with
>> independent voters).
>>
>
> OK for public elections, but for a political party, where voting strategy
> is the name of the game?
>
>
>>  This "usually and by default" rule applies also e.g. to risk of one
>> party naming multiple candidates and minmax not being clone proof.
>>
>> If people start using burial in Condorcet, I believe in most cases their
>> strategy is not a good one since using burial efficiently is so difficult.
>> Typically (I guess "usually and by default") burial attempts will just cause
>> more harm than good to the strategists.
>>
>
> Do you have any references for your statements concerning "usually and by
> defaults"?
>
>
>>
>> I noted already above that having a "candidate" that can not win but that
>> can be used for burial (="X") may make burial easier and more tempting than
>> what it would be with "normal" candidates only.
>>
>
> Well, burial applies for complete ballots too and I think it is just as
> easy and tempting than with an added null candidate.
>
>
>>
>>
>> Thus, I think that the voter by default should be able to give a partially
>> blank vote, by completely ranking the candidates and the "null candidates"
>> using ">" and "=".
>>
>> Definition of a generalized ballot:
>> Maybe the discussion could focus more on constraints that can be put on
>> the generalized ballot, than on ballot completion algorithms.
>>
>> A generalized ballot is defined as:
>> i a partiall ordering (i.e. using only "=", ">") of the set C, where C
>> contains
>> ii. s enumerated instances of the h candidates in the election for s
>> seats: A11,..,A1s,...,Ah1,...,Ahs  and
>> iii. s enumerated instances of the "null candidates" X1,...,Xs.
>>
>>
>> (I just note that there are many possible ballot formats. For example one
>> where all candidates are listed and next to them there are possible ratings
>> from 1 to 20 (to be ticked) and a clear cutoff borderline between numbers 10
>> and 11 (=approval cutoff).)
>>
>
> I agree.
>
>
>>
>>
>> Some constraints on the candidate set:
>> 1. Normally we put the constraint in the election that there may only be
>> one instance of each candidate in C, i.e. C={A1,...,Ah, X1,...,Xs - each
>> elected candidate has only one seat and one vote, except for the
>> Null-candidate.
>> 2. We might restrict H in the previous point to only contain candidates ,
>> i.e. C={A1,...,Ah} and no null-hopefuls, disallowing the blank vote and thus
>> requiring a complete ranking of the candidate list.
>>
>>
>> (You didn't define and discuss basic uses of multiple null candidates and
>> multi-winner elections very much.)
>>
>
> Basically in a multiwinner elections you have as many null-candidates as
> seats, which I think is covered by the definition above and by constraint 1
> above, as the number of instances of the null candidate equals the number of
> seats (s) in the election.
>
>
>>
>>
>> Some ideas:
>> An other interesting issue, is if election systems with several election
>> election rounds can improve results in Condorcet elections, for instance, an
>> STV Condorcet election could be held with three seats.
>>
>> Those who get one of the seat go through to the second round (which maybe
>> can be automatical), where one of the candidates is elected in a Condorcet
>> election, where a Condorcet winner is guaranteed.
>>
>> Maybe an election type could be devised which makes a bottom-up
>> proportional ranking. At the start of the election, as many seats as there
>> are candidates are elected, then in each subsequent round one candidate is
>> dropped util we have a Condorcet winner.
>>
>> Example: start with six candidates and elect five of them in a five-seat
>> Condorcet-STV election, check if we have a Condorcet winner, if not, out of
>> these five, elect four of them in a four-seat election and check if we have
>> a Condorcet winner if not elect three of them in a three-seat election. Amon
>> the three elected there is always a Condorcet winner.
>>
>> Well, it's a new method at least.Could be worth trying out, maybe it will
>> help resist burying or have some other nice properties.
>>
>> Do you or anyone else around on this list have a reference to where the
>> debate between IRV and Condorcet stands today (pros and cons of the methods
>> respectively)?
>>
>> Personally I am not yet convinced that Condorcet is a "better method" than
>> IRV when it comes to resisting tactical voting.
>>
>>
>> They are quite different methods with respect to strategic voting. To me
>> the promise of Condorcet methods is that in typical political elections they
>> may avoid (rational) strategic voting even completely.
>>
>
> If you mean public elections, then maybe. If you by "typical political
> elections" mean elections in a political party, then I do certainly not
> aggree.
>
>
>>  If there is a top level cycle, then people may afterwards think "I
>> should have voted that way", but it is not easy to know what to do (except
>> to vote sincerely) before the election.
>>
>
> I don't aggree. There is polling and the voter normally knows who is the
> biggest competitor to the "favored" candidate. The competitor is buried. The
> voters for the competitor bury your favorite candidate, and the winner is a
> "nobody" that no-one cared enough about to out-maneuver and noone supports,
> but also noone dislike. In a polarized environment that is not an unlikely
> scenario.
>
> I do not personally like the idea of keeping the voter "uninformed" of the
> workings of an election system and their different strategies.
> That is a path I do not want to walk.
>
>
>>  In IRV one may end up sooner in situations where e.g. some voter group
>> knows that it should compromise (and thereby improve the result of the
>> election). This may happen e.g. when a Condorcet winner is about to be
>> eliminated at the first round and as a result "the other side" is likely to
>> win. This example is not really on "resisting tactical voting" but on
>> "requiring tactical voting". Maybe this describes my first thoughts on this
>> topic well enough. I will not try to prove these claims here (that would
>> require too many lines of text :-). IRV had some problems at least in
>> Burlington in 2009 (the Condorcet winner was eliminated).
>>
>
> Well I think that IRV might be a good approach to find the two or three
> candidates to meet in the second round.
>
> When I look at the Burlington result, then what first comes to mind is that
> the winner (Bob Kiss) didn't get 50% of the votes, but only 4313 out of 8980
> votes (48%), since there were 606 "Exhausted votes" in the final round, i.e.
> IRV used dynamic droop quotas.
>
> Thus IRV didn't respect the partially blank vote and this might be a reason
> why there is so much controversy around this election.
> A second option would have been to require complete ballots without the
> possibility to blank vote, which however might have triggered a new
> candidate "None of the Above" OR "Mr. Blank" in the election :o).
>
> So let us assume Bob Kiss wasn't elected, since he didn't get >50% of the
> votes in the end, what would have happened?
>
> Well, one approach mighet have been to hold a second round election, would
> be held, which is how presidents and such are elected most over Europe.
>
> In the second round either two or three candidates could meet depending on
> the favoured result (IRV or Condorcet).
>
> If there was only one round for the election, then I would have favoured to
> eliminate Bob Kiss (he got his chance, but didn't make 50%), and re-run the
> election.
>
> With Bob Kiss eliminated, Andy Montroll would have won and everyone would
> have been happy. I did a quick and dirty run on the reduced election data
> with Kiss, Wright and Montroll (http://rangevoting.org/JLburl09.txt, at
> the end) and Bob Kiss eliminated. Andy Montroll got more than the 4490 votes
> needed (4968 votes)
>
> Maybe a new IRV method could be considered: IRV with static quotas.
> If the IRV winner doesn't make >50%, then the IRV winner deleted and the
> IRV election is re-run.
> The generalized ballot can also be used for IRV-STV, but then we would have
> to add the rule that the null candidate(s) cannot be deleted.
>
> Ballot files used for Burlington (X are the blank ballots):
>
> With Kiss (K)
> 1332 M>K>W
> 767 M>W>K
> 455 M
> 2043 K>M>W
> 371 K>W>M
> 568 K
> 1513 W>M>K
> 495 W>K>M
> 1289 W
> 147:X
>
> Without Kiss (K):
> 1332:M>W
> 767:M>W
> 455:M
> 2043:M>W
> 371:M>W
> 568:X
> 1513:W>M
> 495:W>M
> 1289:W
> 147:X
>
>>
>> To summarize my thoughts also after reading the mail...
>> - I like explicit cutoff marks when they carry a clear agreed message that
>> voters can easily and sincerely (not to implement a strategy) rank (e..g.
>> between acceptable and non-acceptabe candidates)
>> - Ranked ballots can thus be efficiently used for collecting also
>> additional information in addition to basic ranking data
>> - In elections where there is no clear cutoff information to be collected,
>> basic rankings will work fine (i.e. no need for fixes in the basic case, it
>> works fine as it is)
>>
>   - There are many possible rules on how to take the cutoffs into account
>> in the vote counting process (check impact on strategic voting)
>>
>
> Yes here I am OK with you.
>
>
>>
>> Juho
>>
>>
>>
>>
>> Best regards
>> Peter Zborník
>>
>>
>> On Sun, May 29, 2011 at 4:29 PM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:
>>
>>
>>
>>> On 29.5.2011, at 16.06, Peter Zbornik wrote:
>>>
>>> > On the other hand I might rather prefer "My Political Opponent" to be
>>> elected than "Pol Pot".
>>> > Thus a ballot on the form A>X>My Political Opponent>Pol Pot, might be a
>>> good idea to allow.
>>>
>>>
>>> I like this kind of explicit cutoffs more than implicit ones (at the end
>>> of the ranked candidates) since implicit cutoff easily encourages
>>> truncation. If people like to truncate their strongest opponents we might
>>> end up having bullet votes only. That would mean that we would be back in
>>> plurality, and all useful information of the ranked votes would be gone.
>>>
>>> The explicit cutoff works well in elections where it is possible not to
>>> elect anyone (maybe keep the old elected alternative, or maybe arrange a new
>>> election after a while). One could also have elections where there are many
>>> possible outcomes, e.g. a seat for 6 months or a seat for 2 years
>>> (A>2y>B>C>6m>D). In these cases it is possible to measure quite reliably
>>> which candidates fall into which categories (e.g. "approvable enough"). The
>>> detailed rules on how to interpret e.g. a pairwise defeat to a cutoff entity
>>> have to be agreed.
>>>
>>> Using the cutoff to give "negative votes" to candidates below the cutoff
>>> line (in the sense that such "negative votes" would really decrease their
>>> chance of winning candidates above the cutoff line) may be problematic since
>>> people could start giving negative votes to their worst competitors as a
>>> default strategy.
>>>
>>> There have been also various proposals allowing strength of preference to
>>> be expressed (e.g. A>B>>>C>D>>E).
>>>
>>> Juho
>>>
>>>
>>>
>>>
>>> ----
>>> Election-Methods mailing list - see http://electorama.com/em for list
>>> info
>>>
>>>
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list
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>>
>>
>>
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>>
>>
>
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