[EM] Generalized symmetric ballot completion

Fri Jun 3 04:35:55 PDT 2011

Hi Juho,

I am sending two corrections to my email below and a fourth formulation of
the approval cutoff.
I mixed up Rule 2 and Rule 1. My appologies for the spamming.

In order to avoid further mistakes,
I call Rule 1 the  "Absolute approval cutoff" or "A beats max(X,B) for all
B". Rule 1 has three different formulations 1a, 1b and 1c.
I call Rule 2 the "Approval cutoff" or "A beats X". Rule 2 has also three
different formulations 2a, 2b and 2c. Better names for the cut-off rules are
greeted.

I wrote below:
"...each member of the smith set will have have to obey rule 2 and if none
of them does, obey rule 1 and if none of them does proceed as normal."

Correction 1: Rule 1 should be Rule 2 and vice versa in the text above.
Thus the text above should read:
"...each member of the Smith set will have have to satisfy Rule 1 (the
absolute approval cutoff) and if none of them does, satisfy Rule 2 (the
approval cutoff)."

---
I wrote below:
> Thus the Woodall method, which goes: "Score candidates according to the
Hare
> [IRV] elimination order, and chose the Smith set candidate with best
score",
> could be modified to read:
> "Score candidates according to the Hare [IRV] elimination order, and chose
> the Smith set candidate which satisfies rule 2 with the best score. If
> no such candidate exists chose the Smith set candidate which satisfies
rule
> 1 with the best score."

Correction 2: Rule 1 should be Rule 2 and vice versa in the text above.
Woodalls' hybrid method should thus be modified as follows:
"Score candidates according to the Hare [IRV] elimination order, and chose
the Smith set candidate which satisfies Rule 1 (the absolute approval
cutoff) with the best score. If no such candidate exists, chose the Smith
set candidate which satisfies Rule 2 (the approval cutoff) with best score."

I don't know if the absolute majority criterion really is needed.

Best regards
Peter Zborník

On Thu, Jun 2, 2011 at 6:10 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
> Hi Juho,
>
> I am sending a two corrections:
>
> ----
>
> I wrote below:
> "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."
>
> That was not entirely unambigous, as Kristoffer pointed out.
>
> Rule 2 can be formulated as three different rules:
>
> Rule 2a. The election winner A needs to be ranked above X on >50% of the
> votes (A>X or approved by >50% of the votes).
>
> Rule 2b: The election winner needs to beat X head-to-head (A>=X, weak
> approval, allowing for neutral stances, "=" with 0.5 votes for X and A).
>
> Rule 2c: The election winner wins a Condorcet election, which includes X.
>
> ---
>
> In rules 2a and 2b, X is ranked on the ballot (either explicitly or
> implicitly) but is not a candidate in the election.
> In rule 2c, X is a candidate in the election.
>
> Rules 2b and 2c are equivalent in IRV (in the round A vs X, which occurs
> after the IRV winner gets the votes of the runner-up B where B>A ).
> Rules 2a, 2b and 2c are equivalent in IRV, if the voter is not allowed
> to rank X equal to A (X=A or A neutral).
>
> To see that Rule 2a is not equivalent to Rule 2b.
> Compare the election:
> 2:A=X
> 2:A>X
> 1:X>A
> According to Rule 2a A does not win the election (X doesn't win either
> though)
> According to Rule 2b A beats X and thus wins.
>
> Rule 2c is probably different from rule 2b as Kristoffer pointed, but we
> don't have an example to prove it yet. Such an example probably requires
> four candidates, including X, where the winner doesn't beat X in the
> pairwise comparison.
>
> Rule 2c does not require extra rules "outside" the Condorcet election a
has
> some nice properties coming out from it - margins and winning votes are
> equal and have the same pairwise comparison matrix if we use soccer
scoring
> (0.5 wins each for a tie using winning votes).
>
> With rule 2c, the election has always a winner, even though the winner can
> be the vacant seat, which also is a nice "completeness" property (or
> whatever that is called). With the other approval rules we can have a tie
> where none of the candidates wins.
>
> Rule 2c is not possible to substitute with explicit cut-offs, as A can win
> the Condorcet election even though X beats A, i.e. A has less than 50% of
> the preferences and conversly X can win the election even though A beats
X,
> i.e. the election will not have a winner even though A is preferred before
> no winner on >50% of the votes.
>
> Rule 2a and 2b are simpler to understand than 2c, but require an extra
rule
> "outside" the Condorcet election.
>
> I have no special preference between the formulation of the rules 1a, 1,b
or
> 1c and 2a, 2b or 2c. Each one of them have their pros and cons depending
on
> what they will be used for.
>
> ---
>
> I wrote below:
> "Rule 1 [...]
> 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."
>
> That was also not entirely unambiguous.
>
> Rule 1 can be formulated as three different rules, anogously to rule 2:
>
> Rule 1a. The election winner A needs also to be strictly preferred
to both B
> and X on >50% of the votes in the pairwise conparison (A>B and A>X have
> both to be true for A to get a vote in A vs B). A vote for A in A vs B is
> not A=B>X nor X>A>B or the blank vote.
> This rule is the same as strictly approving A before B and X.
>
> Rule 1b. The election winner A needs to be weakly preferred to both B and
> X on >50% of the votes in the pairwise comparison (A gets one vote in A vs
B
> if A>B and A>X, and half a vote in other cases where A>=B and A>=X).
> This rule is the same as weakly approving A before B and X (i.e allowing
to
> be neutral, "=", which counts as half a win).
>
> Rule 1c. Instead of writing "A>B and A>X", one might write "A>max(B,X)",
> where max(B,X)=B, if B>=X and max(B,X)=X. if X>B. Rule 1c states, that the
> election winner A needs to beat the compounded candidates
Y1=max(B1,X),...,
> Yk=max(Bk,X), in a Condorcet election, with the candidates A, B1,...Bk.
>
> Applying Rule 1c, we might talk about an absolute majority Smith set where
> its members win according to rule 1 against the other candidates.
> ---
>
> In rules 1a and 1b, X is ranked on the ballot (either explicitly or
> implicitly) but is not a candidate in the election.
> In rule 1c, max(X,B) is a candidate in the election.
>
> Rules 1 and 2 satisfy Woodall's plurality criterion
>
> Rules 1b and 1c are equivalent in IRV (last round).
> Rules 1a, 1b and 1c are equivalent in IRV, if the voter is not allowed
> to rank X and B equal to A (A=X and A=B are not allowed), i.e. if
equalities
> are not allowed.
>
> To see that Rule 1a is not equivalent to Rule 1b.
> Consider the election:
> 2:A=B>X
> 3:A>B>X
> 1:B>A>X
> 1:X>A=B
>
> We have the election A vs Y (Y=max(B,X))
> 2:A=Y
> 3:A>Y
> 1:Y>A
> 1:Y>A
> According to Rule 1a: A is strictly preferred to B and X on 3 ballots out
of
> 7. A doesn't win.
> According to Rule 1b A wins with 4 votes to 7.
>
> Rule 1c is probably different from rule 1b as Kristoffer pointed, but we
> don't have an example to prove it yet. Such an example probably requires
> five candidates, including X, where the winner A doesn't beat max(Bi,X)
the
> pairwise comparison for some i, 1<i<k, in .
>
> ---
>
> After reading the paper on hybrid methods, that Kristofer
> recomended (http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf), the
> hybrid IRV-Condorcet methods (Woodall, Benham, Smith-Hare and Tideman)
could
> be adjusted to accomodate the empty vote, similarly as I propose for IRV,
so
> that each member of the smith set will have have to obey rule 2 and if
none
> of them does, obey rule 1 and if none of them does proceed as normal.
>
> Thus the Woodall method, which goes: "Score candidates according to the
Hare
> [IRV] elimination order, and chose the Smith set candidate with best
score",
> could be modified to read:
> "Score candidates according to the Hare [IRV] elimination order, and chose
> the Smith set candidate which satisfies rule 2 with the best score. If
> no such candidate exists chose the Smith set candidate which satisfies
rule
> 1 with the best score."
>
> ---
>
> Juho, I like your approach to translate the ballot to normal language.
> That's the way to go.
> We need to translate the "ballot code" to language that everybody
> understands.
> No abstract playing with numbers and apocryphic ballot code words, if they
> are not absolutely needed.
> Maybe there could be several shorthand options spelt out for the most
common
> ballot choices and on the same time the full expressiveness of the
> generalized ballot could be retained for voter who request it.
>
> Best regards
> Peter Zborník
>
> On Tue, May 31, 2011 at 6:52 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
>>
>> 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."
>>>> 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
>>>> info
>>>>
>>>>
>>>> ----
>>>> Election-Methods mailing list - see http://electorama.com/em for list
>>>> info
>>>>
>>>
>>
>
>
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