[EM] Strategy-free criterion
Chris Benham
cbenhamau at yahoo.com.au
Mon Jun 10 04:35:04 PDT 2024
CLC,
I assume no-one posts a ballot "intending to be irrelevant" (and
whether they do or not I don't see as relevant).
Normally I wouldn't expect irrelevant ballots to be literally "empty",
just containing no information about any of the remotely viable information.
> An equal-ranking isn’t a way to express indifference (or else
> equal-ranks would never happen); it’s a way of pleading the fifth
What?
> Learning that a voter refuses to say whether they prefer Bob or Bill
> provides an important piece of information.
>
Which is?
> Learning a voter has cast a completely blank ballot is an extreme
> case, where the ballot provides a very important piece of information:
> it means the voter expects a participation failure, because a nonempty
> ballot will hurt them.
But an empty one might "help" them ?? Hilarious.
> A rational response to this is to raise the threshold for a defeat,
> because setting the bar for a defeat closer to 50% prevents cycles
> (and therefore participation failures). In other words, these ballots
> are /very/ relevant.
Of course, you anonymous STAR Voting advocate.
Chris B.
On 7/06/2024 1:33 am, Closed Limelike Curves wrote:
> Yeah, MAMPO seems like it might behave more sensibly there.
>
> IIB doesn’t make sense to me outside of positional voting systems
> (which trivially satisfy it). If an empty ballot was genuinely
> intended to be irrelevant, the voter wouldn’t have cast it in the
> first place. An equal-ranking isn’t a way to express indifference (or
> else equal-ranks would never happen); it’s a way of pleading the
> fifth. Learning that a voter refuses to say whether they prefer Bob or
> Bill provides an important piece of information.
>
> Learning a voter has cast a completely blank ballot is an extreme
> case, where the ballot provides a very important piece of information:
> it means the voter expects a participation failure, because a nonempty
> ballot will hurt them.
>
> A rational response to this is to raise the threshold for a defeat,
> because setting the bar for a defeat closer to 50% prevents cycles
> (and therefore participation failures). In other words, these ballots
> are /very/ relevant.
>
> On Thu, Jun 6, 2024 at 7:40 AM Chris Benham <cbenhamau at yahoo.com.au>
> wrote:
>
> Kevin,
>
>> I would not like to see SFC as totally obsolete, since it was one of the motivating
>> criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
>
> Inventing those methods was some achievement as a thought
> experiment to demonstrate that certain criteria are mutually
> compatible.
>
> But MDDA spectacularly fails the maximum-absurdity criterion
> Mono-add-Plump, a very interesting fact that isn't mentioned on
> its electowiki page.
>
> https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval
>>
>>
>> Procedure
>>
>> The voter submits a ranking of the candidates. The candidates
>> explicitly ranked are considered/approved/by that voter.
>>
>> A candidate is/dominated/if more than half of the voters rank
>> some other candidate strictly above him.
>>
>> All dominated candidates are eliminated, unless this would
>> eliminate all the candidates.
>>
>> Of remaining candidates, the one approved by the most voters is
>> elected.
>>
>>
>> Criteria
>>
>> *MDDA*satisfies theFavorite Betrayal criterion
>> <https://electowiki.org/wiki/Favorite_Betrayal_criterion>,Strategy-Free
>> criterion <https://electowiki.org/wiki/Strategy-Free_criterion>,
>> theStrong Defensive Strategy criterion
>> <https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion>(andMinimal
>> Defense criterion
>> <https://electowiki.org/wiki/Minimal_Defense_criterion>),
>> andmonotonicity <https://electowiki.org/wiki/Monotonicity_criterion>.
>>
>> It failsClone-Winner
>> <https://electowiki.org/wiki/Strategic_nomination>, thePlurality
>> criterion <https://electowiki.org/wiki/Plurality_criterion>,
>> theGeneralized Strategy-Free criterion
>> <https://electowiki.org/wiki/Generalized_Strategy-Free_criterion>,
>> theCondorcet criterion
>> <https://electowiki.org/wiki/Condorcet_criterion>, theSmith
>> criterion <https://electowiki.org/wiki/Smith_set>,Participation
>> <https://electowiki.org/wiki/Participation_criterion>,
>> theMajority criterion for solid coalitions
>> <https://electowiki.org/wiki/Majority_criterion>,
>> andLater-no-harm
>> <https://electowiki.org/wiki/Later-no-harm_criterion>.
>>
>>
>
> 25: A>B
> 26: B>C
> 23: C>A
> 04: C
>
> 78 ballots (majority threshold = 40)
>
> B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
>
> All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
>
> Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
>
> 100 ballots (majority threshold = 51)
>
> B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
>
> Now only B is without a "majority-strength defeat", so the winner changes from C to B.
>
> Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.
>
> This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method would also fail Irrelevant Ballots Independence. It may be far less bad.
>
> https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition
>
>>
>> Procedure
>>
>> The voter submits a ranking of the candidates. The candidates
>> explicitly ranked are considered/approved/by that voter.
>>
>> The/score/for candidate/X/against candidate/Y/is equal to the
>> number of voters ranking/X/above/Y/. The/max score/of
>> candidate/X/is the largest score of any other candidate against/X/.
>>
>> If nobody is approved by more than half of the voters, then the
>> candidate approved by the most voters is elected.
>>
>> Otherwise, the candidate with the lowest max score, who is
>> approved by more than half of the voters, is elected.
>>
>
> Chris B.
>
>
>
> On 2/06/2024 7:23 am, Kevin Venzke wrote:
>> Hi all,
>>
>> When I test for SFC compliance the rule on cast votes is that if there is no
>> majority over A, and A has a majority over B, then B can't win.
>>
>> This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
>> in terms of a graph of majority-strength defeats, it would say that if A has a
>> majority over B and B doesn't have a majority over anyone, then B can't win.
>>
>> MD basically says that if there are two frontrunners and everyone truncates their
>> less liked frontrunner, then the worse frontrunner won't win. If this property
>> doesn't hold, it means the majority has done something to stop the method from
>> "seeing" their majority, which is surely that they ranked other candidates above
>> the preferred frontrunner. So MD is mostly about compromise incentive.
>>
>> SFC is probably going to be about truncation. When a method fails it, most likely
>> it's because the majority gave the election away to a less liked compromise choice.
>> For example:
>>
>> 20 C>A>B
>> 35 A>B
>> 5 B
>> 40 D
>>
>> Here B is the implicit approval winner, but by SFC B should not win, because it
>> means it was not safe for the A voters to rank B.
>>
>> I would not like to see SFC as totally obsolete, since it was one of the motivating
>> criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
>>
>> Kevin
>> votingmethods.net <http://votingmethods.net>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240610/d6ce63ab/attachment-0001.htm>
More information about the Election-Methods
mailing list