[EM] Strategy-free criterion

[Chris Benham]

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
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