[EM] Strategy-free criterion

[Closed Limelike Curves]

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 the Favorite Betrayal criterion
> <https://electowiki.org/wiki/Favorite_Betrayal_criterion>, Strategy-Free
> criterion <https://electowiki.org/wiki/Strategy-Free_criterion>, the Strong
> Defensive Strategy criterion
> <https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion> (and Minimal
> Defense criterion <https://electowiki.org/wiki/Minimal_Defense_criterion>),
> and monotonicity <https://electowiki.org/wiki/Monotonicity_criterion>.
>
> It fails Clone-Winner <https://electowiki.org/wiki/Strategic_nomination>,
> the Plurality criterion <https://electowiki.org/wiki/Plurality_criterion>,
> the Generalized Strategy-Free criterion
> <https://electowiki.org/wiki/Generalized_Strategy-Free_criterion>, the Condorcet
> criterion <https://electowiki.org/wiki/Condorcet_criterion>, the Smith
> criterion <https://electowiki.org/wiki/Smith_set>, Participation
> <https://electowiki.org/wiki/Participation_criterion>, the Majority
> criterion for solid coalitions
> <https://electowiki.org/wiki/Majority_criterion>, and Later-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 :)
>
> Kevinvotingmethods.net
>
>
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