[EM] Strategy-free criterion

Fri May 31 19:56:59 PDT 2024

On Fri, May 31, 2024 at 19:04 Chris Benham <cbenhamau at yahoo.com.au> wrote:

> It [SDC] doesn't talk about just any "Condorcet winner".  It says that if
> A is the sincere CW and more than half the voters vote A above B, then the
> voters who prefer B to A can't make B win just by truncating.
>

Exactly. That was what I meant to say. Forgive me if I didn’t say it.

But maybe they can if less than half the voters vote A over B (with A still
> being the sincere CW and pairwise-beating B) and maybe they can by
> order-reversal Burial.
>

Of course.

Sincere Defense  [Minimal Defense (MDC)] says that if more than half the
> voters prefer A to B, they can stop B from winning by voting A over B and
> truncating against B.  From a Kevin Venzke webpage:
>
> https://votingmethods.net/em2005
>
> *Minimal Defense*. *(Due to Steve Eppley.)*
>
> *If more than half of the voters rank candidate A above candidate B, and
> don't rank candidate B above anyone, then candidate B must be elected with
> 0% probability.*
>
> Yes.

Steve Eppley has defined and discussed Minimal Defense here [broken link]
> <http://alumnus.caltech.edu/~seppley/> and here [broken link]
> <http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm>.
> Satisfaction of this criterion implies compliance with Mike Ossipoff's *strong
> defensive strategy criterion*, although the reverse is not necessarily
> true. That criterion can be found here [broken link]
> <http://www.barnsdle.demon.co.uk/vote/stfree.html>.
>
> Yes, it’s true that they aren’t the same, because MDC requires stipulation
of a balloting (usually ranked)…but SDSC is universally applicable, because
it’s a preference-&-sincere
criterion.

Note that the ballot must accept all preference orders; in particular, the
> voter must be able to rank multiple candidates above no one (usually by
> truncation), and to *strictly* rank any number of candidates. If the word
> "strictly" were dropped, then Approval
> <https://votingmethods.net/em2005#methappr> would satisfy, as could other
> methods using a "limited slot" ballot
>
> Yes, Approval doesn’t pass SDSC, due to the definition of “sincere” for
the preference-sincere criteria, though SDSC applies to Approval.  …& I
didn’t apply MDC to Approval.

Because I prefer preference-sincere criteria, I didn’t define a version of
MDC for Approval-balloting.

Anyway, MDC was Eppley’s version. …& the version that was
generally-accepted. …& therefore the one that I usually refer to.  …which
is fine, because we only use it for comparison of rank-methods.

> . (Approval <https://votingmethods.net/em2005#methappr> satisfies Mike
> Ossipoff's *weak defensive strategy criterion* for this reason.) In my
> opinion, the word "strictly" should be dropped, since Approval
> <https://votingmethods.net/em2005#methappr> can already be made to
> satisfy Minimal Defense just by allowing the voter to number his approved
> candidates, without analyzing the ballot any differently.
>
> Sure, if that would make the votes-only criteria apply to Approval, Score
& STAR.

> Minimal Defense deals with the issue of what a majority need to do to get
> their opinion counted. Specifically, if they are united in preferring
> candidate A to candidate B, all they have to do is not rank B. They need
> not do anything special regarding A. For instance, on these ballots:
>
> 49 B
> 13 C>A
> 13 D>A
> 13 E>A
> 12 F>A
>
> The A>B voters (i.e., the voters preferring A to B) are a majority, and do
> not rank B at all, so that Minimal Defense guarantees that B won't win.
> However, candidate B is the winner in e.g. Plurality
> <https://votingmethods.net/em2005#methfpp>, Instant Runoff
> <https://votingmethods.net/em2005#methirv>, and Descending Solid
> Coalitions <https://votingmethods.net/em2005#methdsc>. Under these
> methods, if the A>B majority want to prevent B from being elected, they
> need to insincerely raise candidate A in their rankings.
>
> —& that problem remains to some significant degree with any Condorcet
version that isn’t autodeterent.

> A more general way to view this problem is by noting that this election is
> primarily a contest between A and B. In that light, it would be very
> undesirable for the election method to elect the *wrong one* of these
> two. Minimal Defense ensures that the method can't be "confused" by the
> introduction of weaker candidates preferred to the major candidates.
>
> As for the methods which satisfy Minimal Defense, Schulze
> <https://votingmethods.net/em2005#methsch> elects A in the above scenario
> (as would any Condorcet method <https://votingmethods.net/em2005#methcond>),
> and Equal Majorities <https://votingmethods.net/em2005#methcdtt> elects
> either C, D, E, or F. (This is because all candidates besides B are in the
> CDTT; when Random Ballot <https://votingmethods.net/em2005#methrb> is
> used to break the tie, only these four candidates have any first
> preferences. Minimum Opposition
> <https://votingmethods.net/em2005#methmmpo> gives the same result,
> incidentally, although it doesn't satisfy Minimal Defense when there are
> more than three candidates.)
>
>
>
> On 1/06/2024 8:38 am, Closed Limelike Curves wrote:
>
> OK, so SFC prevents offensive truncation from defeating the Condorcet
> winner, while minimal defense provides a simple way to stop order-reversal?
>
>
> On Fri, May 31, 2024 at 4:01 PM Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> Evidently, then,  SFC merely says that the candidate can’t win without
>> order-reversal, while Minimal-Defense says he can’t win at all if the
>> minimal defensive-strategy is used.
>>
>> It seems to me that Eppley’s Minimal-Defense was the votes-only criterion
>> based on SDSC.
>>
>> …& that SDSC was the original, preference-&-sincerity version.
>>
>> I preferred preference-&-sincerity because of its universal
>> applicability, where votes-only had to stipulate a balloting.
>>
>> On Fri, May 31, 2024 at 12:33 Chris Benham <cbenhamau at yahoo.com.au>
>> wrote:
>>
>>> Why are we having a public discussion about a voting method criterion
>>> without anyone giving its definition, and with apparently most of the
>>> participants in the discussion knowing nothing about it besides its name?
>>>
>>> https://electowiki.org/wiki/Strategy-free_criterion
>>>
>>> The *strategy-free criterion* is a voting system criterion
>>> <https://electowiki.org/wiki/Voting_system_criterion> for evaluating voting
>>> systems <https://electowiki.org/wiki/Voting_system>.
>>> Definitions
>>>
>>> A sincere vote is one with no falsified preferences or preferences left
>>> unspecified when the election method allows them to be specified (in
>>> addition to the preferences already specified).
>>>
>>> One candidate is preferred over another candidate if, in a one-on-one
>>> competition, more voters prefer the first candidate than prefer the other
>>> candidate.
>>>
>>> If one candidate is preferred over each of the other candidates, that
>>> candidate is called "Condorcet candidate" or "Condorcet winner".
>>> Statement of criterion
>>>
>>> If a Condorcet candidate exists, and if a majority prefers this
>>> candidate to another candidate, then the other candidate should not win if
>>> that majority votes sincerely and no other voter falsifies any preferences.
>>>
>>> In a ranked method, it is nearly equivalent to say:
>>>
>>> If more than half of the voters rank *x* above *y*, and there is no
>>> candidate *z* whom more than half of the voters rank above *x*, then *y*
>>>  must not be elected.
>>>
>>>
>>> I think this evolved into the Minimal Defense criterion, the "votes-only
>>> version" of which says that if more than half the voters vote A over B and
>>> B no higher than equal-bottom then B can't win.
>>>
>>
>>>
>>>
>>>
>>> On 31/05/2024 9:46 pm, Michael Ossipoff wrote:
>>>
>>> Some time ago, I wrote a criterion that I called Strategy-Free-Criterion
>>> (SFC).
>>>
>>> Is that what you were referring to?
>>>
>>> It was about a circumstance in which wv Condorcet is strategy-free. At
>>> that time, autodeterence hadn’t been considered.
>>>
>>> SFC didn’t catch-on, & I haven’t heard mention of it lately, & so I
>>> don’t know it’s definition. But wv Condorcet is strategy-free in a
>>> meaningful sense.
>>>
>>> On Fri, May 31, 2024 at 05:07 Michael Ossipoff <email9648742 at gmail.com>
>>> wrote:
>>>
>>>>
>>>>
>>>> On Wed, May 29, 2024 at 14:15 Closed Limelike Curves <
>>>> closed.limelike.curves at gmail.com>
>>>> Ppwrote:
>>>>
>>>>> I'm trying to work out how the strategy-free criterion actually
>>>>> relates to strategy, because it just sounds like it means the
>>>>> majority-Condorcet criterion ("if a candidate majority-beats every other,
>>>>> they have to win if everyone is honest"). @Michael Ossipoff ?
>>>>>
>>>>  Closed, isn’t “Strategy-Free Criterion” your new name for FBC.
>>>>
>>>> It’s a very inaccurate name. FBC-complying methods aren’t strategy-free
>>>> in any sense.
>>>>
>>>>  But they’re free of any need for *drastic* defensive strategy
>>>> (favorite-burial or any defensive order-reversal).
>>>>
>>>> You want strategy-free? The wv Condorcet methods, such as RP(wv) &
>>>> MinMax(wv), are strategy-free in a meaningful sense…effectively free of
>>>> need for any defensive strategy…due to their autodeterence.
>>>>
>>>
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>>
>
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