[EM] Anti-defection strategy device for IBIFA

[Michael Ossipoff]

This is just an early preliminary reply. PAR & PAR' aren't something that
can be commented on at a glance.

...except to say that, due to their considerably greater complexity, they'd
of course be proposals for a 2nd reform, where one better method is
proposed to replace another better method (the 1st reform from Plurality).

Likewise, Conditional Bucklin is almost surely too complicated for a 1st
reform from Plurality.

But Conditional Approval is probably not to complicated for a 1st proposal
from Plurality.

It seems to me that Bucklin doesn't really significantly improve on
Approval.

But the conditional-option's elimination of the chicken-dilemma _is_ a
significant improvement.

Therefore, I'd rather propose Conditional Approval than ordinary Bucklin.

...but, as I was saying, activists & organizations seem to want a rank
method, and may not be convincable otherwise.

And, in fact, maybe some overcompromisers, and some rivals, need rankings,
to soften, to reduce the harm of their voting-errors.

So I'd offer ordinary Approval, Conditional Approval, Score, and ordinary
Buckin in a proposal for a 1st reform from Plurality.

Now, to reply to parts of your post that can be replied to in an early
preliminary reply:

On Fri, Nov 4, 2016 at 4:23 PM, Jameson Quinn <jameson.quinn at gmail.com>
wrote:



> I think that exploring possibilities for rules on when middle votes should
> help or not could be productive.
>


Yes, this kind of conditional-vote option is new, and the matter of the
details of methods that use it calls for more discussion.


> That's essentially what I'm doing with PAR and PAR-prime. But I think that
> conditional approval, as stated, is not a good rule; it makes center
> squeeze seriously worse.
>

Wait a minute:

"Center-squeeze" was defined as the problem of protecting a CWs, when the
CWs is the least favorite candidate.

Then how does Conditional Approval worsen that problem?

...compared to ordinary Approval?

You mean voters might apply the conditional option when approving the CWs?

No, that option is only for chicken-dilemma situations. The CWs isn't the
"B" in the chicken-dilemma scenario. B in that scenario isn't CWs.

In Approal, you shouldn't expect the CWs's voters to approve your favorite.
The CWs's voters can get their best result (the election of their favorite)
by plumping. For that goal, they should plump. Don't feel offended, and
don't feel cheated or defected against if they plump. That isn't defection,
when done by the CWs's voters.

If you have a strong top-set & a strong bottom-set, then your optimal
strategy is always to approve only all of your strong top-set.

But, maybe there's an agreement among your wing that no one will approve
past the CWse (expected or evident CWs).  Or maybe you don't have a strong
top-set, and then your optimal strategy is to plump if the CWs is your
favorite.

So you aren't cheated, and it isn't defection, if the CWs's voters plump.
You should approve the CWs, unless you have a strong top-set and s/he isn't
in it. ...and, when you approve hir, you shouldn't make it conditional.

Save the conditional vote for a chicken-dilemma.

Let me completely define Conditional Approval. This definition is brief
enough to be a proposal for a 1st reform from Plurality:

Conditional Approval:

You can approve as many or as few candidates as you want to, by marking
their names, on the ballot.

You also have a place on the ballot where you can indicate your favorite.

(in a variation of these rules, you could indicate more than one favorite
if you want to.)

For any approval that you give, you have the option of marking it as
"conditional".

A conditional vote is given only if the vote-receiving candidate is
designated favorite on more ballots than is your ballot's
favorite-designated candidate.

(...or (if ballots are allowed to designate more than one favorite) on more
ballots than is the candidate favorite-designated on your ballot who is
favorite-designated on the most ballots.)

The winner is the candidate with the most approvals.

This method, Conditional Approval, might or might not be briefly-defined
enough to propose. I'd say it's probably as briefly defined as ordinary
(non-conditional) Bucklin, suggesting that it's proposable as a 1st reform
from Plurality.

A few preliminary comments:

You mention a method that fails FBC. I suggest that FBC is essential.

And avoiding the slippery slope isn't as good as completely avoiding the
chicken-dilemma.

Michael Ossipoff

>
> Let me brainstorm some rules that might work, starting with the rules for
> PAR and PAR':
>
> -A middle-vote counts if all the top-votes on that ballot have been
> "eliminated" (PAR)
> -A middle-vote counts if, for other non-eliminated candidates, there are
> at least as many bottom-votes as top-votes on the ballot. (PAR')
> -Do a series of elimination rounds. In each round, choose the
> most-bottom-ranked candidate X as "vulnerable", and tally approvals for X
> when they are unbeaten on a ballot, and for Y≠X when Y is unbeaten by X on
> a ballot. If X wins, they are the overall winner; otherwise, eliminate them.
> ... The above is actually a Condorcet system, and not as far as I know
> equivalent to any other existing Condorcet system.
> -A middle-vote counts iff it goes to the CW. (this is simple to define.
> You could also have it go to all members of the Smith set. Or have an A>B
> ballot count for B iff B beats A pairwise.)
>
> ...As far as I can tell, all of the above systems have good outcomes in
> realistic scenarios. The problems are difficulty of explanation, and
> abstruse FBC or other violations. I think that the first filter for the
> above should be ease of explanation.
>
> Here's an attempt at an FBC method in this spirit. This method is far, far
> too complicated to ever propose seriously, but it does hit the trifecta of
> FBC, good center squeeze performance in clear-cut cases, and
> no-slippery-slope on the chicken dilemma.
>
>
>    1. Voters can Prefer, Accept, or Reject each candidate. Default is
>    Accept.
>    2. Candidates with a majority of Reject, or with under 25% Prefer, are
>    eliminated, unless that would eliminate all candidates.
>    3. Find the winner using an adjusted preference tally.
>       1. First, take a preference tally for each non-eliminated candidate.
>       2. Find the average preference tally for a non-eliminated candidate
>       X, and find the "above-average preferences" (AAP(X)) for each
>       non-eliminated candidate by taking their preference tally minus the
>       average, or zero if this is negative. For an eliminated candidate Z, AAP(Z)
>       is just their raw preference tally.
>       3. For each X including the eliminated candidates, find X's
>       "pairwise opposition portion" for each other candidate Y (POP(XY)): the
>       portion X-preferring ballots which reject Y and do not prefer any candidate
>       with a higher tally than X (breaking ties arbitrarily but consistently).
>       4. For each pair X and Y, subtract from Y's adjusted preference
>       tally, AAP(X) times POP(XY). (don't change the AAPs as you're doing this.)
>       5. When you're done, the highest adjusted preference tally wins.
>
>
> Wow. That's a crazy-complicated method. But in the Tennessee example, even
> if somehow Memphis were not eliminated in step 2 (which won't happen) and
> Knoxville and Chattanooga mutually prefer each other, you subtract 8.6667
> from Knoxville and Chattanooga, which is enough to put them below Nashville
> — a correct outcome, robust to 2 combined (and implausibly strong and
> well-organized) strategies. In other words, Nashville wins in a strong
> equilibrium, even if the Nashville voters use the self-destructive
> anti-strategy of not rejecting Memphis.
>
> And I'm pretty sure it meets FBC. By not preferring a candidate, you can
> increase another candidate's score, but not by more than 1 point; a point
> of margin you could give otherwise by just adding a preference for the
> candidate you want to win and against the one you want to lose.
>
> And in a chicken dilemma situation, it will pick the largest subfaction,
> even if that subfaction is significantly more cooperative than the other
> one (as long as the other faction cooperates enough to give a majority). No
> slippery slope.
>
> I am impressed with that method's near-perfect strategy resistance, but
> it's massively impractical as a real-world proposal. It's just a
> demonstration that these characteristics are not actually incompatible.
>
> I'm calling that method QQQ, Quinn's Quixotic Quintessence.
>
> 2016-11-04 12:16 GMT-04:00 Michael Ossipoff <email9648742 at gmail.com>:
>
>> Sure:
>>
>> 3-Slot Conditional Bucklin:
>>
>> The ballot allows voters 3 rank positions in which to rank candidates.
>>
>> The voter can use (rank someone at) as many or as few rank positions as
>> s/he wants to, but may not skip a rank and then use a rank below the
>> skipped rank.
>>
>> A voter can rank any number of candidates at any of the 3 rank positions
>> that s/he uses.
>>
>> The bottom, rank 3, is the default.
>>
>> Additionallly, the ballot has a favorite-designation place, in which the
>> voter indicates hir favorite. (Or, if preferred, the rules could let the
>> voter indicate more than one favorite).
>> ------------------------------------------------------------
>> ----------------
>> First, a description of the Bucklin count. Then the conditional-vote
>> option will be described.
>> ------------------------------------------------------------
>> ----------------
>> Bucklin is just stepwise Approval, in which the Approval votes are given
>> one at a time, instead of all at once (and, as they're given we check for
>> any candidate acquiring a majority).
>>
>> The Bucklin count consists of several rounds. In each successive round,
>> each ballot gives a vote to each candidate in the rank position where it
>> hasn't yet given votes.
>>
>> In other words, in the 1st round, each ballot gives a vote to the
>> candidate(s) in its 1st rank position.
>>
>> And in the 2nd round, each ballot gives a vote to the candidate in its
>> 2nd rank position.
>>
>> ...etc.
>>
>> If, in any round, one or more candidates acquire a vote total greater
>> than half of the number of voters, the one with the highest vote-total wins.
>>
>> If, after each ballot has given to all of it candidates, no one has a
>> majority, then the winner is the candidate who has the highest vote total
>> at that time.
>>
>> Because this is 3-Slot Bucklin, there are 3 rank positions, and voters
>> can rank as many candidates as they want at any rank position (But of
>> course you can only rank a particular candidate at one rank position.).
>> ------------------------------------------------------------
>> -----------------------
>>
>> The conditional-vote option:
>>
>> A voter can designate any vote, to any candidate, at any rank-position,
>> as "conditional".
>>
>>
>> On any particular ballot, a conditional vote in the 1st round is given
>> only if the vote-receiving candidate is designated as "favorite" by more
>> voters than the candidate who is designated favorite on that ballot.
>>
>> (If voters are allowed to designate more than one favorite, then for any
>> particular ballot, the conditional vote is given only if the vote-receiving
>> candidate is designated favorite on more ballots than is any of the
>> candidates designated as favorite on that ballot.)
>>
>> In subsequent rounds, after the 1st round, a conditional vote is given b
>> a ballot only if the vote-receiving candidate has a higher vote-total (just
>> before that round) than any candidate who is designated favorite on that
>> ballot.
>>
>> ------------------------------------------------------------
>>
>> [end of method description]
>>
>> People don't like complicated method-definitions. I'd probably save
>> conditional votes for a later refinement, and offer only ordinary,
>> non-conditional Bucklin first.
>>
>> But Conditional Approval would be simpler and could maybe be offered as a
>> 1st reform.
>>
>> Michael Ossipoff
>>
>>
>>
>>
>>
>>
>>
>>
>> On Fri, Nov 4, 2016 at 11:27 AM, Jameson Quinn <jameson.quinn at gmail.com>
>> wrote:
>>
>>> Could you state Conditional 3-slot Bucklin as you would define it for
>>> somebody who didn't know what "Bucklin" was?
>>>
>>> 2016-11-04 11:15 GMT-04:00 Michael Ossipoff <email9648742 at gmail.com>:
>>>
>>>> I'd said that, like 3-Slot ICT, Conditional Bucklin doesn't let you
>>>> give full protection to the distrusted voters candidate, or to any
>>>> candidate that you merely approve, because you aren't helping hir get a
>>>> majority.
>>>>
>>>> But then, in a later posting, i said that the favorite-designation
>>>> shouldn't give anything in the points-count, because that would create a
>>>> strategic need to give that favorite designation to a compromise, or to the
>>>> distrusted voters' candidate.
>>>>
>>>> So the favorite designation would be distinct from the ratings that
>>>> give points, such as an Approval ballot, or the 1st rank of a Bucklin
>>>> ballot.
>>>>
>>>> Well, my 2nd comment fixes the problem that I mentioned in my 1st
>>>> comment.
>>>>
>>>> Have a favorite-designation that doesn't count for points in any way,
>>>> and whose only use is for determining whether the conditional approval
>>>> should be given.
>>>>
>>>> Below that is the Approval ballot, or the Bucklin ballot, starting with
>>>> its 1st rank position.
>>>>
>>>> Then, the method is Conditional Approval, or Conditional Bucklin, with
>>>> a favorite-designation used only for determining whether the conditional
>>>> approval will be given.
>>>>
>>>> In Conditional Buckllin,  every vote given by a ballot, at every stage
>>>> of the count (or every vote other than the the one given in the 1st round),
>>>> can be conditional, if the voter so marks it.
>>>>
>>>> A special case of that would be 3-Slot Conditional Bucklin, in which,
>>>> in addition to the favorite-designation, the ballot has a 3-Slot Bucklin
>>>> ballot
>>>>
>>>> As I said last night, at any particular round of Conditional Bucklin,
>>>> the conditional vote would be given if the vote-receiver's vote total, just
>>>> before that round is greater than that of the giving ballot's designated
>>>> favorite with the highest vote total at that time.
>>>>
>>>> But maybe it would be better to only allow a ballot to designate one
>>>> favorite, partly to simplify the count rule, shortening the definition,
>>>> making it easier to propose.
>>>>
>>>> So: Conditional Approval, or Conditional Bucklin--which would include
>>>> Conditional 3-Slot Bucklin.
>>>>
>>>> As I said, no doubt Chris's improved interpretation of majority is
>>>> indeed an improvement, but it's too complicated for a first reform from
>>>> Plurality. It would be a good refinement for later.
>>>>
>>>> When there are two or more candidates getting a majority in a round, or
>>>> when there are no majorities at the end of the count, I prefer declaring
>>>> the winner based on vote-total, rather than top-count.
>>>>
>>>> For one thing it results in a briefer definition.
>>>>
>>>> And it makes the votes given at the various non-top stages of the count
>>>> more effective, which seems more in keeping with Bucklin's purpose..
>>>>
>>>> And it chose D in Forest's example that I was discussing last week.
>>>>
>>>> I understand that using the top-count instead of the vote-total helps
>>>> the chicken dilemma situation some, but it doesn't eliminate the chicken
>>>> dilemma..That's especially ok if the chicken dilemma problem is eliminated
>>>> by Chris's conditional vote option.
>>>>
>>>> Michael Ossipoff
>>>>
>>>>
>>>> On Thu, Nov 3, 2016 at 8:53 AM, C.Benham <cbenham at adam.com.au> wrote:
>>>>
>>>>> I normally don't like explicit strategy devices, and (beyond
>>>>> considering it desirable to elect from the
>>>>> voted Smith set) don't care very much about the "center squeeze"
>>>>> effect.
>>>>>
>>>>> (I like truncation resistance, so I'm happy with some of the methods
>>>>> that meet the Chicken Dilemma criterion.)
>>>>>
>>>>> Nonetheless here is  version of  IBIFA with a device aimed at
>>>>> addressing the Chicken Dilemma scenario.
>>>>>
>>>>> * Voters mark each candidate as one of  Top-Rated, Approved,
>>>>> Conditionally Approved, Bottom-Rated. Default is Bottom-Rated.
>>>>>
>>>>> A candidate marked "Conditionally Approved" on a ballot is approved if
>>>>> hir Top Ratings score is higher than the highest
>>>>> Top Ratings score of any candidate that is Top-Rated on that ballot.
>>>>>
>>>>> Based on the thus modified ballots, elect the 3-slot IBIFA winner.*
>>>>>
>>>>> ("Top-Rated"  could be called 'Most Preferred' and "Bottom-Rated"
>>>>> could be called 'Unapproved' or 'Rejected').
>>>>>
>>>>> To refresh memories, IBIFA stands for "Irrelevant-Ballot Independent
>>>>> Fall-back Approval", and the 3-slot version goes thus:
>>>>>
>>>>> *Voters rate candidates as one of  Top, Middle or Bottom. Default is
>>>>> Bottom.  Top and Middle is interpreted as approval.
>>>>>
>>>>> If any candidate X  is rated Top on more ballots than any non-X is
>>>>> approved on ballots that don't top-rate X, then the X
>>>>> with the highest Top-Ratings score wins.
>>>>>
>>>>> Otherwise the most approved candidate wins.*
>>>>>
>>>>> http://wiki.electorama.com/wiki/IBIFA
>>>>>
>>>>> 35: C
>>>>> 33: A>B
>>>>> 32: B (sincere might be B>A)
>>>>>
>>>>> In the scenario addressed by the Chicken Dilemma criterion, if all
>>>>> (and sometimes less than all) of A's supporters only "conditionally"
>>>>> approve B then the method meets the CD criterion.  Otherwise it meets
>>>>> the Minimal Defense criterion.
>>>>>
>>>>> http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion
>>>>>
>>>>> http://wiki.electorama.com/wiki/Minimal_Defense_criterion
>>>>>
>>>>> Of course it meets the Plurality criterion and doesn't have any
>>>>> random-fill incentive.
>>>>>
>>>>> The downside is that the use of  Conditional Approval can cause a
>>>>> vulnerability to Push-over strategy.
>>>>>
>>>>> 48: C
>>>>> 27: B
>>>>> 25: A>>B
>>>>>
>>>>> The A supporters are all only conditionally approving B, but that has
>>>>> the same effect as normal approval because B has a higher Top Ratings score
>>>>> than A.  But now if 3 to 22 of the C voters change to C=A  then A's
>>>>> Top Ratings score rises above B's so the "conditional" approval is switched
>>>>> off
>>>>> and then C wins.
>>>>>
>>>>> I dislike this "at the same time"-no-help failure, but the new result
>>>>> doesn't look terrible and of course if the B voters really prefer A to C
>>>>> then
>>>>> they were foolish not to conditionally approve A. If they'd done that
>>>>> then the attempted Push-over would have just elected A.
>>>>>
>>>>> (It crossed my mind to try to make Push-over strategising  more
>>>>> difficult and riskier with the same mechanism I suggested a while ago for
>>>>> IRV
>>>>> or Benham that allows above-bottom equal-ranking, but that would have
>>>>> broken compliance with FBC.)
>>>>>
>>>>> Chris Benham
>>>>>
>>>>>
>>>>
>>>> ----
>>>> Election-Methods mailing list - see http://electorama.com/em for list
>>>> info
>>>>
>>>>
>>>
>>
>
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