[EM] Double Defeat Hare

[Richard, the VoteFair guy]

On 6/22/2024 1:31 AM, Chris Benham wrote:
 > I think those of us who are extra hung-up about frustrating Burial
 > should look more closely at Double Defeat, Hare.  ...

What is Double Defeat Hare?

I didn't try to find it on Electowiki because lately that website has 
not been responding when I click on links to it.

Richard Fobes
the VoteFair guy
(and now the only Richard here)


On 6/22/2024 1:31 AM, Chris Benham wrote:
> Kevin,
> 
> Something I didn't address in my previous email:
> 
>>> And what is wrong with your "Improved
>>> Condorcet Approval" method ?  I think it would be good using
>>> unrestricted ranking ballots with an explicit approval cutoff.
>> ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my 
>> recent simulations
>> on frontrunner truncation strategy, C//A is among the best Condorcet 
>> methods. In
>> random elections I am disturbed that ICA and C//A are worse than WV 
>> methods at
>> strong FBC (i.e. what I call compromise incentive).
>>
>> You've asked me many times about C//A(explicit) and I still think it's 
>> bad. The
>> entire notion of C//A(implicit) being good at deterring burial is 
>> based on the
>> fact that if you use burial to prevent there from being a Condorcet 
>> winner, then in
>> the "cycle resolution" you cannot prefer any candidate to the one you 
>> raised
>> insincerely.
>>
>> In C//A(explicit), burial only backfires if it actually creates a fake 
>> CW. Creating
>> a fake cycle is never bad for your favorite.
> 
> In these mass public elections the chance that an individual voter's 
> ballot will be pivotal is negligible. I would think that if the method 
> is making some attempt to minimise the number of "wasted votes", then 
> many voters would want to be able to express their full sincere ranking 
> and also would at least not mind giving their sincere or semi-sincere 
> approval cutoff. For example in a Hare (aka IRV) election (with 
> unrestricted strict ranking from the top) I can't imagine it ever 
> crossing my mind to vote insincerely (and I never have).
> 
> Also I think the method needs to have some justification on the 
> assumption that the voters are sincere. So if voters complain "Why 
> aren't I allowed to rank among the candidates I don't approve?" and "How 
> do we know that the voted CW is really the CW if we have been forced to 
> truncate our rankings?", we need some answer that isn't just about 
> "deterring burial".  We could say "Well this is more simple, and it's 
> not strictly a Condorcet method but rather an Approval-Condorcet hybrid 
> that is trying to produce a high SU winner" but I expect that a lot of 
> voters would not be fully satisfied with that answer.  (I wouldn't be.)
> 
> I have become firmer in my support for Double Defeat (explicit) methods 
> and my favourite of these is Margins-Sorted Approval. Those method allow 
> voters to rank however many candidates they wish and also give a 
> approval cutoff, and no candidate that is pairwise-beaten by a more 
> approved candidate is allowed to win. Much of the time this is by itself 
> decisive.
> 
> I think those of us who are extra hung-up about frustrating Burial 
> should look more closely at Double Defeat, Hare.  I suspect that it has 
> most of the Condorcet efficiency of an actual Condorcet method while 
> retaining most of the Burial resistance of Hare, while possibly tending 
> to give higher SU winners than both.
> 
> Chris B.
> 
> On 21/06/2024 9:32 pm, Kevin Venzke wrote:
>> Hi Chris,
>>
>>> On Mono-add-Plump as a weak version of Participation:
>>>> Yes but almost all proposals fail Participation, so we will be in a 
>>>> lot of trouble
>>>> if we insist on this kind of thinking.
>>> What sort of "trouble"?  I don't see how your conclusion follows from
>>> your premise. Why do "almost all proposals fail Participation"?  It
>>> isn't because there is anything inherently wrong with "that kind of
>>> thinking". It is because it just happens that Participation is very
>>> expensive (in terms of other desirable criterion compliances, such as
>>> Condorcet).  But in that way Mono-add-Plump is very very cheap (if not
>>> free), and some of us are currently "in trouble" due to disregarding
>>> "this kind of thinking".
>> What I'm saying is that if we pursue criteria in the vein of 
>> Participation (or
>> monotonicity), we cut down the list of methods we can consider, and we 
>> aren't
>> necessarily getting anything of value except that fewer people can 
>> call the method
>> absurd. What I call inherently of value would be things like sincere 
>> Condorcet
>> efficiency or reduced strategic incentives.
>>
>>> Suppose a mini-bus with a driver is contracted to pick up a group of
>>> people and take then on a trip to one of  X, Y or Z  after polling the
>>> passengers on their ranking-preferences among these alternative
>>> destinations. After the bus is nearly full it is mistakenly assumed that
>>> there will be no more passengers and the driver applies some algorithm
>>> to the rankings of those present and announces that winning alternative
>>> is X.
>>> Then it is learned that there are two more passengers to come to fill up
>>> the bus.  They do so and the driver says to them  "I've polled all the
>>> other passengers and at the moment the winning destination is X. Where
>>> would you like to go?" and they reply "X is our first preference and Y
>>> wouldn't be too bad and we are very glad we aren't gong to Z".
>>> The driver replies "You prefer Y to Z?  In that case the new winning
>>> alternative is Y".   Now if these two voters (and perhaps others whose
>>> first preference was X) were enlightened election-method experts, they
>>> might think "Obviously this fellow's election-method algorithm fails
>>> Participation (and presumably Later-no-Harm).  Perhaps it meets
>>> Condorcet, which we know is incompatible with both Participation and
>>> Later-no-Harm. Perhaps before we showed up there was a top cycle and our
>>> Y>Z preferences turned Y into the Condorcet winner.
>>> But we know that Condorcet is also incompatible with Later-no-Help so us
>>> revealing our second preferences could have just as likely helped us, so
>>> I suppose we were just unlucky."
>>> Or if they were not experts but charitably minded they might think "I
>>> suppose it is possible that this fellow made an honest mistake due to
>>> him being thick and us confusing him with too much information".
>>> Now replay this scenario except this time the new passengers just say
>>> "Great!  We just really want to go to X and we don't know or care about
>>> any other destination."  And then the driver says "In that case the
>>> winning alternative changes from X to Y".
>>> The response could only be that the destination-decider (supposedly
>>> purely based on the passengers' stated preferences) is insane (or
>>> malevolent, in any case illegitimate)  and that Y is obviously an
>>> illegitimate winner.
>>> Did you notice a very different vibe from the first case, which was a
>>> failure of Participation and  Mono-add-Top but not Mono-add-Plump?
>> The difference in vibe is quite similar to your own difference in vibe 
>> when you
>> compare these situations.
>>
>> In one case, some voters are willing to say "I guess there were other 
>> considerations
>> in play; we were unlucky" but in the other case they won't go there. 
>> And that's
>> fine, that is their right.
>>
>>> In December 2008 on EM I argued that Schulze's Generalised Majority
>>> Criterion is a mistaken standard because the concept is vulnerable to
>>> Mono-add-Plump.
>> But given their compatibility, isn't that a strange thing to say?
>>
>>> Your new MDDA 2 method fails the example I gave:
>>> 25 A>B
>>> 26 B>C
>>> 23 C>A
>>> 04 C
>>> (78 ballots, majority threshold = 40)
>>> Implicit approval scores:  C 53,   B 51,  A 48.   No candidate is
>>> disqualified due to sub-majority approval.
>>> B>C 51-27,   C>A 53-25,   A>B 48-26.     All candidates have a
>>> "majority" strength defeat, so it "isn't possible" to disqualify any
>>> candidate on that basis.  So, according to the rules of MDDA 2, we elect
>>> the most approved candidate, C.
>>> Now say we add 22 ballots that plump for C to give:
>>> 25 A>B
>>> 26 B>C
>>> 23 C>A
>>> 26 C
>>> (100 ballots, majority threshold = 51)
>>> Implicit approval scores:  C 75,   B 51,  A 48.   Now A has sub-majority
>>> approval and so is disqualified.
>>> B>C 51-49,   C>A 75-25,   A>B 48-26.    Now C and A have
>>> majority-strength defeats and B doesn't, so (according to the rules of
>>> MDDA 2),  A (again) and C are disqualified leaving B as the new winner.
>>> The contention that C is the right winner when there were just 78
>>> ballots but when we add 22 ballots that plump (bullet vote) for C the
>>> right winner is no longer C is .... completely crazy.
>> The voters' behavior had a side effect of strengthening B. All sorts 
>> of monotonicity
>> failures take such an appearance.
>>
>> And again, there could be differences in severity, e.g. what percent 
>> of voters think
>> a given phenomenon is absurd. But I don't find that very interesting 
>> because it
>> doesn't tell us about the merits of the method. It's basically 
>> marketability.
>>
>>>> Well, in an environment where the concept of "median voter" is likely
>>>> to be meaningful,...
>>> What "environment" is that?  And why is that the environment the one we
>>> should primarily focus on?
>> One where voter and candidate preferences can be explained by an 
>> underlying issue
>> space. In this case if you could project everyone onto a plane or 
>> spectrum it would
>> be a bit easy to find the median voter and their preferred candidate.
>>
>> I think this usually describes public elections, but it probably 
>> wouldn't cover a
>> vote on what color is the best, or a vote on what cuisine to have 
>> delivered. So I
>> think we should probably have IIB for those cases.
>>
>>> I think that is the sort of thinking that
>>> leads some people to support Median Ratings methods, which we know are
>>> garbage because they fail Dominant Candidate and Irrelevant Ballots
>>> Independence, and the voters have a strong incentive to just submit
>>> approval ballots (giving the same result as Approval). And it has led
>>> you to the absurdity of suggesting a method that fails Mono-add-Plump.
>> Not at all, median rating methods aren't motivated by the notion of a 
>> single median
>> voter. There are multiple median voters on different posed questions, 
>> and that's
>> true on a pairwise matrix as well.
>>
>>> I think for the purposes of properly analysing single-winner election
>>> methods and inspiring the invention of  new ones, we can and should do
>>> without criteria that refer  to irrelevant ballots dependent "majority"
>>> thresholds or pairwise defeats.  Those have almost no positive point
>>> aside from marketing.
>> You're saying that criteria directly specifying "majority" and not 
>> something else
>> is what lacks positive points aside from marketing? That could be true.
>>
>>> My suggestion for something as close as possible to Minimal Defense:
>>> *If the number of ballots that vote X above bottom and Y no higher than
>>> equal-bottom is greater than Y's maximum pairwise support, then Y can't
>>> win.*
>> I don't hate that. I don't know what you gain from using "max pairwise 
>> support"
>> instead of "votes in total."
>>
>>> I propose Double Defeat (Implicit) as something that can substitute for
>>> the votes-only versions of Minimal Defense and SFC and also Plurality.
>>> *Interpreting ranking (or ranking above equal bottom) as approval, no
>>> candidate that is pairwise-beaten by a more approved candidate is
>>> allowed to win.*
>> It's interesting but it doesn't cover SFC. In an SFC failure scenario the
>> disqualified candidate might very well have more approval than the 
>> candidate who
>> disqualifies them. The concern is that supporters of the latter gave 
>> the election
>> away.
>>
>>> That already inspires a simple method suggestion:  DDI,MMM: *Elect the
>>> candidate  not disqualified by Double-Defeat (Implicit) that is highest
>>> ordered by MinMax(Margins).*
>>> What do you think of that?
>> I don't like it but it might be fine.
>>
>>> And what is wrong with your "Improved
>>> Condorcet Approval" method ?  I think it would be good using
>>> unrestricted ranking ballots with an explicit approval cutoff.
>> ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my 
>> recent simulations
>> on frontrunner truncation strategy, C//A is among the best Condorcet 
>> methods. In
>> random elections I am disturbed that ICA and C//A are worse than WV 
>> methods at
>> strong FBC (i.e. what I call compromise incentive).
>>
>> You've asked me many times about C//A(explicit) and I still think it's 
>> bad. The
>> entire notion of C//A(implicit) being good at deterring burial is 
>> based on the
>> fact that if you use burial to prevent there from being a Condorcet 
>> winner, then in
>> the "cycle resolution" you cannot prefer any candidate to the one you 
>> raised
>> insincerely.
>>
>> In C//A(explicit), burial only backfires if it actually creates a fake 
>> CW. Creating
>> a fake cycle is never bad for your favorite.
>>
>> Kevin
>> votingmethods.net
>>
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