[EM] RE : Ranked Preference benefits

[Chris Benham]

Juho,

> You mentioned "strongest indicated preference gap" as the approval  
> cut. How about defining it dynamically so that one would find the  
> strongest preference relation that still has non-eliminated  
> candidates at both sides of it? (like in RP) 

CB: I did. Or if I didn't make it clear, I meant to. Otherwise there 
wouldn't be any point to the lower ranked  "preference gaps".

> "Interpreting ballots as approving all candidates above the  strongest 
> indicated preference gap...
>
> Recalculate (among remaining candidates) the DM set and repeat the  
> whole process until an X is elected." 

When we "repeat the whole process", "strongest indicated preference gap" 
refers to "preference gap among remaining candidates".

BTW, the initials "RP" are well taken by  "Ranked Pairs" so if  your 
method is going to stick around maybe it should have a different name. 
The name
"ranked preferences" seems to just refer to the ballot style, which has 
been previously on EM called a  "dyadic ballot".

Chris  Benham



Juho wrote:

> On Nov 3, 2006, at 19:50 , Chris Benham wrote:
>
>> Juho wrote:
>>
>>> On Nov 2, 2006, at 1:29 , Kevin Venzke wrote:
>>>
>>>> Juho, --- Juho <juho4880 at yahoo.co.uk> a écrit :
>>>>
>>>>> Example 1. Large party voters consider C better than the other  
>>>>> large party candidate, but not much. 45: L>>C>R 40: R>>C>L 15:  
>>>>> C>L=R Ranked Preferences elects L. (first round: L=-10, C=-70,  
>>>>> R=-20; second round: L=-10, R=-20)
>>>>
>>>> In my opinion, if C is able to convince *every voter* to  
>>>> acknowledge that he is better than the major party alternative,  
>>>> then C is surely not a bad result.
>>>
>>> There is no need to convince every voter. This example is  
>>> simplified (for readability) but not extreme since there could  well 
>>> be a mixture of different kind of votes. (See e.g. example  4.) The 
>>> utility of C could be really low to the voters even though  it was 
>>> ranked higher than the worst candidate (in Range terms e.g.  R=99, 
>>> C=1, L=0). One of the key points of Ranked Preferences is  that also 
>>> weak preferences can be expressed and they may have impact.
>>
>> CB: So in your example is electing C a "bad result" or not?!
>
>
> I'd say it would be a bad result. If we only knew the flat  
> preferences then C would be a good choice (Condorcet winner). But  
> when we know the preference strengths electing C doesn't look  
> sensible. We may have different ways to estimate at which point C  
> should not be elected. Range would give one style of measuring it.  
> Ranked preferences gave another one which I think is quite natural.
>
>>> I'd prefer methods where voters can simply vote sincerely without  
>>> considering when it is beneficial to truncate and when not.
>>
>> Yes, don't we all.  You like methods  that  meet  Later-no-Harm   
>> and  Later-no-Help, so how
>> then is your method supposed to be better than IRV?
>
>
> This is a topic that I was planning to write more about. Ranked  
> Preferences actually can support also IRV style voting in addition to  
> Condorcet style flat preferences and many kind of more complex  
> styles. IRV style ballots would look like A>>>>B>>>C>>D>E. If all  
> voters vote this way the behaviour of the method resembles IRV.  
> Voters are thus not forced to vote in IRV style but they can do so if  
> they so want, possibly for defensive reasons (later-no-harm etc). The  
> tied at bottom rule has also a similar defensive impact.
>
> I have no clear proofs (due to complexity and insufficient background  
> work) but I believe the Ranked Preferences method quite well balanced  
> e.g. in the sense that voting IRV style is not the only or  
> recommended or optimal way to vote but just one of the alternatives,  
> for voters that really feel that way. I hope the readers of this list  
> will point out any potential weaknesses.
>
> I hope the method is better than IRV for the same reasons I believe  
> it is (in some/many aspects) better than Condorcet. It is more  
> expressive and therefore takes voter preferences better into account.  
> Maybe without introducing too many weaknesses that would spoil the idea.
>
>>> Condorcet voters need not leave non-approved candidates unlisted.  I 
>>> think Ranked Preferences provides some improvements. I'll try to  
>>> explain. If A and B voters would all truncate we would end up in  
>>> bullet voting and falling to a plurality style election. Not a  good 
>>> end result. 45: L>C=R 40: R>C=L 15: C>L=R
>>
>> Since it gives the same winner as your suggested method, why not?
>
>
> It gives the same winner in this particular case but not in general.  
> And of course I try to make the method more expressive than  
> Condorcet, not less expressive :-). (Range easily becomes Approval in  
> competitive situations. I don't want Condorcet (or Ranked  
> Preferences) to become Plurality.)
>
>>> I think it is a problem of basic Condorcet methods that they  easily 
>>> elect the centrist candidate.
>>
>> No, that is their theoretical strength.
>
>
> I agree that ability to elect centrist candidates is one of their  
> strengths. I just want to add that centrist Condorcet winners are not  
> always the best choice when we have also preference strength  
> information available when making the decision.
>
>> One big (over-looked by you) reason why  the "weak,
>> low-SU, centrist CW" is mostly a non-issue is that Condorcet  methods 
>> create strong incentive
>> for "strong" high-SU centrists to be nominated.  This idea is well  
>> explained in James Green-Armytage's
>> July 2003 essay/post  "the responsiveness of  Condorcet".
>>
>> http://lists.electorama.com/pipermail/election-methods- 
>> electorama.com/2003-July/010083.html
>
>
> Yes, good centrists probably beat the bad centrists. It however  
> doesn't harm if the method also takes strength of preferences into  
> account in a natural way. My assumption was that there are such  
> Condorcet winners whose utility (in Range terms) is low and therefore  
> should probably not be elected. Maybe the question is simply if the  
> Condorcet criterion should always be respected, e.g. when the voter  
> utilities are 49: L=99, C=1, R=0; 2: C=99, L=0, R=0; 49: R=99, L=1,  
> L=0, where C is loved by 2% and hated by 98% of the voters. It would  
> be another discussion if Ranked Preferences draws the line in the  
> correct place.
>
> In the example C is still "the compromise candidate" but does it make  
> sense to elect a generally disliked candidate. Note also that for R  
> supporters electing L would be only marginally worse than electing C.
>
> James Green-Armytage did good job in describing the benefits and  
> flexibility of the Condorcet methods. Trying to use his terms, my  
> intention has been to make the responsiveness to voter preferences  
> even stronger. Unfortunately he didn't cover the preference strength  
> related matters in that mail. But he clearly proved that centrist  
> candidates can also be ousted. Note btw that in elections it is also  
> typical that Democrats try to look like republicans and the other way  
> around in order to get the centrist votes (and some of the other  
> party votes too).
>
> It may still be a problem that if there are two major candidates/ 
> parties of equal size and one small centrist candidate/party in the  
> middle, flat preference Condoret methods have no way of expressing if  
> the centrist candidate is a well liked compromise or hated but still  
> better than the candidate of "the other side".
>
>>> If preference strengths are not known electing the Condorcet  winner 
>>> is a good choice (and basic Condorcet methods are good  methods). If 
>>> preference strengths are known, then the choice is  not that 
>>> obvious. Ranked Preferences takes into account the  relative 
>>> strength of preferences (but not the "absolute strengths"  in the 
>>> Range style). The end result is more expressive than basic  
>>> Condorcet but still quite immune to strategies (?).
>>
>> The "end result" is a horribly complicated, very awkward- to- operate 
>> monstrosity that we know
>> fails both Condorcet and  *Majority Loser* ( but you hope is "quite  
>> immune to strategies".)
>
>
> Complicated yes, but I wouldn't say horribly. As already discussed, I  
> think failing Condorcet can be justified with the inclusion of  
> preference strengths in the calculation process. Or actually the  
> methods doesn't fail Condorcet but intentionally deviates from it in  
> some cases :-).
>
> On Majority Loser we exchanged some private mails earlier. I try to  
> come back to that later but I'll skip it now to keep the length of  
> this mail in reasonable limits.
>
> On immunity to strategies I'd welcome some nasty examples where the  
> Ranked Preferences can be "cheated" with strategies.
>
>> I am a great fan of  "Definite Majority Choice" (DMC).
>> http://wiki.electorama.com/wiki/DMC
>
>
> I also find it very interesting. One could say that Ranked  
> Preferences tries to expand the idea of including additional  
> information in the Condorcet methods. DMC adds the approval cutoff.  
> RP adds different strengths of preferences (that could be seen also  
> as numerous approval cutoffs with strengths).
>
> DMC tries to stay within the Condorcet compatible domain. RP  
> intentionally took a different path and sometimes doesn't elect the  
> (flat preference) Condorcet winner.
>
> Also versions where RP style preference strengths were used but  
> Condorcet criterion would be kept are possible. Being approved (in  
> DMC style) could be defined dynamically depending on which candidates  
> are still in the race.
>
> These two methods are actually closely related. I have had it on my  
> agenda to find examples where these two methods differ and then  
> analyse them. Hope to have time to do that.
>
>> But suppose I was on the "same page" as you and thought that if   the 
>> CW is a "weak low-SU
>> centrist"  then it is desirable to elect a  "higher-SU" candidate,  
>> and also that the "ranked preference"
>> style of ballot you suggest should be used.  In that (hypothetical)  
>> case I suggest:
>>
>> "Interpreting ballots as approving all candidates above the  
>> strongest indicated preference gap ("ties"
>> resolved by approving as many as possible without approving any  
>> ranked bottom or equal-bottom)
>> calculate the Definite Majority set (i.e candidates not pairwise  
>> beaten by a more approved candidate).
>> If  that set contains one candidate X only, elect X.
>>
>> If not eliminate (drop from the ballots and henceforth ignore) the  
>> candidate with the fewest top (among
>> remaining candidates) preferences.
>> (I prefer above bottom equal-ranking to be not allowed, but if it  
>> is, then "fractional").
>>
>> Recalculate (among remaining candidates) the DM set and repeat the  
>> whole process until an X is elected."
>
>
> Aha, we are almost on the same track now. This variant is worth a study.
>
> You mentioned "strongest indicated preference gap" as the approval  
> cut. How about defining it dynamically so that one would find the  
> strongest preference relation that still has non-eliminated  
> candidates at both sides of it? (like in RP)
>
>> That at least meets  Majority Loser  and is relatively easy to  
>> operate. Also in common with IRV it meets
>> Dominant Mutual Third, Majority for Solid Coalitions and  Condorcet  
>> Loser.
>
>
> As we discussed earlier I think many criteria like Condorcet loser  
> lose their original idea in some extreme cases like with strong  
> cycles. For many criteria it is also ok if they are met in all the  
> "usual" cases, not necessarily in 100% of the cases. Therefore I  
> think it is best not to treat the criteria as boolean values (filled  
> or not) but as nice exact definitions that should be supported by  
> practical examples (real life failure cases) that demonstrate that  
> the vulnerabilities are real, not just theoretical.
>
>>> 45: L>C>R 20: C>>R>L 35: R>>C>L
>>
>> In this example you give your method electing L, failing  Majority  
>> Loser.
>
>
> Note that the method sees C>>R>L (at the first round at least) as  
> C>R=L. That means that also R is in a way a majority loser.
>
>> My suggested alternative (first) interprets the 45 L>C>R as L>C>>R  
>> and so calculates the initial DM set
>> as {C} and so elects C.
>
>
> Also Ranked Preferences (the version described in my earlier mail)  
> would elect C if L>C>R votes would be L>C>>R instead.
>
>> If instead the votes were
>>
>> 45: L>>C>R 20: C>>R>L 35: R>>C>L then all the candidates are in the  
>> initial DM set, so C is eliminated and then the "new DM set" is {R}  
>> so R wins.
>
>
> In this case Ranked Preferences would elect L. At the first round  
> this is like bullet voting in Plurality and therefore C will be  
> dropped (just like your variant does). At the second round RP gives  
> victory to L since although L would lose to R in a pairwise  
> comparison, R would be beaten even worse by C. RP thus doesn't see  
> the second round as a comparison between L and R but as a comparison  
> of three candidates (although it is already agreed that C can not win).
>
> Your variant followed in a way the IRV logic where eliminated  
> candidates do not have influence any more and the final round is a  
> plurality election between the two remaining candidates. My variant  
> followed the Condorcet logic of pairwise comparison of all the  
> candidates (the tied at bottom rule adds some details to this), with  
> the exception that it had to pick the second best option since C was  
> already eliminated.
>
> In principle I think all the candidates should be compared  
> simultaneously against each others. I'm actually not 100% happy with  
> the serial "drop the weakest" rule of the RP for this reason but it  
> works almost perfectly and other candidates seemed too complex.
>
>>> Example 4. Some of the large party voters think C is good but  
>>> majority of them think C is no good. 15: L>C>>R 30: L>>C>R 14:  
>>> R>C>>L 26: R>>C>L 15: C>L=R
>>
>> Initial approvals:  L45,  C44,  R40
>> C>R,  C>L,  L>R,  so initial DM set is {L,C}.
>> Initial top preferences: L45,  R40,  C15.
>>
>> C is eliminated  and L wins  (agreeing with your method).
>>
>>
>> Chris  Benham
>
>
> Thanks for the challenges. These surely help pointing out potential  
> problems with the RP method (and alternative paths as well). I'm not  
> sure if I covered everything. I'll try to evaluate your examples bit  
> more still (after getting some sleep first :-). Let's see if I find  
> something more.
>
> Juho Laatu
>
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