[EM] RE : Ranked Preference benefits

[Juho]

Ok, sorry for not capturing your intention. You also mentioned "top  
(among remaining candidates) preferences".


On the name of the method:

Name Ranked Preferences indeed seems to conflict with Ranked Pairs  
when abbreviated. I'll try to think if that could be improved. Ranked  
Preferences however sounds quite natural to me (refers also to the  
counting process, not only to ballot style).

Dyadic Ballot and Dyadic Approval do not seem to be very good base  
for naming Ranked Preferences since it doesn't have the dyadic  
properties (strength divided by 2, pairwise tree) of the Dyadic  
Approval system (that was described by Forest Simmons in http:// 
lists.electorama.com/pipermail/election-methods-electorama.com/2001- 
April/005741.html).

One name I considered earlier was Ranked Rankings but that name is  
quite cryptic. Word ranked is descriptive since the key addition to  
basic Condorcet voting is the ability to rank also the preference  
strengths in addition to ranking the candidates. Another one was  
Pairwise Comparison with Ranked Preferences (PCRP or PRP). Maybe  
simple addition Ranked Preference(s) Method would be enough to make  
the difference to Ranked Pairs. Abbreviation RPM would be in conflict  
with another familiar abbreviation but that one falls outside of the  
EM domain :-).

Juho Laatu


On Nov 4, 2006, at 4:17 , Chris Benham wrote:

> 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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>>

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