[EM] RE : Ranked Preference benefits

[Juho]

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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