[Election-Methods] Clone related problems in Range/Approval

[Juho]

Yes, the difficulty of deciding how far to compromise may have some  
negative impacts on the outcome.

When trying to encourage voters to indicate all their preferences one  
approach that I didn't mention in my previous mail is to use some  
group names like party names.  It would be quite easy to vote e.g.  
Obama>Democrats, which means that all other Democrats would be ranked  
second.  It would be easy to add also other parties (e.g.  
Obama>Democrats>Greens) and drop some candidates lower (e.g.  
Clinton>Democrats>Greens>Obama).  If there is a limit on how long  
preference lists voters are willing to generate (e.g. 7 as you  
mentioned) then use of group names would make it easier for the  
voters to express their true preferences especially in elections that  
have very many candidates (e.g. >50).

If all truncated votes would be completed using the opinions of the  
first candidate (or some other named candidate, or the party of the  
first candidate, or whatever published list) then one could fine-tune  
the method by balancing the difficulty of using the automatic  
completion option and voter giving full rankings.  If there is a  
generic group Others then the voter can bullet vote quite easily by  
voting BestCandidate>Others.  This vote would not be automatically  
completed since it already lists all the candidates.  If no such  
"Other" group would be available then the voter could e.g. list all  
the parties to avoid his/her vote to be automatically completed.   
There are many ways to balance these rules.  It is thus possible to  
make most of the votes non-bullet-votes if there is a need.  And it  
is possible to allow the voters to either rely on the automatic  
completion or to define the preference order in more detail  
(partially or fully) by themselves.

You mentioned also the withdrawal option. As discussed before there  
may be a risk of voters getting irritated if the winner will be  
decided after the election in cabinets by the parties and candidates.  
The withdrawal option has however some strategic benefits.

I'll discuss further some methods that could be used instead of after- 
election withdrawals.

One approach to withdrawal could be to do it already before the  
elections. If one sees e.g. that some party recommends to use some  
weak candidate to bury another one then that candidate could  
withdraw. Or better than that, the candidate could declare that he/ 
she will withdraw conditionally if the strategic voting scenario  
materializes. Since the strategic scenarios are cyclic the withdrawal  
rules could be limited only to cases where there is a loop. And  
withdrawals could be limited to cover only certain pairwise  
comparisons. Some candidate could thus just indicate that he/she can  
not be used to bury some given set of candidates. Making the  
"withdrawal" rules clear already before the election would keep the  
elections fair in the sense that there would be no possibility of  
horse trading or coercion or agreed deals to withdraw in favour of  
some other candidate (maybe party favourite) after the elections.

The withdrawal rules could be hierarchic, determining levels of  
closeness to other candidates. Here's one classical strategic example.

45: A>B>C
25: B>A>C
30: C>B>A

B is the Condorcet winner but candidate A supporters could bury B  
under C and make A the winner.

45: A>C>B
25: B>A>C
30: C>B>A

If C would have declared that he/she sees B as a compromise candidate  
that should be elected in case of a cycle then B would not be beaten  
by anyone and would still win even though the A supporters tried to  
bury him/her.

One could also use the declared preferences of C to determine the  
possible "withdrawals". (Maybe better to call them just conditional  
or partial withdrawals, or friendly relationships or cancellations of  
pairwise victories.) C's declared preferences probably are C>B>A in  
line with his/her voters' preferences.

The process of counting what relationships should be considered  
friendly could be also more complex. If there is a loop and A is  
about to win then from C's preferences one can derive that C would  
like B to win instead of A. Therefore one should not consider B to  
have lost to C. If one looks at the preferences of B one can see that  
he/she wins A but there is no interest to cancel that pairwise  
victory. A of course has no reason to cancel its pairwise victories  
at this point.

We may then proceed an declare B as the tentative winner. If A has  
given the sincere "A>B>C" as his/her declared opinion then his/her  
pairwise victory over C will not be cancelled and B will stay the  
winner.

If A had given the insincere "A>C>B" as his/her declared opinion  
(giving such false preferences may not be always politically wise)  
then his/her pairwise victory over C could now be cancelled and C  
would become the winner. There would be a loop of cancellation plans  
and we need rules to handle that. One option is to use lottery if  
there are several candidates that don't lose to anybody. Also other  
possibilities exist.

If we want to avoid the loops one could force the preference  
structure to be loop free. I have sometimes proposed a tree like  
structure. That is a quite natural way for people to think. In the  
example above a complete tree like structure could either group any  
two of the candidates together (in the same subtree).

If A and B are together (looks probable based on the sincere  
preferences) then in the case of a loop and when considering partial  
withdrawals they would favour each others. The automatic partial  
withdrawals may happen at voter level. The C voters would be free to  
withdraw either for the benefit of A or B. The A>C>B voters would not  
be allowed to withdraw (in case of a loop) to support C (at least not  
in order to beat B, maybe for other uses).

One could also have rules for circular preferences within a party  
(for methods like minmax where pure party internal loops may matter).

If a tree structure is used all parties could maybe be given to  
option to one way or another to join the tree in such a way that they  
can get best possible defence by being in some binary branch when  
seen from the top of the tree down.

I wrote a long story just to point out some possibilities to do some  
withdrawal like tricks without having to do them after the election  
in cabinets. In real life many decisions may happen in cabinets after  
the election (e.g. in many systems the formation of the government).  
I however prefer to try to make the system such that the voters would  
be in charge.

Sorry about not being more formal, but maybe this is (long) enough  
for now. I may come back with a more formal definitions of the  
proposed methods.

Juho


On Apr 14, 2008, at 16:50 , Steve Eppley wrote:

> Hi,
>
> I've been making the claims Juho described below, that enough spoiling
> potential exists in Approval and Range Voting to deter parties from
> nominating more than one candidate, periodically for several years in
> this maillist, beginning with Approval.  The problem, as I see it, is
> that many voters are willing to compromise as far as needed to  
> defeat a
> "greater evil" but don't want to compromise more than necessary and
> won't know how far they need to compromise.  Some voters will fail to
> compromise far enough.  Centrist compromise candidates may be  
> unapproved
> or underrated by enough voters to cause them to lose, which may deter
> candidates from trying to be the best compromise.  Political elites
> (politicians, big donors, etc.) will expect this and will avoid the
> center.  As Juho wrote, they will avoid nominating multiple candidates
> at non-centrist positions too.
>
> There is real world evidence to support the claim regarding Approval,
> since a method extremely similar to Approval--voting Yes or No--is  
> used
> in public voting on ballot propositions.  If not for the spoiling
> problem, competing propositions would be expected more frequently.
> Almost always, the choice is between two alternatives, the proposition
> and the status quo.
>
> Juho also made a point about whether a similar problem might exist  
> given
> ranked ballot voting methods.  Voters could have trouble ranking all
> their party's candidates.  If so, parties could be deterred from
> nominating more than one candidate (or a smaller number than they  
> would
> nominate otherwise) and would continue to rely on expensive and
> haphazard primary elections to winnow their contenders.  If the ranked
> ballot voting method is Condorcetian, which would normally favor
> centrist compromise candidates, I think the point also covers centrist
> compromise parties and candidates, since if some voters fail to rank a
> "needed" compromise candidate (needed to defeat a greater evil)  
> because
> too many candidates are on the ballot, we could continue to see two  
> big
> polarized parties each nominating only one candidate per office.  I've
> written about this point too.  I first heard about it from Mike  
> Alvarez
> of Caltech years ago.  Another friend of mine found research that
> suggests people have trouble meaningfully ranking more than about 7
> items.  My proposed solution (which I've also written about several
> times) is the family of voting methods in which each voter simply
> selects one candidate on election day, and prior to election day each
> candidate publishes a rank ordering of the candidates. (The simplest
> good method in this family is the one that allows candidates to  
> withdraw
> after the votes are published, then counts each vote using plurality
> rule for the non-withdrawn candidate ranked highest in the selected
> candidate's published ordering.)
>
> Regards,
> Steve
> ----------------------
> Juho Laatu wrote:
>> It was pointed out to me that this is actually the Burr dilemma. I
>> should have remembered this example. Just coming to the same
>> conclusions using a different route. I guess the conclusions are
>> valid, and in addition to Approval and Range there are some
>> implications also on the ranked methods.
>>
>> Juho
>>
>>
>> On Apr 14, 2008, at 1:23 , Juho wrote:
>>
>>
>>> Let's assume that the set of candidates consists of groups of  
>>> clones.
>>> For example there can be multiple parties and each of these parties
>>> has multiple candidates. We further assume that typical voter
>>> preferences are such that they prefer all their own party candidates
>>> clearly over the other candidates (A1>A2>A3>>X>Y>...).
>>>
>>> The claim that I don't recall having seen before is that in Range  
>>> and
>>> Approval it makes sense to the parties not to nominate multiple
>>> candidates. I'll explain this using a simple example. There are two
>>> parties, Republicans and Democrats. The voter preferences are  
>>> roughly
>>> as follows.
>>>
>>> 54: R>D
>>> 46: D>R
>>>
>>> Let's see what happens when the Republicans nominate three
>>> candidates. If all the candidates are roughly equally popular the
>>> preferences could look as follows.
>>>
>>> 9: A>B>C>>D
>>> 9: A>C>B>>D
>>> 9: B>A>C>>D
>>> 9: B>C>A>>D
>>> 9: C>A>B>>D
>>> 8: C>B>A>>D
>>> 1: C>>B>A>D
>>> 8: D>>A>B>C
>>> 8: D>>A>C>B
>>> 8: D>>B>A>C
>>> 8: D>>B>C>A
>>> 7: D>>C>A>B
>>> 7: D>>C>B>A
>>>
>>> If Republicans have only one candidate practically all Republican
>>> voters could be expected to approve (or give full points to) only  
>>> the
>>> Republican candidate. If there are several Republican candidates one
>>> can probably not expect every republican voter to approve (or give
>>> full points to) to ALL Republican candidates. If many of them do not
>>> do so the Democratic candidate may well win even if the Republicans
>>> have majority. Nominating several candidates thus, with good
>>> probability, means that the party will lose some approvals/points.
>>>
>>> In the example preferences above there is also one voter whose
>>> sincere preferences are C>>B>A>D. This voter may not approve (or  
>>> give
>>> full points to) any other Republican candidate than C. This type of
>>> voters may make C win if the Republicans have majority. Also A and B
>>> supporters may have similar interests (or incentive as a result of
>>> noting that some C supporters are going to vote only for their
>>> favourite). Or maybe some voters will approve (or give full points
>>> to) only two of the three Republican candidates. Any tendency of the
>>> Republican voters to follow these paths naturally would make the
>>> situation of the Republicans worse.
>>>
>>> Each Republican candidate can in these elections thus easily  
>>> become a
>>> spoiler to the other Republican candidates.
>>>
>>> One can not expect all Republicans to follow the optimum strategy
>>> that would keep the multiple clone candidate case as beneficial to
>>> the party as the single candidate case is.
>>>
>>> Some Democrats may also "fail" to (optimally) approve (or give full
>>> points to) only the single Democrat candidate (but would approve /
>>> give some points to some "Democrat friendly" Republicans too). But
>>> this phenomena is probably less strong than Republicans not  
>>> approving
>>> (or giving full points to) all the three Republican candidates.
>>>
>>> An additional problem to the Republicans is that the Republican
>>> voters have no way of indicating which one of the three Republican
>>> candidates are better and which worse (since for strategic reasons
>>> they are supposed to approve them all, or give full points).  
>>> Interest
>>> to express one's preference between the Republican clones would lead
>>> to problems as described above. (Range voters could reduce just few
>>> points from the other Republican candidates, but this is risky too.)
>>>
>>> These characteristics of the methods may well lead to Republicans
>>> arranging a primary and nominating only one candidate. If they would
>>> have three candidates while Democrats would have only one would
>>> obviously be an unnecessary risk (without even adding the  
>>> possibility
>>> to select the best of the three).
>>>
>>>
>>>
>>> Now let's assume that all parties will nominate only one single
>>> candidate each. There may still be multiple parties that are  
>>> close to
>>> each others. The right wing might have another small party in
>>> addition to the Republicans. In this case the expected (optimal)
>>> voting behaviour is such that the small party supporters should
>>> approve (or give full points to) both their candidate and the
>>> Republican candidate in order not to become spoilers. So far so  
>>> good.
>>>
>>> (This also works within one party and its "clone candidates". The
>>> situation is a bit safer (but maybe not enough) if there is clearly
>>> one leading and other minor candidates that are not serious
>>> contenders to the main candidate.)
>>>
>>> The situation gets worse when the small party or parties are no more
>>> small but become serious contenders to the Republican party. Then  
>>> the
>>> clone related problems (as described at the beginning of this mail)
>>> hit also the "coalition" of the right wing parties.
>>>
>>> It is less probable than in the party internal case above that the
>>> right wing parties could arrange a joint primary. Independent  
>>> parties
>>> may well want each to nominate their own candidate. This means that
>>> some of the clone related problems may materialize.
>>>
>>>
>>>
>>> The key point was that naming clone candidates (several  
>>> candidates of
>>> one party) doesn't seem to be sensible in Approval and (competitive)
>>> Range. And that also having having several politically related (non-
>>> insignificant) parties seems to cause similar weakening of the  
>>> "party
>>> coalition".
>>>
>>> I just wrote this down since I haven't seen this anywhere and this
>>> seems to be a clear enough rule to be noted.
>>>
>>> Juho
>>>
>>>
>>> P.S. Similar problems may hit also the ranked methods if voters are
>>> too lazy to rank at least all the (strongest) own party clones.
>>> Bullet voting for one's favourite clone only may thus be a problem.
>>> If this is common parties will have the incentive to limit the  
>>> number
>>> of candidate also in ranked methods like Condorcet and IRV. One (ad
>>> hoc?) approach to fighting against these problems could be to
>>> interpret bullet votes as ranking also the other candidates of the
>>> same party ("R1" => "R1>R2=R3=R4") (or those candidates that this
>>> candidate has listed as his/her second favourites) unless the voter
>>> explicitly has indicated that the intention really is to bullet  
>>> vote.
>>> This could be also hierarchical ("party1" =>
>>> "party1>party2=party3=party4>wing1=wing2=wing3>...") or a full
>>> preference order as given by party1. (Why not also changing
>>> "party1>party3" to "party1>party3>..." using party1's other
>>> preferences to complete the ballot.)
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> 		
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