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

Mon Apr 14 06:50:34 PDT 2008

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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