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

[Juho]

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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