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

Juho juho4880 at yahoo.co.uk
Sun Apr 13 15:23:01 PDT 2008

```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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