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

[Juho Laatu]

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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