[EM] Trees and single-winner methods

Juho juho4880 at yahoo.co.uk
Sun Mar 11 14:59:19 PDT 2007

P.S. Neutrality maybe needs some additional words. The candidate tree  
makes the behaviour of the method slightly different with respect to  
different candidates. Otherwise similar ballots but with different  
names do not always behave the same way. The method is neutral as a  
whole (candidate set-up is seen as part of the method) although the  
ballots calculation process is not (when candidate set-up is seen as  
an external input to this process).


On Mar 11, 2007, at 22:50 , Juho wrote:

> Here's one more election method for you to consider. I often
> represent the view that in public large scale elections the risk of
> successful strategic voting is not that big (at least in countries
> where strategic tricks are not widely used). This one however tries
> to study the other extreme - what kind of tricks would we need to
> eliminate as many of the discussed strategic voting scenarios as
> possible. Please check it and tell what it is good for (and what not).
> Let's start from a Condorcet method (it doesn't matter much which
> one). Then we allow the candidates to form groups. Each group will be
> handled as if it was a single candidate. The group will be considered
> as good as the best candidate within it. In one ballot the group will
> be considered better than another group (or candidate) if the best of
> its members is considered better than the best member of the other
> group (or the single candidate). These groups are typically alliances
> of similar minded candidates. Their members could be called
> "clones" (but in another meaning than what term "clone" typically
> refers to in the EM list).
> In order to reduce the vulnerability to strategies the ultimate thing
> we could do would be to arrange the candidates in embedded small
> groups so that the in the end the candidate set-up would become a
> binary tree where each level contains just two alternative groups (or
> candidates).
> The individual candidates and groupings and parties are expected to
> make decisions on what the tree (binary or not) looks like. The
> election organizers maybe would create the root part of the tree if
> the groups/candidates/parties were not able to provide just one tree
> that would already contain all the candidates. Creating just a flat
> list at the root level is maybe not a good idea if maximum defence
> against strategies is sought since in that case other parties/groups/
> candidates could leave those parties/groups/candidates that they
> intend to bury to the flat list. (One could arrange the biggest
> subtrees closest to the root, or maybe just make a random binary tree
> (with balanced root part).)
> The tree structure limits the way voters can express themselves. With
> candidate tree structure (A1, A2), (B1, B2) vote A1>B1>A2>B2 and vote
> A1>A2>B1>B2 have the same impact. Voters are only allowed to tell
> which branch they prefer. And then within the winning branch which
> one of the candidates of that branch they prefer. (The tree structure
> will also not respect the Condorcet criterion in all cases.)
> On the other hand having a structure among the candidates is
> informative to the voters. Especially if the number of candidates is
> big, then having a grouping between them has some value. It is also
> possible to vote for a group. In the example above one could vote
> A1>A2>B where "B" represents the whole branch (B1, B2) ("B" is the
> name of that branch).
> In the extreme binary three format this method becomes in practice a
> majority vote between two "candidates" at each level. This is what I
> meant with the idea to eliminate as many strategic voting scenarios
> as possible. Would the binary variant of the method solve some of
> your worst nightmare scenarios where laws of jungle rule today :-) ?
> Additional observations:
> - It would be also possible to use the tree structure for tie
> breaking only (but "strategy elimination" would not be as strong)
> - I have recommended the tree structure also for multi-winner
> elections ("tree voting") => maybe more natural there, but not
> without benefits in the single-winner case either
> - It is possible to use also bullet style or Approval style ballots
> in addition to the ranking style ballots discussed above (also multi-
> winner)
> Juho Laatu
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