[EM] Trees and single-winner methods

Juho juho4880 at yahoo.co.uk
Sun Mar 11 13:50:51 PDT 2007

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  

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- 

Juho Laatu

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