# [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
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 :-) ?

- 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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