[EM] Trees and single-winner methods

Juho juho4880 at yahoo.co.uk
Wed Mar 14 22:45:08 PDT 2007

On Mar 14, 2007, at 19:23 , Chris Benham wrote:

> Juho wrote:
>> Here's one more election method for you to consider....
>> 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.
> I reject this on the same grounds that I reject the "candidate  
> withdrawal option" (in say IRV) and
> "Asset Voting":  I am only interested in single-winner methods  
> where the result is purely determined
> (as far as possible) by voters voting, and not by the machinations  
> of candidates/parties.
> Chris Benham

That sounds quite strict. The voters still have all the power  
although the algorithm threats different candidates slightly  
different (depending on what the candidate tree looks like). A  
majority of the voters can pick any candidate they want.

Note that it is very typical in elections that the parties will  
decide on what candidates will be offered to the voters to choose  
from in any case. So the parties will have some impact in most  
elections anyway. They may arrange preliminaries, decide if they  
nominate more than one candidate etc.

How about multi-winner elections - do you say that open and closed  
list elections are no good and only flat candidate structures like in  
STV, are ok?

I see candidate withdrawal related problems to be quite different  
from what I see in the proposed three based method. The biggest  
problem I see in candidate withdrawal is that if the person/group  
that makes the decision on withdrawal already knows the given votes,  
then it is possible to decide the winner in a small group, partially  
bypassing the opinions that the voters expressed in the ballots. This  
also opens the door to horse trading or even blackmailing. The  
proposed method at least is based on giving full information to the  
voters already before the election and letting the voters decide.

Maybe you have some examples where the proposed method would behave  
in some unacceptable way. That would help evaluating what the method  
is good for.

Note that the main reason for proposing this method is to try to  
study methods that would bypass the strategy and method alternative  
jungle of the Condorcet group in a more radical way so that Condorcet  
like ranking based methods would be usable even in some badly  
strategic environments. For this reason I'l like to invite you all to  
point out also the potential strategic problems of the method.


P.S. The proposed candidate tree structure allows candidates to be  
arranged in many different ways. They could be grouped simply into  
parties in a two layer structure or the structure could be deeper. It  
is also possible that the structure would stay flat if no strategic  
voting is expected. One approach would be to arrange the candidates  
of one party into a list. We could mark the list [A B C D] and that  
would mean a binary tree structure ((((A B) C) D). This structure  
would favour the beginning part of the list (unless the voters  
clearly express that D is the best). Since the structure of the tree  
is visible to the voters they may make their decision on what to vote  
based on what the tree is like. => If some candidate is bundled with  
another one that I don't like, maybe I won't give my support to  
either of them. Probably the candidates are similar minded after all.  
The structure gives also useful information to the voters.

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