[EM] Condorcet corresponding to some variant of IRV?

[Kevin Venzke]

Bjarke,

Your idea seems to be similar to one I described awhile ago:
http://groups.yahoo.com/group/election-methods-list/message/11258
Mine didn't interest anyone.  Yours at least permits strict ranking.

I wouldn't call your method a variant of IRV or Condorcet at all,
because it has neither eliminations nor pairwise contests.  It's
more like a Bucklin variant that isn't summable.

I'll make some comments:


 --- Bjarke Dahl Ebert <bjarke2003 at trebe.dk> a écrit : 
> Here's an idea:
> 
> If you modify IRV to not cancel first votes when progressing to secondary
> votes, would that method find the Condorcet Winner?
>
> Further explanation of the counting algorithm:
> Everyone votes for their first candidate on the ballot.
> Then, in each turn, each voter enters a vote for their next candidate on
> their list, unless the "current election winner" is more preferred by them.

I think this would be better:
Every voter ranks all the candidates that they would be willing to approve
at some point.  They don't rank candidates they would never approve.  In
the first round, everyone approves their favorite.  On each subsequent
round, they approve every candidate they prefer to the worst candidate
that was the leader at any stage.  (You don't want voters withdrawing
approval.)

It will be more fair if you don't stop as soon as you have a majority.  If
you stop then, supporters of the initial leader may feel cheated.  You should
stop when the leader stops changing.

Of course, these are just suggestions, based on my own method's rules.

> 
> Example:
> 48% A>B>C
> 25% B
> 27% C>B>A
> 
> First round:
> A: 47%
> B: 25%
> C: 27%
> 
> Now, the 27% will place a vote for B also:
> A: 48%
> B: 52%
> C: 27%
> 
> So B is the winner.
> 
> This can be seen as a "simulated series of Approval Voting elections". In
> each turn, voters lower their "threshold for approval", until they are
> satisfied with the current winner.
> 
> This method will always find a unique winner (unless there is vote count
> equality, of course).
> Questions:
>   A: Will this winner always be in the Smith set?
>   B: If there is a Condorcet Winner, will it be the same as the one found by
> this method?
> (A implies B).

With my suggestions: No, and no.
I am pretty sure your original idea would not do it, either.
Either way, the count is much more complicated than Condorcet!

> In case of B, it could serve as an alternative justification of Condorcet
> Voting: "Just like IRV, but don't forget candidates just because they were
> temporarily discarded (until we knew better)".

I don't think you would convince anyone.  IRV supporters note that lower
preferences can't cause higher preferences to lose.  In my method, your
method, and my suggestions for your method, you can fairly easily cause
a higher choice to lose to a lower choice.

Also, without eliminations it just doesn't look like IRV.

I like the idea, though.


Kevin Venzke
stepjak at yahoo.fr


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