[EM] 12/30/02 - Alex, Irving still holds the Trump Card:

[Adam H Tarr]

Donald wrote:

>In an Approval election there is no reason for the supporters of the two
>leading candidates to make any lower choices, but suppose ten percent do
>make lower choices.  

It depends what you mean by "supporters".  If you mean those whose first choice 
is the front runners, then I agree with you.  If you mean, those who would vote 
for the front runners in a plurality election, then many of them might actually 
prefer a lower choice.  In this case, it's entirely possible that more than ten 
percent would pick a lower choice.

Anyway, for the sake of argument, I'll agree with you here.

In an Approval election it is to the advantage of the
>supporters of the lessor candidates to make lower choices, that is, if they
>wish to have any say as to which of the two leading candidates is to win
>the election.  So, let's suppose fifty percent of the supporters of the
>lessor candidates make lower choices.

Sounds reasonable.  I'd expect more than fifty percent would make extra choices, 
but again, I'll agree for the sake of argument...

>Now, let's see what we now have.  The lower choices made by ten percent of
>the supporters of the two leading candidates are not enough to help any of
>the lessor candidates win the election.  But, the lower choices made by the
>supporters of the lessor candidates can be enough to decide the election
>between the two leading candidates.  This result is the same as if the
>lessor candidates were eliminated and their votes transferred to the next
>choices.  You should be able to realize that this ending to the election is
>the same ending as an Irving election and that the Approval election has
>turned into a variant of Irving.

Or, it is equally valid to say, "You should be able to realize that this ending 
to the election is the same ending as an Approval election and that the Irving 
election has turned into a variant of Approval."  Or, "You should be able to 
realize that this ending to the election is the same ending as an Condorcet 
election and that the Approval election has turned into a variant of Condorcet." 
 Or, "You should be able to realize that this ending to the election is the same 
ending as an Irving election and that the Condorcet election has turned into a 
variant of Irving."  Or...

The point is that EVERY alternative voting scheme, with the exception of the 
Borda count, will end up essentially throwing everyone's votes to one of the top 
two candidates when there are two clear front-runners.  So saying that the 
election "turns into a variant of Irving" is no more valid than saying it turns 
into a variant of Condorcet or Approval.

The "two strong front-runners" example is more or less the base case to examine 
for alternative voting schemes.  Only Borda screws this case up; every other 
voting scheme comes out the same.  So using this case to compare the relative 
merits of two schemes is sort of a waste of time.  The "success" of IRV in 
public elections has centered around the fact that it has kept things stuck in 
the "two strong front-runners" situation.

I don't expect Donald to respond to this message, much like he hasn't responded 
to my other recent queries to him on this list.

-Adam

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