[EM] To Eliminate or Not to Eliminate, that is the question:

[Blake Cretney]

" " <donald at mich.com (Instant Runoff Voting supporter)>, on the subject
of '[EM] To Eliminate or Not to Eliminate, that is the question:', is
quoted as:

>     For those who do not like eliminating candidates, consider this
point:
>What would the voters do if they could repeat the election, after
knowing
>the results of the first election??   (Voltaire: They would eliminate
the
>lowest candidate in the repeat election)

Can you give a reference to where Voltaire said that?

>     Suppose an election with only one choice per voter that resulted
in no
>majority, like say: 40 A,  40 B,  20 C.  I claim that in the repeat
>election, the voters of the top two candidates would vote the same way,
no
>change. The A and B voters would not change their votes, they don't
need
>to. It is not to their advantage. They are members of the top two
factions.
>They have every reason to believe that they will still be in the top
two
>factions after the repeat election, it is best for them to stonewall,
to
>keep their same positions.
>     But, it would be different for the C voters, they will have to
think
>hard about what to do. They will know that the A and B voters will be
>stonewalling. I'll say that in the repeat election, most of the C
voters
>will change their votes to either A or B. (the C voters will eliminate
the
>C candidate)

You haven't fully spelled out your argument.  I think it goes something
like, if plurality voters had an election to do over, they would change
their votes just as IRV does.  

My view is the following, and you can tell me if you disagree.  Here is
one scenario that matches the example you give, but gives full
preferences for each voter.

40 A C B
40 B C A
20 C A B

Now, under IRV, A wins.  A also wins in a two round plurality, if voters
vote as you suggest.  You make the claim:

> The A and B voters would not change their votes, they don't need
to.

But that is false.  After all, A wins.  The B voters could have
prevented this by abandoning B in favour of C.  So, it appears that the
B voters do indeed "need" to change their votes, at least if they want
to get the result that is best for them.  Of course, if they change
their votes, then C wins.

More generally, if a plurality election is held where X wins, even
though Y is the sincere Condorcet winner, then, by definition, more
people prefer Y to X than the other way around.  So, if they had it to
do over, the Y over X voters would have been better off voting Y in
first place.  Since all X-1st voters prefer X to Y, and since there are
more people who prefer Y to X than X to Y, it follows that if they do
that, then there will be more Y-1st than X-1st voters.  So, Y will win. 


In other words, where a sincere Condorcet winner fails to win a
plurality election, it is because some people didn't vote their best
strategy (given the other votes).  The same result can be proven for IRV
and Approval.  It is even true of Condorcet criterion methods.

As I say, you didn't clearly specify what you were trying to prove with
your analysis, but it seems to point more towards Condorcet than IRV.

---
Blake Cretney