[EM] possible improved IRV method

[Abd ul-Rahman Lomax]

At 10:00 PM 6/28/2006, Allen Pulsifer wrote:
>In certain cases, Condorcet can also result in a strange outcomes.  Take for
>example, the following (admittedly contrived) situation:
>
>166:A>B>D>C
>166:A>C>D>B
>  83:A>D>B>C
>  83:A>D>C>B
>  83:B>C>D>A
>  83:B>D>A>C
>  83:B>D>C>A
>  83:C>B>D>A
>  83:C>D>A>B
>  83:C>D>B>A
>   2:D>A>C>B
>   1:A>B>C>D
>
>The total votes is 999.  Candidate A, with 499 top rankings, is only 1 vote
>shy of a majority.  His two second rankings would bring him across the
>threshold.  Nonetheless, Candidate D, with 2 first preferences and 498
>second preferences is the Condorcet winner.  Doesn't that seem backwards?

No. In the A vs. D pairwise election, A gets 499 votes to 500 for D. 
A (bare) majority of voters prefer D to A. Now, if we knew the 
*strength* of preference, that is, if we were using something like 
Range, we might be able to extract sufficient information to warrant 
electing A.

That an election outcome (which might determine the direction of a 
jurisdication for years into the future) would be different with one 
vote changing is, indeed, strange, but it is a common characteristic 
of all binary-output election methods. It's my view that elections 
contribute to social instability, if they are the core of a system 
attempting to be democratic. But once one has accepted that elections 
are the way to go, this flip from a single vote is par for the course....

Note that D is certainly not a bad winner. D is the first or second 
choice of 417 voters, and D is the last choice of only one voter.

However, what is strange, actually, is the vote pattern. This is a 
highly polarized election, actually, between largely A partisans and 
a divided opposition to A.

But if the other candidates drop out, and it is just A against D, 
would we think it strange if D wins with 500 votes to 499 for A?

Of course, the problem with Condorcet, shown by an election like 
this, is that tertiary choices, which might not be made all that 
carefully by voters, can determine the election. In an election this 
close, I'd be much happier if there were an actual runoff between the 
top two Condorcet winners. I.e., D and A. But if we knew that the 
votes expressed above were the true and considered choices of the 
voters, it must be said that D is the majority choice.

Unless you think that the voters who had first preferences other than 
A an D should somehow be devalued and disqualified from influencing 
the outcome.