[EM] IRV vs Condorcet

[Markus Schulze]

Dear Dave,

you wrote (24 July 2003):
> DIFFERENCE:  While Condorcet compares EACH pair of candidates and develops
> a matrix of pair counts to identify best liked, IRV puts emphasis on
> patterns, giving preference to those that are ranked first.  See example
> below where B is much more popular than A, but IRV never sees this for C
> is more popular than B among B backers - even though all these C backers
> like B better than A.
>       Some call this an argument for IRV, claiming that those C votes
> were against B.  Could be, sometimes, but more likely is a simple minor
> disagreement within B's party that does not create a smidgen of desire to
> have A win.

I wouldn't say that this is an argument for IRV against Condorcet or
an argument for Condorcet against IRV. In my opinion, this is simply
a description of the count. An argument is something like "Method X
violates independence from clones while method Y meets independence
from clones." but not something like "Method X counts the votes in
this manner while method Y counts the votes in that manner."

******

You wrote (24 July 2003):
>       Condorcet precinct results are a matrix small enough to publicize
> at that level, as well as being summable and publicizable at any level,
> including the whole district - even state level for governor.  Even 10
> candidates would be manageable for this - a 10x10 matrix.
>       IRV must forward a count of how many voters vote each pattern, or
> take part in the counting by forwarding first the first rank counts, and
> then forwarding changes as each loser is eliminated.  Given 10 candidates
> there are a zillion possible patterns to forward - too many to publicize
> something understandable for many candidates at precinct level.

I guess that IRV supporters would argue ...

... that when you want to document the voters' profile then you have to
    publish how many voters vote each pattern even when Condorcet is being
    used since the voters are also interested e.g. in how many first
    preferences the different candidates have got.

... that when you only want to document the count then when IRV is being
    used you only have to publish the number of votes at each stage since
    the other information is irrelevant for the IRV count.

... that when V is the number of voters and C is the number of candidates
    then the runtime to calculate the pairwise matrix is O(V*C*C) while
    the runtime to calculate the IRV winner is only O(V*log(C)) so that
    while the Condorcet supporters are still summing their matrices the
    IRV winner is already preparing his inaugural speech.

The main question is whether summability is a desirable or an undesirable
property. I am aware that there are scientists who consider this property
undesirable (e.g. Nurmi, Bartholdi, Bowler) since compliance with this
property means that it is easier to get the information you need to run
a strategy. But I don't know any scientist who considers this property
desirable.

******

You wrote (24 July 2003):
>       While IRV gets away from most of Plurality's spoiler problems,
> it has a few of its own.  Condorcet simply DOES NOT DO spoilers.

The problem is that IRV supporters when they use the term "spoilers"
usually mean "clones" (due to Tideman's terminology) while Condorcet
supporters when they use the term "spoilers" usually mean "irrelevant
candidates" (due to Arrow's terminology). I have observed IRV supporters
and Condorcet supporters discussing for hours without even noticing
that they were discussing different kinds of "spoilers."

Markus Schulze