[EM] Dan W-J; IRV is 2nd best (=worst); CVD tells Maryland 'no research ever'

Markus Schulze markus.schulze at alumni.tu-berlin.de
Fri Dec 26 03:05:01 PST 2003

```Dear Craig,

your 25 Dec 2003 example is not an example showing that Alternative
Voting violates monotonicity. Your example lets me think that your
claim that Condorcet and monotonicity were incompatible is possibly
caused by a misunderstanding of what "monotonicity" means.

******

You wrote (26 Dec 2003):
> At the moment I have no idea what Mr Schulze means by "positional".

A "positional" single-winner election method has the following
properties:

a1 >= a2 >= a3 >= ....

a1, a2, a3, ... are defined in advance and do not depend on how
the voters vote.

Every candidate gets a1 points for every first preference,
a2 points for every second preference, a3 points for every third
preference, ...

The probability that a given candidate is elected depends only on
his number of points.

******

Examples:

FPP is a positional method with a1 = 1 and a2 = a3 = ... = 0.

Suppose N is the number of candidates.
Borda is a positional method with a1 = N-1, a2 = N-2, a3 = N-3, ...

Burnitz-Varrentrapp is a positional method with a1 = 1, a2 = 1/2,
a3 = 1/3, ...

******

You wrote (26 Dec 2003):
> It explains that Mr Shulze has a greave problem with the last preference
> in the idea of the weightings that papers are multiplied by when
> contributing to the "prefers X over Y" subtotal, particularly in the
> comparison of the 2 cases:
>  (1) (...X...Y) : Y is the last preference
>  (2) (...X...) : now Y shifted over the edge.

Could you please post some examples to explain what you

******

You wrote (26 Dec 2003):
> Basic obvious errors with no defence. It is just like some fish
> looking up through bits of grass and through the water saying:
>
>   "what's the matter?: don't you believe in pairwise comparing?"

In my paper, I prove e.g. that my method satisfies Pareto, monotonicity,
resolvability, independence of clones, and Woodall's plurality criterion.
None of these criteria implicitly or explicitly presumes that the used
election method is a pairwise method. Therefore, you don't have to
"believe in pairwise comparing" to see that my method satisfies many
criteria that are considered in the scientific literature to be
important.

Markus Schulze

```