[EM] Markus, those aren't the kind of criteria that you said you like.

[Markus Schulze]

Dear Mike,

I wrote (10 Feb 2004):

> I propose the following defensive strategy criteria.
>
> Criterion 1:
>
>    Suppose Q1 is the number of voters who strictly
>    prefer at least one candidate to candidate A.
>
>    Suppose Q2 is the number of voters who strictly
>    prefer candidate A to candidate B.
>
>    Suppose Q1 < Q2.
>
>    Then candidate B must be elected with zero probability.
>
> Criterion 2:
>
>    Suppose Q1 is the number of voters who strictly
>    prefer candidate B to at least one candidate.
>
>    Suppose Q2 is the number of voters who strictly
>    prefer candidate A to candidate B.
>
>    Suppose Q1 < Q2.
>
>    Then candidate B must be elected with zero probability.

You wrote (11 Feb 2004):

> Markus, referring to the above, and also to your subsequently
> posted criteria: You said that you don't like criteria that
> mention voters' preferences, and that you only like criteria
> that only mention voted ballots.

My criteria refer to a set of preferences without asking where
this set of preferences comes from. When I give you a set of
preferences and I tell you who the winner is, then you can check
whether in this example these criteria have been violated without
having to know where this set of preferences comes from. This is
exactly the kind of criteria that I said I like.

I wrote (31 Jan 2004): "Election methods are usually defined as
a function from a given input (e.g. a set of partial rankings of
the candidates) to a given output (e.g. a probability distribution
on the set of candidates). Where this input comes from is of no
concern for the analysis of this election method."

I wrote (2 Feb 2004): "In so far as election methods are defined
only on the cast preferences and not on the sincere preferences,
whether a given election method satisfies a given criterion must
be reflected in the way this method uses the cast preferences.
Therefore, there is no need to include the sincere preferences
in the definition of a criterion."

Markus Schulze