[EM] Approval, IGB, and Participation

[Markus Schulze]

Dear Kevin,

you wrote (22 Sep 2003):
> I don't think they're the same thing.  For Participation, the same candidate
> doesn't have to win in both sets.  Participation is harder in that sense.
> But perhaps Consistency is harder in that the winner of the set has to be
> evaluated, not just its ranking order.  Consistency doesn't require that the
> new set consist of identical ballots.

Actually, the term "identical" in the definitions of participation, mono-add-top,
and mono-delete-bottom is superfluous. You can ignore this term and the meanings
of these criteria don't change. But the additional presumption that these ballots
are identical makes it more simple to discuss these criteria.

The original definition of "participation" says that a single additional voter
who strictly prefers candidate A to candidate B must not change the winner from
candidate A to candidate B. The problem of this original definition (even if it
is described in a probabilistic manner) is that a single voter usually cannot
change the winner from one candidate to another candidate, but only from one
decisive situation to an indecisive situation or from one indecisive situation
to a decisive situation so that it is usually not clear whether a violation of
the original definition of participation is really an intrinsic problem of the
proposed election method or only a problem of the suggested method to solve
indecisive situations. Therefore, it makes more sense to talk about a set of
additional voters who strictly prefer candidate A to candidate B and who change
the result from a decisive win of candidate A to a decisive win of candidate B.
By talking about a "set of voters", you circumvent the question which voter
worsened the result of the elections; you can simply add one voter after the
other and --as you know that adding all additional voters changed the result
from a decisive win of candidate A to a decisive win of candidate B-- one
of these additional voters must have worsened the result of the elections.
However, to guarantee that the original definition and the new definition
of participation are identical, it is not necessary that all the additional
voters vote in the same manner.

Markus Schulze