[EM] Issues, Condorcet, and IRV (was: IRV vs. plurality)

[Markus Schulze]

Dear Eric,

you wrote (13 Aug 2003):
> James Green-Armytage wrote (13 Aug 2003):
> > Eric Gorr wrote (13 Aug 2003):
> > > If a voter sets the cutoff in the wrong spot and approves an option
> > > they really did not want to see win, but then causes that option to
> > > win, they have made the result worse from their point of view.
> >
> > I don't think so, assuming that they will also be approving all of the
> > candidates whom they like better than that candidate. So the addition
> > of their ballot won't help the less-liked candidate beat any of the
> > more-liked candidates -- it will be neutral in that regard. Thus it
> > will make the outcome neither better nor worse from their point of view.
>
> Who says it was less-liked by the majority of the population?
>
> We are talking about only a few voters or even just a single voters
> point of view.

Suppose that the original winner of Approval Voting is candidate A
who has got N_old(A) approvals. Suppose that the additional voter
approves candidate B who has originally got N_old(B) approvals. In so far
as candidate A is the original winner, it must be N_old(A) >= N_old(B).

If the additional voter prefers the original winner to candidate B
then this voter will also approve the original winner, so that
N_new(A) = N_old(A) + 1 and N_new(B) = N_old(B) + 1. Therefore,
N_new(A) >= N_new(B) so that candidate A is still the winner of
Approval Voting.

Markus Schulze