# [EM] Schwartz and Mono-add-top compatibility

Kevin Venzke stepjak at yahoo.fr
Sat Jan 31 12:06:03 PST 2004

```I increasingly think that Schwartz and Mono-add-top must be incompatible.

Suppose we aim to meet both of these criteria with a method called
"Schwartz//MaxJ" where we elect that Schwartz member who maximizes property
J.  Say that in scenario S, candidate A is elected.  Suppose candidate B
who is not in the Schwartz set has a better J score than A does.  By adding
ballots with A ranked first, A is guaranteed to remain in the Schwartz set
(as well as, e.g., remain the FPP winner if he was before).  We can't
guarantee, though, that B stays out of the Schwartz set in this new
scenario T (let's call it).  If B joins the Schwartz set and has a superior
J score to A, then A's victory won't be preserved from S to T.

Consider "Schwartz//Best Winner" where we elect the Schwartz member who wins
the most decisive contest won by a Schwartz member (over any other candidate).
We'll encounter the problem if it is a Schwartz non-member who wins in the strongest
contest between ANY pair of candidates, since adding new ballots could move
that pairwise winner into the Schwartz set.

Same problem with "Schwartz//FPP."  Unless the winner of this method is also
the FPP winner among all candidates, we can't guarantee that adding new ballots
with that winner ranked first, will preserve his victory.

Can anyone think of any approach for coming up with some property "J" that
would permit Schwartz//MaxJ to meet Schwartz and Mono-add-top?

Kevin Venzke
stepjak at yahoo.fr

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