# [EM] Scott Ritchie's FAVS criterion - uniquely favors range voting

Warren Smith wds at math.temple.edu
Fri Dec 15 12:08:14 PST 2006

```About Scott Ritchie's "feel alike vote same FAVS" criterion
that all members of a feel-alike group should want to vote the same.

FAVS is falsified by IRV if incomplete information:
either A or B need 5 more votes to surpass the hated C and/or the 50% mark
(but you do not know which) and your group has 10 votes.  So split them.

I am not sure whether FAVS is satisfied by IRV in complete information scenarios.

FAVS also is satisfied by Approval and Range and Plurality Voting
in complete information scenarios.  That
is because, the group decides what is the best candidate they can make win, and then they
can always make him win by voting for him max and the rest get min.

Juho Laatu pointed out that FAVS is falsified by Condorcet methods (at least in
incomplete information  scenarios) because the group may wish to create a cycle.
This can rule out the opponents being Condorcet Winners but leave that still
possible for their favorite.  A similar technique can be made to
show FAVS falsity for the Copeland (which
is a Condorcet) method even in a complete info scenario.

FAVS also is falsified by plain old approval voting in incomplete information scenarios.
See   http://rangevoting.org/RVstrat1.html#examples
and scale up the example appropriately.

I also claim FAVS is falsified by every vector-additive
method where the allowed vote-vectors
form a discrete set (e.g. Borda, Plurality) in incomplete information scenarios.  To
prove that, we set up a situation where the "best" vote is not allowed by
the rules of the voting system but is attainable as a convex linear combination
of two or more allowed kinds of votes.  (The same thing was happening in
the approval example last paragraph).

In some vector-additive methods, FAVS can also be falsified in this
way even in complete information scenarios.  For example, in vote-for-and-against voting
if the current totals are
Good   10
Lousy  15
Cruddy 15
then 4 more voters can elect Good by voting (+1,0,-1) twice and (+1,-1,0) twice
but any unified 4 votes will not do the job.  This same example also works
against Borda voting because it is equivalent to vote-for-and-against in
the 3-candidate case.

CONCLUSION: so far, all the prototypical methods (Condorcet; Weighted Positional including
Approval, Plurality, Borda; and IRV) have falsified FAVS in incomplete info scenarios.
But RANGE VOTING obeys FAVS in both complete & incomplete info scenarios.
Proof:  suppose I lied.  Then just take the vector-average of all the