Is STV house-monotonous?

[Mike Ositoff]

Nonmonotonic results are probably uncommon in the methods that
have them, but of course would be embarrassing in a single-winner
election where one seat result has everyone's attention.

When I used to be into PR, I remember that there was discussion
about Largest Remainder being equivalent to Hare STV, where
a voter votes only for 1 party's candidates, and everyone ranking
a party's candidates ranks all of them, in the same order.
Largest Remainder is without a doubt house nonmonotonic &
vote nonmonotonic. That was why it got into trouble in the 19th
century when it was the official method for apportioning 
the House of Representatives. When it was official, it was never
used--they instead chose the house-size so that Largest Remainder
(known in apportionment as "Hamilton's method") and
Webster's method (Sainte-Lague) would give the same result.
Webster was officially adopted in 1900, having been use for
a long time unofficially. But, curiously, in 1941, Webster,
the only unbiased monotonic apportionment method, was replaced
by a method which is instead slightly biased in favor of small
states. Ironically, that method is usually known as "Equal Proportions".
Instead of its promotional name, "Hill's method" would be a better
name for it. Huntington promoted it relentlessly & mercilessly,
but apparently Hill first proposed it. 

But Hill's slight favoring of small states is nothing compared
to how they're favored by the "Great Compromise", which gives
even the smallest state 2 senators, and the Presidential electoral
votes that go with them, and also gives every state at least 1
Representative, regardless of its size (I'd have a difficult time
arguing against that though :-)

***

If it happens only rarely, when doing STV with increasingly large
values of N, that the N-1 candidates that you've already chosen
aren't all among the N that STV currently chooses, then the
method I suggested works fine without the use of a single-winner
method: The current candidate, among the current N, that isn't
one of the previous N-1 candidates, is added to the list as the
Nth candidate.

But if not all of those N-1 are among the current N, then a
good single-winner method can pick which of the N candidates
(excluding, of course, any that are already in the list) should
be the Nth candidate in the list.

***

When talking about Largest Remainder's nonmonotonicity, I
don't mean any criticism of its use, wherever it's currently
in use, for PR. I always advocated Sainte-Lague instead, but,
for one thing, an occasional nonmonotonic result isn't such
a serious embarrassment in PR as in single-winner elections
(though Congressmembers spoke fiercely about it, because
apportionment was a hard-fought issue). In any case, it matters
little which allocation rule is used, as a practical matter.

Mike Ossipoff