# [EM] Possibly making Sainte-Lague even more STV-like

Vidar Wahlberg canidae at exent.net
Wed Sep 4 02:19:58 PDT 2013

```On Wed, Sep 04, 2013 at 12:14:36AM +0200, Kristofer Munsterhjelm wrote:
> If you're electing just one seat, then C should win; anything else
> would be unfair to a majority. But if you're picking two, then if
> you give the first seat to C, giving the second to L will bias the
> assembly to L and giving the second to R will bias the assembly to
> R. So the right outcome for two seats would be {LR}. But {C} is not
> a subset of {LR}, so house monotonicity is not desirable. You might
> argue that {C1, C2} would fix the problem, but that would just push
> the problem itself into the three-seat case.

Very well explained. Some quick thoughts this early morning:
I fully agree with you that it would make much more sense for {LR} to
win in a 2-seat election.
If you were to elect some of the seats using a quota, then resolve any
remaining seats using a pairwise method, I do see some issues once you
get more parties into the equation, let's assume a 4-seat election:
28: A>B>D>F>E>C
1: B>C>A>F>E>D
27: C>B>D>F>E>A
11: D>B>F>A>C>E
7: E>B>D>C>A>F
26: F>B>D>A>E>C

B is despite receiving very few first preference vote, still a candidate
that every voter rank high, but depending on how you'll weight down the
votes after distributing the directly (quota) won seats, B may end up
winning no seats at all. That's not quite fortunate either.
Not saying that the monotonocity criterion must be fulfilled. In your
example I would agree that in a 2-seat election then L and R should win
each their seat (and C should win in a 1-seat election), but in my
example above I would expect B to win at least one seat, regardless of
the amount of available seats (with the possible exception of 3 seats,
where 3 parties stand out, but still not enough to reach the quota).

> Second, a voter may gain undue power with additional preferences.
> Say a voter's preference is H > FRP. Then when a H seat is chosen,
> that will deweight his preference for H over AP (say), but it won't
> deweight his preference for FRP over AP. Thus some of his pairwise
> preferences get counted at full strength even though he got his
> first choice.
>
> If you want to go down this sequential deweighting route, I think
> you should instead deweight the ballots themselves. So say H gets a
> seat. Then everybody who voted for H first should have his ballot
> deweighted, including later preferences (e.g. FRP > AP). That method
> isn't summable, but it's better[1]. You'd end up with something
> somewhat similar to Forest Simmons and Olli Salmi's "D'Hondt without
> lists", but with Sainte-Laguë instead of D'Hondt. See http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-August/008561.html
> .

Interesting read, and I absolutely see your point about subsequent
preferences remaining at full strength.
Some months ago I believe I actually tried this approach (that is,
reweighting the entire vote and not just the vote strength for parties
who already won some seats), but I scrapped the idea and the code after
receiving some peculiar results. I can't rule out that the
implementation was flawed, I might give this another shot.

--
Regards,
Vidar Wahlberg

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