# [EM] Comparing ranked versus unranked methods

Forest Simmons fsimmons at pcc.edu
Wed Feb 13 19:23:08 PST 2002

```On Tue, 12 Feb 2002, Adam Tarr wrote:

> (Side note: I'm almost
> sure sequential and non-sequential PAV are equivalent if there is no
> overlap in the votes between various voting factions.)

That's right!

As I mentioned, in some cases a pecking order is actually desirable.
Here's another example of that. Suppose that we have a closed list method
and we want to know which order to fill the list's (eventual) quota. The
party could have a sequential PAV primary.  Better yet use an open list
instead of a primary, and let sequential PAV decide the order of filling
the quota.

>
> Using d'Hondt's rule, this sort of offensive strategic manipulation
> by clever vote-splitting appears to be impossible... it seems obvious
> from playing with examples, although I'm having trouble coming up
> with a clean way to explain it.  So, it looks like d'Hondt might be
> the better choice for PAV for strategic reasons.  I consider this to
> be a shame, since Webster's is the most proportional method we could
> choose.

It's like the question of rounding up or rounding down. The bank rounds
up if you owe them any part of a penny, and rounds down if they owe you
any part of a penny.

The D'Hondt rule is the rule that comes out just right on the borderline
cases: if there are n+1 candidates in a race for n seats, and there are
two disjoint factions of size m and n*m, respectively, then the larger
faction gets the first n-1 seats, and it is a toss up between the two
remaining candidates. The case of n=1 is the case of two candidates
competing for one seat.

Off the top of my head I don't remember which of Hamilton or Jefferson
matches with d'Hondt, but if you say it was Jefferson, I'll go along with
you.

In sequential PAV d'Hondt gives a seat to the smallest party sooner than
Webster or Hamilton, so it helps the small guys.  So I guess Jefferson
wanted to favor the small states, Hamilton wanted to favor the large
states, and Webster was aiming for the middle.

Correct me if I'm wrong on this.  I'm too lazy to look it up right now.

> But when it comes to campaigning for the methods, d'Hondt
> has two advantages: it seems more intuitive, and it can be called
> Jefferson's method.

> And no good American can disagree with our
> illustrious third president.
>

How about Bart? He's a good American :-)

Forest

```