[EM] Comparing ranked versus unranked methods

[Adam Tarr]

Forest wrote:
>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.

This is an excellent idea for a PR method, although it makes for bizarre 
voting instructions (vote for candidates in only one list, but as many 
candidates as you like _within_ that list).  But when you think about it, 
the advantages of this system over straight PAV with a d'Hondt quota are 
minimal.  The only one I can see is that you could use a Webster Quota on 
the parties without too much fear of manipulation.  But I don't think this 
makes it worth it to go with this over PAV.

>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.

"just right" is a sort of subjective term.  In the case of this example, 
Webster gives the first.n/2 seats to the large party, then gives one to the 
smaller party, then gives the rest to the larger party.

d'Hondt gives the smaller party a seat as soon as giving it a seat will 
still leave it with a larger ratio of votes/seat than the other 
party.  Webster in stead gives this party a seat as soon as the error 
(difference between actual votes/seat and ideal votes/seat) is largest for 
this party.  This could also be seen as "just right."

The problem with Webster and PAV is not its fairness in allocation, which 
is arguably impeccable in the ideal, but rather its manipulability as 
compared to d'Hondt.  Since d'Hondt has a (very slight) bias toward larger 
parties, it eliminates the incentive to split parties and encourages 
coalition building, which is crucial for PAV to work.

>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.

I think you've got it backward here; Jefferson/d'Hondt gives the smallest 
party a seat _later_ which is what prevents the party-splitting strategy 
from working.  A good link that illustrates this is 
http://www.aec.gov.au/pubs/electoral_systems.htm#proportional - it calls 
Jefferson, d'Hondt and Webster, Sainte-Lague.

I haven't looked at Hamilton at all, so I can't comment on it.  Webster was 
aiming for the middle, it appeared.  I'd say Jefferson was just trying to 
make the most reasonable-looking system, although it's possible that he was 
aware that his formula would slightly favor his native Virginia.

-Adam