[EM] Proportional election method needed for the Czech Green party - Council elections

[Abd ul-Rahman Lomax]

At 01:07 PM 4/29/2010, Jameson Quinn wrote:

>One device that is used by Borda Count, which is a related method, 
>is to have as many ranks as candidates. While I generally favor this 
>(it allows voters to use their ability to compare preferences to 
>generate a rank order), it may be collecting noise, if there are a 
>lot of candidates. My sense is that 3-rank Bucklin (which means 3 
>approved ranks), with an added rank within the disapproved set, is 
>enough for most purposes, but some studies should be done with 
>simulations to determine how much results are improved with additional ranks.
>
>
>1. I don't see how Borda is "related" to Bucklin.

Borda is Range Voting with a special restriction: equal ranking is 
not allowed, and the number of ranks is equal to the number of 
candidates. Strictly, real Borda rules do allow equal ranking, but 
only at the bottom, and the voter is essentially penalized with a weak vote.

Another way to put it is that Borda with equal ranking allowed and 
therefore empty ranks is Range. Thus we can recognize that the Borda 
count that is promoted by Saari is simply Range with the hands of the 
voters tied.

And the ballot that feeds Bucklin is strategically optimal if it is a 
Range ballot covering the approved set. That's the connection.



>2. As I've said before, I favor only 2 ranks for Bucklin. This keeps 
>strategic opportunities to an absolute minimum, and allows simple 
>one-word labels for each rank (preferred, approved, unapproved).

Sure, but there is more flexibility for handling large candidate 
sets. "Strategic opportunities" are ways in which voters can more 
accurately express their preferences. It's a good thing, not a bad 
one, and Bucklin handles these well. Key to Bucklin: the ranking, at 
least the ranking that can elect a candidate, is of approved 
candidates only. Not willing to cause the election of a candidate, 
don't vote for the candidate in an approved rank. The "unapproved" 
rank that Mr. Quinn mentions is the default rank of no-vote.


>Bucklin is very easy to understand and vote. Natural voting 
>tendencies are sound strategy!
>
>Agreed.

Cool. I hope it's correct!


>Of course, the issue with Bucklin is that it uses a different 
>(simpler) balloting style than STV or Condorcet.
>
>
>It can use the same ballot, the same set of preferences. A Range 
>ballot can be used for STV or Condorcet analysis. That the ballot is 
>simpler is not exactly correct. A three-rank ballot looks the same 
>as a three-rank STV (IRV) ballot. It's counted differently in Bucklin.
>
>
>While you can modify STV to allow equality, the well-known versions 
>do not. Thus, the ballot is not the same. The Bucklin ballot is more 
>permissive and thus simpler.

Bucklin can be no-equal-ranking allowed, and was, unfortunately, 
simulated that way by Warren, accounting for its less than optimal 
performance, I suspect. Bucklin can use exactly the same ballot as 
STV or Condorcet. (either one can allow or not allow equal ranking.) 
The only critical difference is analysis. Bucklin uses the ballot to 
control a series of approval elections with declining approval 
cutoff. STV has complicated rules that I won't describe. Condorcet 
only considers the pairwise data, which can neglect preference 
strength, but some Condorcet methods do use preference strength 
information estimated from rank distance or vote counts.

>Also, for a council, 3 rankings is not nearly enough for STV. You 
>should really require nearly-full ranking. With Bucklin, as few as 2 
>rankings is enough (and, in my opinion, optimal).

Remember, 3-rank Bucklin, standard ER, allows complete ranking of 
candidates into four groups, and this is adequate for good analysis. 
With the "overvoting" scheme I've mentiond, the same ballot would 
allow ranking into six groups. With the disapproved rank used, (which 
would only be used for the proportional representation part of an 
election as is being considered, or possibly to determine preference 
in a runoff, or just for information so that voters can make good 
choices in a runoff, knowing a truer picture of overall preferences), 
which turns Bucklin into 4-rank, in a way, there are eight possible 
rankings. Add an explicit zero, and it's nine rankings. Don't you 
think that's enough for STV? Given that one can equal rank?

With 2-rank Bucklin, you have three ranks. You can't use the ballot 
for serious Condorcet analysis, probably, particularly if we consider 
write-ins allowed. There are reasons why they used three ranks, 
usually, a century ago. They were actually able to handle an election 
with over ninety candidates, and the result seems to have been 
popular. I should find that, as I recall, they did find a majority, 
which is quite a trick with that many candidates!

With 2-rank Bucklin, the election can handle full ranking of only 
three candidates, which, with a write-in, means two on the ballot. 
That's pretty primitive, given how easy it is and how harmless it is 
to add a third rank.

Mr. Quinn seems to have a common response: that "strategic" voting is 
Bad. He doesn't say what he means by it, but Bucklin voters were 
allowed to leave a rank empty. So if they had a strong preference for 
their favorite, but were still willing to accept, in the end, the 
election of another candidate, they could rank their favorite in 
first rank and the other in third rank, which represents a sincere -- 
but smart -- vote. It reduces the chance, which does exist with 
Bucklin, that a multiple majority would be found in the second round, 
and that thus they'd be possibly abstaining from that election, 
having voted for both of these candidates.

Note that this outcome isn't a bad one.... if it were actually bad, 
the voters wouldn't have added the additional approval, I assume. In 
a two-round system, they gain additional flexibility, they can 
postpone the "hold my nose" vote till the end, when it is far more 
obvious that it's a necessity. They will have some pretty good 
information from the primary.