[EM] Fair and Democratic versus Majority Rules

[Jonathan Lundell]

On Nov 16, 2010, at 5:57 AM, Kristofer Munsterhjelm wrote:
> 
> I suspect that one can't have both quota proportionality and monotonicity, so I've been considering divisor-based proportional methods, but it's not clear how to generalize something like Webster to ranked ballots. I did try (with my M-Set Webster method), and it is, to my knowledge, monotone, but it's not very good in the single-winner instance.

Woodall in 2003 formalized a method he called "Quota-Preferential by Quotient" (QPQ), based on a suggestion by Olli Salmi on this list. Woodall demonstrates that it satisfies DPC, but doesn't say much about other criteria.

http://www.votingmatters.org.uk/ISSUE17/I17P1.PDF

(The URL in the paper for Salmi's message is obsolete; I think it might be this: http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2002-September/008616.html)

I've written an implementation of QPQ as a module in my Droop STV counter: http://code.google.com/p/droop/

I'm not 100% sure it's correct, but it count's Woodall's examples correctly.


A plug for Droop: it's a general-purpose STV counter (well, and QPQ) whose claim to fame is that a rule can be modularly implemented on its own terms in a manner that can be seen to follow the formal description of the rule. If you have a look at the QPQ, Scottish STV and Minneapolis STV rule modules, for example, you can see how the implementation is interleaved with the legislative description of the rule. 

As a side benefit, Droop supports exact (rational) arithmetic, as well as a somewhat more efficient "guarded arithmetic", which is conditionally exact.