[EM] 3 or more choices - Condorcet

[Kristofer Munsterhjelm]

On 09/30/2012 12:51 AM, robert bristow-johnson wrote:
> On 9/29/12 4:49 PM, Juho Laatu wrote:
>> What is a "strong" Condorcet method?
>>
>
> yeah, and Kristofer, since the word is quoted, who is using the label? i
> think it might very well be something to agree with (the use of a really
> general adjective like "good" or "favorable" or even "optimal"), i would
> like to know w.r.t. what? it's like my high school teacher prohibited us
> from writing "This book was good" in a book report. certainly not saying
> the word is meaningless in context, but it semms to me meaningless when
> naked.

I am. See my reply to Juho for information of what I meant :-)

> but, that said, i still think that a cycle with a Smith set bigger than
> 3 is soooo unlikely since i still believe that cycles themselves will be
> rare in practice. since Minmax, Ranked-pairs, and Schulze all elect the
> same candidate in the case of the Smith set of size 1 or 3, it seems to
> me that simplicity of tabulation becomes a "strong" property for two
> different but related reasons:

That's a good point. I don't think that a Smith set larger than three 
would be vanishingly unlikely in the long run, but perhaps we should 
just be pragmatic and pick any Condorcet method. We could then reason 
that by the time large Smith sets show up, society will be pluralist 
enough that it'll be up to the task of picking a better method.

After all, every Condorcet method is cloneproof when there's a CW. In 
fact, it's stronger than that. Every Condorcet method meets IIA when 
there's a CW: if you remove a non-CW, the CW doesn't change.

On the other hand, we should be careful not to repeat IRV's mistake. 
Some IRV proponents say that IRV's counterintuitive behavior doesn't 
matter because it only comes into play when third parties get strong 
enough; thus, by the time it happens, we'll be out of the domain of 
two-party rule already. Yet Australia, while escaping strict two-party 
rule, got stuck in "two and a half party rule".

> 1. simplicity is a strong selling point and a necessary one in an
> environment of public opposition to "tricky" government procedure.
> sometimes complexity in government is unavoidable (how many pages of
> text is in a typical bill?) and sometimes the simplest method is clearly
> not the best (say, flat income tax rates vs. progressive income tax
> rates). but when it comes to seeing how our leaders are elected and how
> our miscreants and recalcitrants are dealt with, the public has an
> interest in transparency and some of this transparency is mandated in
> our national constitutions. but we *do* put up with reasonably complex
> regulations and tax codes, we can put up with a teeeny bit of complexity
> (the Ranked ballot vs. the "traditional" ballot) in voting.
>
> but the method of tabulation must be reasonably simple for the method to
> gain public acceptance and trust. i think most people can understand the
> statements: "If more voters prefer Candidate A to Candidate B, then
> Candidate B is not elected." and i think that people can understand the
> concept that if Candidate A is ranked above Candidate B on their ballot,
> this voter would simply vote for A on a traditional ballot if only the
> two candidates were running.
>
> selling the additional "burden" of having to commit to and mark their
> contingency vote(s) is the challenge, and i usually respond with the
> common argument we used in the old IRV days, and it still applies: it is
> worth it to collect your (and others) contingency vote because, to get
> it later (in a run-off) decreases voter participation and makes the
> election less legitimate, particularly if it's close.

I think the simplest modification to a system to make it Condorcet would 
be something to the effect of: line the candidates up in order of 
victory from left to right, then of the leftmost two, remove the one 
that loses pairwise to the other. That modification directly represents 
what you say: "if A beats B, B shouldn't win". This is like Simmons's 
UncAAO, only with "A is retained if A beats B" instead of "if A covers 
B", and a later society could replace "beats" with "covers" to get a 
better method. However, it's still somewhat artificial, or "bolted on".

As far as intrinsically Condorcet methods go, Ranked Pairs feels simple 
to me. The only tricky part is the indirect nature of the "unless it 
contradicts what you already affirmed" step. But perhaps matrix-based 
logic would be seen as simpler, in which case Minmax wins ("pick the 
candidate whose worst defeat is mildest" or "pick the candidate who 
would most comfortably win his closest runoff"). Simplicity is not an 
algorithmic measure, so I can't say for sure which would be considered 
simpler. Perhaps Borda-IRV would even be considered simpler than these.

> lastly, i know is anecdotal, but the Burlington 2009 IRV election really
> bolsters my confidence in cycles being rare (and then cycles bigger than
> 3 being even more rare). it was a close election. one candidate was the
> Plurality winner, one candidate was the IRV winner, and one candidate
> was the Condorcet winner. all three candidates were viable players and
> there was a fourth, independent, candidate that had a lot of support but
> was the first to be eliminated. but when ordered by Condercet, it is
> clear who is consistently preferred over everyone else. remove the CW
> and it is clear who comes in next. remove the 2nd-place CW and it is
> clear who came in 3rd. it was very consistent and nothing would change
> if various candidates were removed from the roster and the same voters
> came and vote (ranked) identically in another election. no spoiler
> scenario in any manner. and that was a close election.

Currently, single-winner elections very rarely have cycles and large 
Smith sets are even more rare. Plurality can't support a party system 
where that would not be the case. But as I've mentioned, it may well be 
that the political environment expands (or contracts) to fit the space 
supported by the election method in question. If so, more accurate 
methods could give greater variety, and the strategy becomes a question 
of whether we select "good enough" (a simple method) and then fix it 
later, or consider that something worth doing is worth doing well and 
pick a method with a considerable margin of safety (like RP or Schulze).