[EM] Weak Condorcet winners

[Jameson Quinn]

Juho is right that the term "weak CW" is not inherently clear. The point is,
that we're defining the meaning of this term for the purposes of discussion.
The paradigmatic case is something like:
45: A>C
40: B>C
15: C

C is only "weak" in the sense of first-choice support. The narrowest
pairwise defeat is 55:45, which is not a weak result. So "weak" should not
be understood to mean weak in every way.

Also, in discussing this problem, we've repeatedly said that the principal
problem is not the result itself, which may in many cases be perfectly
correct in any meaningful sense; but the fear of the result. A method which
could potentially elect a weak-CW, could theoretically thereby elect a
relatively-unknown candidate; voters can be convinced to fear that.

It is perfectly true that sometimes the weak-CW is the correct answer, but
it's also beside the point.

Jameson

2011/9/23 Juho Laatu <juho4880 at yahoo.co.uk>

> I think term "weak CW" should not be used as a general term without
> referring to in what sense that winner is weak. There are different
> elections and different needs. In some of them weak CW is a good choice, in
> some others not.
>
> 51: A
> 49: B
>
> As you can see A is a weak CW here. Not so if you measure the number of
> first preferences, but very much so if you compare the strength of the
> winner to the strength of its competitors.
>
> 45: A>B>C
> 5: B>A>C
> 5: B>C>A
> 45: C>B>A
>
> Here B is a strong CW since the alternatives are
>
> A = set tax level to 20%
> B = set tax level to 19%
> C = set tax level to 18%
>
> It is obvious that B is the alternative that should be chosen. Other end
> results would be plain wrong. B is not a weak candidate in any way.
>
> Term "weak CW" seems to be heavily linked to the understanding that the
> winner should have lots of first preference support (or it should often
> belong to the most preferred subgroup of the candidates). This is a
> viewpoint that is quite strong in two-party countries (that want to stay as
> two-party countries) since in those countries whoever is in charge has
> typically more than 50% support among the voters. But what is weak in this
> kind of thinking need not be weak in some other set-up.
>
> > Failing the majority criterion is, in my view, a similar flaw to electing
> a weak CW.
>
> I think electing a weak CW is a flaw only in some set-ups with some
> specific requirements that make weak CW a bad choice. Majority criterion is
> a requirement far more often, but not always. There are also elections where
> majority is not a requirement. And there are also elections where it is
> sometimes a requirement to elect against the majority opinion.
>
> Juho
>
>
>
>
> On 23.9.2011, at 12.26, Jameson Quinn wrote:
>
>
>
> 2011/9/23 James Gilmour <jgilmour at globalnet.co.uk>
>
>> Warren Smith  > Sent: Friday, September 23, 2011 1:53 AM
>> > At the present time, Jon Huntsman gets only a tiny
>> > fraction of the USA-republican-presidential-nomination votes,
>> > according to polls. For this reason, certain media people
>> > have been saying it is a travesty Huntsman continues to run
>> > and is allowed in debates, etc.
>> >
>> > However...
>> > it is mathematically possible (and might even be true -- I
>> > have no idea... it's at least somewhat plausible) that
>> > Huntsman is "everybody's second choice" and therefore is the
>> > Condorcet candidate who would defeat every Republican rival
>> > one on one.
>> >
>> > So there's a possible very important example of a "weak
>> > Condorcet winner" in your face right now.
>>
>> Your point is obscure.  My point is not that a "weak Condorcet winner"
>> might exist or be elected, but about the political and
>> Political consequences of such a result.  The electors may vote that way,
>> but once they and the party politicians see what has
>> happened all hell will break loose.  And it will be stirred up by a very
>> hostile media.  At least, that's what I would confidently
>> predict would happen here in the UK.  The "weak Condorcet winner", while
>> being the Condorcet winner, would be totally ineffective in
>> the discharge of the office to which s/he was elected.
>>
>>
> Moreover, the very possibility that a given system might elect a weak CW,
> will be used as an argument against adopting that system in the first place.
> This argument will be especially convincing to officeholders, who would hate
> to be defeated by a weak CW.
>
> Note that a weak CW can win in non-Condorcet systems. In Approval, Range,
> and MJ, a weak candidate can theoretically win even if they are not even a
> CW; but the situation only becomes plausible if they are. In all three of
> those systems, you could argue that this would probably be rare with
> real-world voter behavior; but to my knowledge, only with MJ is there
> published data to back this up.
>
> Failing the majority criterion is, in my view, a similar flaw to electing a
> weak CW. In both cases, it's at worst a "suprise" result that a majority of
> voters easily could have and would have avoided if they'd realized it was
> coming; and in both cases, it's a system flaw that will appear intolerable
> to officeholders. Approval, Range, and MJ all fail the ranked MC; of them,
> only MJ clearly passes the rated MC. Range's MC failure, in particular, is
> often used as an argument against it; whether or not this argument is valid,
> it seems to be telling.
>
> Again, SODA is not subject to either a weak CW or a non-MC result. I
> consider these flaws to be the biggest obstacles to system adoption; and the
> chicken dilemma, also uniquely solved by SODA, to be probably the
> most-common real-world hurdle for a good electoral system. I consider these
> advantages to be important enough that theorists should seriously consider
> SODA even if they have some objections to Asset-style systems. After all,
> SODA's asset-like aspects are entirely optional for the voter.
>
> Jameson
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