[EM] Condorcet How? JL

[Juho]

On Apr 16, 2010, at 4:42 AM, Kevin Venzke wrote:

>>> Ok I see. A3 has no claim over A1 just from the bullet
>> vote. So assume
>>> it's A3>C2. In that case according to your
>> analysis, the A candidates
>>> collectively beat B and C,
>>
>> Only A3 beats the B and C candidates, not all A candidates,
>> no "collective" beating.
>
> I don't believe you: If A3 is the only one who defeated the B and C
> factions, how does A1's name even come up?

Sorry, I was too quick when writing and got the examples mixed. A1 is  
in no special position in this example since it loses to C2. B1 and C1  
lose to A3. (The original votes were 100: A1>A2>A3, 100: B1>B2>B3,  
100: C1>C2>C3, and the additional one A3>C2.)


>>> Yeah I don't like that. I'm trying to pick the most
>> median-like candidate,
>>> not pick a party and then have an internal election.
>>
>> All voters were free to take position on which one of the A
>> candidates was best. Many found them equal (or equal enough
>> not to bother to rank them). In a real life election B and C
>> supporters could well agree with this ranking. There was
>> nothing "internal" except the common pattern of voters
>> truncating candidates that they do not support.
>
> I can't see any rationale for A1 to win unless this is a team sport.

Yes, that was a mistake. And no team based rules assumed in the  
counting of the results (although it seems obvious that the voters  
considered there to be three groupings of candidates).

What I should have said is that I still consider A1, B1 and C1 to be  
the most liked candidates despite of the single additional vote that  
made these three candidates lose to some of the others.

> Otherwise it seems backwards. A3 beats six candidates all by himself,
> but the win is given instead to somebody who didn't beat any of them,
> he just beat the guy who did.

If we look at the candidates as individuals (not as teams), then A1,  
B1 and C1 are beaten slightly by someone. Other candidates are beaten  
strongly by A1, B1 or C1 according to margins. WV says that A1/B1/C1  
are beaten more seriously by some candidate (A3 or C2) than A1/B1/C1  
beat the others (of their own "team").

(Looking at the candidates again as individuals and how good they will  
be if elected, I think it is more important to consider how eager the  
voters are to replace a potential winner with some other candidate  
(measures the dissatisfaction level after the election) than to  
consider how much that winning candidate would be preferred if some  
other candidate had won. The number of candidates that win someone or  
that someone wins is not a good measure because of clone problems.)

>
> It reminds me of this in fact:
>
> 35 A>B
> 25 B
> 40 C
>
> B defeats C, but A says "well hold on, you're on my team (if you  
> didn't
> know), so actually *I* won."
>
> That's the team explanation, I can follow that. If you don't follow  
> that
> explanation then what the heck? Who is this A guy that thinks he won?

With these votes B wins with WV (in typical Condorcet methods). With  
margins A wins (in typical Condorcet methods).

We both agree that the method should contain no hidden assumptions on  
teaming. If A and B are a team in the minds of the voters then maybe  
the sincere opinion of the B supporters is B>A and the given B votes  
are strategic votes. A would have won with sincere votes in both  
margins and WV. With these votes WV gives victory to B (in typical  
Condorcet methods).

Let's then assume that these votes are sincere. It is possible that B  
and C voters don't have any opinion on the preference of the other two  
candidates. But with this assumption I don't have any good natural  
explanation to why A voters like B more than C (if C voters would  
prefer B to A then this could be a linear left-right model, but the  
votes were supposed to be sincere). Are there some better natural  
explanations? Obviously there are no teams (A voters like B but that  
friendship seems to be one-sided). In typical Condorcet methods the  
candidate with the smallest defeat wins when there are three  
candidates. Margins thinks the 40-35 defeat of A is the smallest. WV  
thinks that the 35-25 defeat of B is the smallest. Both agree that C's  
defeat 60-40 is the biggest. This technical comparison of the results  
doesn't make any conclusions based on why people voted as they did.

There may be of course also other natural (real life like)  
explanations to this set of votes. I already mentioned the possibility  
that the sincere opinion of the C voters is C>B. In that case the C  
strategy fails in both margins and WV (in typical Condorcet methods).

>
> As far as B and C voters actually agreeing with Team A's internal
> ranking: Maybe but in a political election there's plenty of room for
> doubt. What are the odds that the Republicans' favorite Republican is
> also the Democrats' favorite Republican? From an issue space  
> perspective
> that's not very likely.

I guess all combinations are possible. Similar preference order is  
maybe more likely. If the stronger (in first preferences among the  
Republicans) Republican candidate is a right wing candidate then the  
opinion of the Democrats is probably reverse. If the stronger  
Republican candidate is a left wing candidate then the opinion of the  
Democrats is probably similar. If the stronger Republican candidate  
just generally a more competent and nicer person than the other  
Republican candidate then the opinion of the Democrats is probably  
similar.

Juho