[EM] The "Turkey" problem

Tue May 27 07:33:12 PDT 2003

On Tue, 27 May 2003 12:50:34 +0200 (CEST) Kevin Venzke wrote:

> Dave,
> 
>  --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> 
>>I stay with what I said.  The collection of candidates to which I assign a 
>>worth of zero are best truncated, for this will give none of them any 
>>ammunition toward winning anything other than last place.  If  I do not 
>>truncate, then I give all but the one I rank last a bit of ammunition 
>>toward winning over the ones I rank lower.  If other voters are enthused 
>>over one of these candidates then the bit of ammunition from my not 
>>truncating could help that candidate win.
>>
> 
> If they are truly worth zero to you, then it makes no difference whether
> you truncate them or order them randomly.  You merely have to fill in
> more bubbles in the latter case.

Go back and look at the example we have been using.  There was no 
truncation, and B won because all agreed B was not the worst candidate.
      If all had truncated, there would have been a tie between A and C.
      If A and C truncated, B voters would have decided which of them won.

> 
> We don't seem to differ much here.  My point was that there is no gain
> in truncating when the worths are not the same.  May I ask: Do you think
> that disliked candidates are all worth 0?  It sounds like you do.
> 

No, I am saying that, PROVIDED I see them as equally bad I properly 
truncate; if I see differences in value I VOTE what I see.

> 
>>Coming back to "universally disliked", if this label is true this 
>>candidate is not going to get ranked high by enough voters to win.
>>
> 
> See below.  A CW doesn't have to be ranked high, he just has to be
> ranked HIGHER.  There are no guarantees about how much he is actually
> liked by anyone.
> 

In the examples B and D get few, if any, votes as best, but ZERO (repeat 
ZERO) voters assert that they are the worst available.  B and D win 
because a LOT of voters agree they are not the rottenest lemons in the pot.

> 
>>>Even if the voters are agreed, nothing inherently prevents the CW from being
>>>the best of the worst lemons.  The point is that Condorcet makes no
>>>guarantees about the value (avg worth to each voter) of the CW, and
>>>that's what the "turkey problem" is.  If that doesn't bother you, that's
>>>fine.  But I'm not so sure it's an "unreasonable fear."
>>>
>>>
>>If the candidate field is all lemons you might get there; if there are ANY 
>>candidates with some attractiveness they should attend to the worst lemons.
>>
> 
> In the scenario envisioned, the candidates who are not lemons are a "love 'em
> or hate 'em" deal, who all have more opponents than fans.  I'll spell this out
> for you:
> 
> 34: A>D...
> 33: B>D...
> 33: C>D...
> 
> D is the CW.  We cannot discern whether D has the greatest worth (possible)
> or whether he's an incompetent but innocuous fool and everyone knows it 
> (also possible) or whether no one knows much about D but would rather take
> their chances with him than with the two "major" candidates they know they 
> don't like.
> 

NONE of these voters rank D as highest possible, or as lowest possible. 
They elect D because all of them agree that D is better than the 
competition though, for each of the others, a minority likes their 
favorite better.

> 
>>>>>Here's an example, as you asked:
>>>>>
>>>>>48: A>B>C  (A worth 100, B worth 15, C worth 0)
>>>>>2: B (B worth 100, A and C worth 0)
>>>>>48: C>B>A  (C worth 100, B worth 15, A worth 0)
>>>>>
>>>>I do not understand "worth" in this context - but think I do not need to.
>>>>
>>>>
>>>"Worth" refers to the degree to which each group of voters likes the
>>>candidates.  It's crucial to the discussion to know how much each
>>>candidate is worth to whom.
>>>
>>>
>>Apparently you see value here that I do not.  I assumed the topic was 
>>Condorcet, for which I can say A>B, A<B, and perhaps A=B, but cannot say 
>>whether the difference is 1 or 99.  You seem to be talking of a more 
>>complex method with a ballot in which the voter can specify a worth value. 
>>  Even given such a method, I do not see how you can come up with a 
>>yardstick in which voters attach the same meaning to a worth value of 10.
>>
> 
> The topic IS Condorcet.  I am not talking about a different ballot.
> I am specifying candidates' values to voters in terms of numbers.  I
> am reading their minds, not asking them to estimate their own feelings.
> 
> I can't believe you don't see the motivation for this.  I'm trying to
> persuade you that a generally disliked candidate can be the CW.  How
> on earth can I give you an example of that without a measure of
> "dislike"?

Let's try it a different way.  It does not matter whether I like all the 
candidates or dislike them all as lemons.  I have to rank highest the one 
I like most or dislike least.  "Generally disliked" does not seem like a 
useful label for a candidate some rank high (and therefore has a chance to 
be CW), though it could apply to the collection I have to choose from.

In an election we are trying to read the collective voter minds.  It 
matters what the sum is, but not any individual voter's opinion.

Neither do we as vote counters get to weigh votes according to what a voter 
thinks - all we have is what they say.
> 
> Merely looking at a candidate's rank to decide how "liked" he is
> amounts to using a point system like Borda, which is inadequate
> for the point I'm trying to make.  Candidate D, in my latest
> example, has a Borda score of 200, I believe.  Surely the highest.
> But that's not enough information to decide that D must really be an
> awesome candidate.  He could be nearly terrible.
> 
Agreed, so why fight?
> 
>>Given this confusion, I will have little to say about other paragraphs.
>>
> 
> So have I ameliorated the confusion?
> 
Yes, for you seemed to know why voters voted as they did, and now say you 
are reading Condorcet ballots and can only guess.
> 
> Kevin Venzke
> stepjak at yahoo.fr

-- 
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   Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
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