[EM] The "Turkey" problem

[Dave Ketchum]

On Tue, 27 May 2003 20:11:47 +0200 (CEST) Kevin Venzke wrote:

> Dave,
> 
> We're not on the same page just yet...


But the more we go around, the less value I see in this concept you call 
worth, with its imaginary values (certainly worth exists - trouble comes 
when you assign it numeric values and then assume they have meaning).

> 
>  --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> 
>>>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.
>>
> 
> The only thing relevant to the truncation issue is that last line.  If
> A and C truncate, B voters decide the winner.  But in the example, A and 
> C are both worth 0 to those voters, ergo it makes no difference TO B VOTERS
> how they order them.


PROVIDED B voters assign equal value to A and C, they properly truncate 
and wish A AND C luck.  That they ranked A vs C said they saw a difference 
in worth and made themselves, as much as possible, part of deciding which won.

> 
> It's true that B won because all agreed B was not the worst candidate.
> But on the whole (not just from individual perspectives), B CAN be
> called the worst candidate because he minimizes (total worth / number
> of voters) by far.  He is a turkey/rogue/lemon.
> 
> Again, I'm not trying to convince you that this is important, only that
> it is possible.
> 

I see you losing ground when you claim your worth mathematics helps 
you call B worst - WHEN - ZERO (NO, NONE of the) voters rank B as worst in 
their eyes as they fill in the ballot.

B could well be the best candidate around for ability to fill the office 
being voted for, and a battle over a hot issue push most voters into 
voting for/against extremist candidates A and C (who may be lemons other 
than for their utility in fighting over this issue).

> 
>>>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.
>>
> 
> OK.  That gives me less to type.
> 
> 
>>>>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.
>>
> 
> Agreed.  I'm not arguing about why they won.  I'm just saying they
> could still be lemons.  COULD.  Actually, the last sentence looks like
> it concedes that point.  (That would be significant because it's the only
> point I am trying to make.)
> 

The whole set of candidates could be lemons.  While that would be cause 
for working for better quality nominations, all we get from counting the 
votes is relative worth, and these votes do nothing toward classifying B 
or D as lemons.

> 
>>>>>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.
>>
> 
> Agreed, again.  I'm saying that in ABSOLUTE terms (adding up worth),
> from a GLOBAL perspective, D could be the worst.
> 

But, you build your house of cards by deciding what numbers to assign as 
worth - I still do not see worth mathematics as having value.

> 
>>>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.
>>
> 
> Ok.  I agree with you, that given the rules of Condorcet, the voter has
> absolutely no reason to think about absolute worth, or preference
> priorities.  The "turkey problem" is not a strategy problem.  It is
> a useful and interesting concept only when comparing Condorcet to
> electoral methods that don't have it.
> 
> 
>>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.
>>
> 
> But this sounds like you are taking my position.  If you sum up worth,
> B is the worst candidate, and D could potentially be.  (Note that I am
> not claiming that B and D shouldn't be elected.  In the ABCD election,
> I am not at all sure I want to elect someone other than D.)
> 

I was saying that we count the votes to interpret, as best we can, what 
the voters think.

I can read your last line as consistent with calling D the best candidate.

> 
>>Neither do we as vote counters get to weigh votes according to what a voter 
>>thinks - all we have is what they say.
>>
> 
> Agreed, given Condorcet as the method.  Other methods (such as Approval)
> require the voter to consider candidates' worth, just to be strategically
> efficient.  In other words, we can get useful information even if the
> voters have no interest in being sincere.
> 

I see no value in a numeric value for worth with Approval - either they 
are good enough that I choose to rank them as acceptable, OR they are not.

> 
>>>>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.
>>
> 
> Come on now.  I can tell you how the voters feel because I'm the one
> designing the scenario.  I'm not looking at the ballots and guessing.
> I'm giving you a worst case scenario, that's it.
> 

Agreed you might find worth useful in designing a scenario.  Stretching it 
  to then claim the worth mathematics is useful in attaching meanings to 
the vote counts.

> 
> Kevin Venzke
> stepjak at yahoo.fr

-- 
  davek at clarityconnect.com    http://www.clarityconnect.com/webpages3/davek
   Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
              Do to no one what you would not want done to you.
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