[EM] The "Turkey" problem

[Kevin Venzke]

Dave,

 --- Dave Ketchum <davek at clarityconnect.com> a écrit : 
> > 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).

Well, numeric values aren't even necessary if all one wants to show
is that the CW might displease EVERYONE (in ABSOLUTE terms, keep in mind;
I'm fully aware that no one ranks B last).  In the ABCD scenario where
everyone ranks D second, I could simply say, "Everyone thinks D is a
twit, and he is the CW."  No interpretation is involved here.  I'm
telling you that's how it is.

If you agree that this situation is possible, we can be done with this.
Note the wording is "D is a twit," not "D is the biggest twit" or "D
is everyone's least favorite."

> > 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.

It is one possible definition of "worst."  "Condorcet Loser" is another
possible definition.  If the election method is Condorcet, you cannot do
any better than the latter definition.  I'm not saying you can.

> 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).

Absolutely.

> >>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.

Agreed.  It sounds like you think I'm saying we could pick someone
better using an identical, Condorcet ballot.  I am not saying that.

I am saying that Condorcet cannot guarantee anything about the "total
worth" of its winner.  Since you think "worth" can't be defined, even
in a hypothetical situation, you should be willing to concede that point.
If "worth" can't be defined, how can Condorcet make any guarantees about
it?

If you say "You are right, but the conclusion is useless" I will be
very content.

> >>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.

You can indeed.  The Condorcet ballot doesn't permit any other means of
picking the "best" candidate.  Note that I never gave any "worth" values
for the ABCD election, so no other basis for "best" or "worst" is
available to me.

> > 
> >>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.

I don't believe you.  If this is true, then there are potentially cases
where you would be willing to approve all the candidates on the ballot,
despite the fact that this "strategy" doesn't improve your prospects.

If you want to use math to make your Approval vote the most strategically
efficient, and more than two candidates are given odds of winning, then
you will have to approximate worth.

> > 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.

I am not claiming that "worth" is a useful idea if Condorcet vote
counts are the only available information.


Kevin Venzke
stepjak at yahoo.fr


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