Condorcet Truncation Example

[Hugh Tobin]

Markus Schulze wrote:
> 
> Dear Rob, dear Hugh,
> 
> you did me wrong. I have never said, that Smith//Condorcet [EM]
> is not "truncation resistant" due to your definition of "truncation
> resistant".
> 

Sorry, I never understood you to have said that, and did not try to
rebut what was unsaid.  Your earlier example assumed a different
tiebreaker than "Smith//Condorcet [EM]"; my point was that truncation
would not be rational strategy even in that case.  I agree with you that
the [EM] tiebreaker (least votes against in worst loss, with no
half-votes for equal rankings or truncations), is unnecessarily
"truncation resistant", as it creates the incentive to insincere votes
that you mention below.  

> The problem looks a little bit different: Usually only downward
> truncation [i.e., the voter gives his worst preference to more
> than one candidate] is discussed, because usually only plain
> Condorcet is discussed. And if plain Condorcet is discussed,
> downward truncation is a usefull strategy.
>

Useful in what circumstances? See previous postings requesting an
example of a plausible expectations that would make truncation a
rational choice for the voter, considering that the voter has two
alternatives: sincere ranking and order-reversal.  What tiebreaker do
you assume for "plain" Condorcet?
 
 
> But the way you have defined "truncation resistant" and
> Smith//Condorcet [EM], the following problems will occur:
> 
> (1)Upward truncation [i.e., the voter gives his best preference
>    to more than one candidate] becomes a usefull strategy,
>    especially if there is the danger that more than one of the
>    most favoured candidates comes into the Smith set and one of
>    the most favoured candidates in the Smith set would have his
>    highest defeat against another of the most favoured candidates
>    in the Smith set.
>

I do not see when this would be useful.   I think "upward" truncation
involves an important sacrifice of voting power for someone who has a
true first choice.

> (2)Distributing the worst preferences random among the least
>    favoured candidates becomes a usefull strategy. That means:
>    If the voter doesn't care, who of his least favoured
>    candidates wins [if one of them should win], then it is
>    nevertheless the best strategy to give them different
>    preferences to maximize the chances of a favoured
>    candidate to win.
>

You are right.  I have objected to the [EM] tiebreaker on this ground. 
Other tiebreakers, such a margins-of-defeat, do not create an incentive
to vote randomly, though (at least in theory) a voter who anticipates a
circular tie and thinks he knows who will win the pairwise race between
his less favored candidates may cast an insincere vote to make the
margin larger.  
 
> Again: Even if none of the other voters votes tactically,
> every Condorcet Criterion method punishes those voters, who
> give full information about their true opinion.

It is more likely to punish them if they fail to give full information.

> This means, that
> they won't give full information about their true opinion.

As previously pointed out, rational tactical voters might reverse order
in limited circumstances, but they would not truncate.  (Indeed, in the
three-way example that you recently posted with reversal by a 40%
plurality, using truncation instead would have failed to achieve the
intended result.)  In Condorcet rational voters are much more likely to
vote when they have no real preference than to abstain insincerely in
pairwise races. 

> This means, that it won't be possible to determine the
> Condorcet Criterion winner due to the opinion of the voters
> even if no voter votes tactically. This means that the Condorcet
> Criterion method won't work.
>

No, what you say is true only if some voters do vote tactically.  If
they omit choices in some pairwise races we may reasonably assume they
are truly indifferent in those races.  Indeed, this is more likely to be
true of voters who cast partial rankings than it is to be true of voters
who do not come to the polls at all.  
It has been pointed out on this list that no system can guarantee that
all rankings will be sincere, so it is not a sufficient argument against
Condorcet to say that we cannot be certain that each voter's ranking
expresses his or her true preferences.  Prior postings have investigated
circumstances in which insincere voting might occur in Condorcet,
despite the substantial risks involved.  Others have argued that
tactical voting strategies are easily defeated in Condorcet; I have
questioned the logic of these arguments and have suggested that
order-reversal might work in certain cases (similar to your most recent
example of reversal by a 40% plurality).  However, as no other system
guarantees sincere votes, I do not see that the possibility of reversal
in Condorcet justifies using a different system that may fail to elect
the Condorcet winner even when there is no significant amount of
tactical voting.  In your recent example, if the expectation of
order-reversal by the plurality forces the other wing to vote for the
center in first place, this is the same type of lesser-evil choice that
may be forced upon voters in other systems.  Because order-reversal
strategy would probably have to be coordinated and publicized in order
to be effective, and because it is the type of cynical manipulation that
might lose support among marginal voters, I think it would be unusual at
that in most cases we could be reasonably confident that rankings would
be generally sincere, at least in the US, where party loyalty is weak
and voters tend to think independently.  In a country where most voters
either have no second preferences or are willing to subordinate them
without question to direction from party leaders, as you suggest, I
agree that Condorcet would have fewer benefits.


> This is what is meant, when it is said in literature, that
> "truncation" is a problem of any Condorcet Criterion method.
>

What literature are you citing? 

Regards,

Hugh Tobin

> Markus Schulze (schulze at speedy.physik.tu-berlin.de)