[EM] Consistency, Truncation, etc. (was CR ballots, etc.)

[Forest Simmons]

On 26 Sep 2001, Buddha Buck wrote in part:

> I see...  What you are saying is that when all precincts report the
> same Condorcet Winner, then any Condorcet method will be consistent,
> and report the same Condorcet Winner as all the precincts.  But for
> any Condorcet method, it is possible to derive a set of ballots such
> that all precincts report the same winner (with, of necessity, at
> least one ballot's winner not a Condorcet Winner, however), yet report
> a different winner for the election as a whole.
> 
> OK, I concede the point, but you know what?  I don't care.
> 
> First of all, consistency isn't an issue when the precincts report
> different winners.  The criterion isn't a guide then.  I suspect that
> most of the time when there fails to be a uniform Condorcet winner
> across precincts, it'll be because different precincts report
> different winners.  So it isn't an issue then.
> 
> Second of all, I consider the resolution methods used in Condorcet
> methods when there is no Condorcet winner to be "tie-breakers".  There
> is a group of candidates between whom the electorate cannot make a
> clear decision -- so the process tries to use the information
> available as best it can.  So when all 10 precincts (say) select
> candidate A with precincts 1-9 having Condorcet Winners, and 10 having
> A selected but not the Condorcet Winner, then I'd say an accurate way
> to report the results is that "A has a clear victory in precincts 1-9,
> but in precinct, the race is too close to call -- a statistical deal
> heat.".
> 
> I'm falling asleep, I'll answer the rest tomorrow...
> 
> Later,
>   Buddha
> 

Pretty good post for a sleepy poster!

I agree 99.99%

The only winner that all Condorcet methods agree on is the CW head-to-head
beats-all winner.

So if A wins in all of the precincts, but B wins the election, then not
all Condorcet methods would agree that A won in all of the precincts and
that B won the election.

So in some appropriate topology, Condorcet Methods are on the boundary of
the set of methods that fail the Consistency Criterion, while IRV is
interior to that set.

In my opinion this line of reasoning is a better apologetic for
Condorcet's relationship to the Consistency Criterion than the apologetic
that tries to discredit the Consistency Criterion itself. 
 
In other words, saying we almost reached the grapes is better than calling
them sour.

A stronger consistency criterion would be this: If candidate A wins in a
MAJORITY of the precincts (by restricting the election to the ballots from
each of the precincts in turn) then candidate A wins the entire election.

This stronger criterion is probably too strong for any practical method to
satisfy.

The Consistency Criterion we are talking about is much weaker, and is
fully satisfied by Plurality, Approval, Cardinal Ratings, and by Borda,
with Condorcet borderline failing.

Here's a weaker version that might be called the Humble Consistency
Criterion, because it requires methods that don't satisfy the regular CC
to admit indecisiveness before they qualify for the HCC. 

Humble CC:

If candidate A wins DECISIVELY in all the subsets in some partition of the
electorate (by restricting the election to the ballots from each of the
subsets of the partition in turn) then candidate A wins the entire
election.

IRV fails even this humble version of the CC.

See my Greek Tragedy example in the archives at ...

http://www.mail-archive.com/election-methods-list@eskimo.com/msg06168.html

Forest