Truncated preferences ok for Condorcet (was Re: [EM] Ignorance)

[Steve Eppley]

Hi,
Several days ago, Augustin asked:
-snip-
>         a couple of weeks ago I wrote to this 
> list asking for your help especially in regard to some 
> theories that are behind the decisions I have made when 
> developing the site.
> 
> The only help I received was in the form of welcome 
> criticism behind the theoretical choices behind my 
> decisions which were made, again, out of ignorance.
> My reply is currently available online:
> http://www.masquilier.org/republic/election/solution.php
> 
> I haven't yet received a definite answer in this matter
> and I am asking you again to enlighten me. 
> 
> The board I am developing has its origin in this discussion 
> thread:
> http://forums.zynot.org/viewtopic.php?t=56
> In it, Charun argues vehemently that for Condorcet to retain 
> its validity/superiority, all the candidates must be 
> strictly ranked from the first to the last. 
-snip-

I read the message thread that Augustin cited.  Based on 
Charun's last message in that thread, I would not 
characterize Charun as insisting that Condorcet voting 
requires each vote to be a strict ordering.  He seemed 
uncertain about the relative merits, and called it a 
"hybrid" to allow votes to be non-strict orderings (that 
is, allowing truncation and allowing equally-ranked 
candidates) and claimed that therefore it should not be 
called Condorcet.  

It seems to me (and I'm sure to most of us) that allowing 
votes to be non-strict orderings is fully deserving of the 
name Condorcet and should not be called a "hybrid."  For 
one thing, it satisfies the Condorcet criterion and the top 
cycle criterion.  My website lists quite a few criteria 
satisfied by the Condorcetian method I think is best, which 
allows votes to express indifference and truncate. (The 
website also provides proofs of satisfaction.  The proofs 
use mathematical symbols from the Microsoft symbol font, so 
I'm curious to know whether a GNU/Linux user like Augustin 
can easily display them.  Someday I'll translate them into 
pdf format, which should take care of any font problems.)

I can think of three possible explanations for Charun's 
belief that strict orderings are required.  The first is 
that much of the social choice literature seeks to simplify 
the discussion by assuming votes are strict orderings.  Not 
as a criterion that should be satisfied, but to make their 
analyses and proofs simpler to write and read.  An unwary 
reader might get the idea that they had a compelling reason 
to restrict our attention to strict orderings.

The second is that some social choice theorists make the 
assumption that each voter's preferences are strict 
preferences, which would mean expressions of indifference 
are strategic rather than sincere.  They reason that such 
strategies can be eliminated at no cost by requiring each 
vote to be a strict ordering.  What they've neglected is 
the possibility that strategic indifference may be 
benevolent.  The thread already made clear that one of the 
gains of allowing indifference is to remove the tedium of 
expressing a strict ordering that includes every candidate. 
(Allowing truncation is part of what's needed to satisfy my 
feasibility criterion, which is defined at my website.)  
Another gain is satisfaction of the minimal defense 
criterion (which is also defined at my website; it's based 
on Mike Ossipoff's "strong defensive strategy" criterion.)

The third explanation is a hold-over from elections that 
tally Instant Runoff (or the proportional representation 
version, Single Transferable Vote) by hand.  To quickly 
tally Instant Runoff by hand: 

   Distribute the ballots into piles, each according to
   its top-ranked candidate.  From the height of each pile,
   you can see at a glance which pile has the fewest
   ballots.  So, if there are more than two piles, take 
   the shortest pile, eliminate its candidate, and
   redistribute its ballots to other piles according to
   their highest-ranked non-eliminated candidate. 
   Repeatedly eliminate & redistribute the shortest pile 
   in this way until only two piles remain and elect the
   candidate of the taller pile.

If ballots express indifference, it would be hard to tally 
the election since such a ballot would either have to be 
split or cloned in order to be placed in more than one 
pile. (And care would need to be taken to unsplit when 
redistributing a pile containing a piece, or to destroy 
rather than redistribute clones until all but one of the 
clone ballots has been destroyed.)  So it was a matter of 
reducing the tallying labor, for elections that haven't yet 
reached the computer age.  Also, if ballots truncate, then 
the winner's final count might not be an absolute majority, 
so advocates of Instant Runoff would have to revise one of 
their misleading claims about electing "the" candidate 
preferred by a majority. (I put "the" in quotes because in 
reality there are multiple simultaneous majorities.  
Instant Runoff merely guarantees that the winner isn't a 
Condorcet Loser, which is an alternative such that, for 
every other alternative, some majority ranked the other 
alternative over it.)

Well, that's all I know about arguments against allowing 
truncation.  Perhaps others will be able to add more.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)