Truncation Resistance #2 criterion (was Re: First Choic

[Hugh Tobin]

Steve Eppley wrote:

[First, here is the relevant portion of Steve’s original post: 
> > > I suggest that when people think about a new method they should
> > > first test them on the following two examples:
> > >
> > >      46:ABC                          46:A
> > >      10:BAC                          10:BAC
> > >      10:BCA                          10:BCA
> > >      34:CBA                          34:CBA
> > >      ------                          ------
> > >      MUST ELECT B                    MUST NOT ELECT A
> > >
> > > In the example on the left, it should elect B (the compromise
> > > centrist who would beat any other in a head to head matchup).  In
> > > the example on the right, it should not elect A, else the supporters
> > > of A have a clear incentive to strategize.  If truncation would
> > > elect A, the method has a serious problem.
> > >
> > > We may as well call this two-example test a criterion: the
> > > "Truncation Resistance #2" criterion, perhaps.  Do we have a
> > > consensus that any method which fails TR-2 should not be posted
> > > here in EM, unless it's accompanied by a solid explanation why it's
> > > better than Condorcet or Smith-Condorcet on some other criterion we
> > > should respect?  Such a consensus would save us all a lot of time.
> > >
> > >[snip]
> > >
> > > ---Steve     (Steve Eppley    seppley at alumni.caltech.edu)]
> >

> Hugh T wrote:
> >Steve's proposed consensus censorship
> 
> Censorship seems too negative a description, since I provided the
> reasonable "escape clause": someone proposing a new method which
> fails TR-2 needs only include some other criterion--maybe I should
> have said "standard"-- satisfied by his/her proposed method better
> than Condorcet or Smith//Condorcet, and explain why that criterion
> matters.
> 
> There may be some value to the list in having people propose methods
> which are inferior on some standards and not superior on any.  It
> could stimulate invention of better methods, or help us understand
> why known methods are better than the proposals.  But I'd like the
> authors of those proposals to be clearer about what they're writing;
> if they think the proposal may be better on some standard, we deserve
> to know which, and if they don't, we deserve to know that too.
> 

On re-reading Steve’s first posting I am inclined to withdraw the term
“censorship” (which I had thought to soften with “consensus”), because
Steve could be read  not as proposing a rule restraining speech, but as
simply seeking an expression of consensus as to what forms of speech
would be most useful.  But I find that Steve rejects the term on other
grounds.  I do think rules that restrain speech, even with "escape
clauses" that the rulemakers deem reasonable, amount to censorship. 
Whether it is good or bad is another question (for example, postings not
germane to the list should be censored).

>If Hugh wants this list to welcome proposed methods which are offered
> up without explaining why they may be better, and they routinely turn
> out to be badly flawed, I'd appreciate it if he would better share
> the burden of analyzing their faults.  Freedom of speech works best
> when there are a lot of people willing to point out the bugs in
> "bad" speech.
> 

Perhaps I am less concerned about such proposals because I do not think
one endorses anything by ignoring it.   I do not think anyone has an
obligation to analyze, respond to, or include in a FAQ any proposal that
is not accompanied by an explanation of what advantages it has, or at
least why it is worth investigation.  But some such proposal might have
a glimmer of merit even if the proposer does not explain it accordance
with Steve’s proposal, or does not even grasp it himself.  (A properly
titled posting that merely defines a method may have value on a list
called “Election Methods”). Someone may have a very cogent narrative
explanation of the value of a system or certain of its features, and
might be deterred from posting it by rules that require formal standards
or criteria, or that insist  that the poster accept as the premise for
discussion that TR-2 is important.  Those who support Condorcet with
other tiebreak methods than [EM] may not agree that there is anything
wrong with an A victory in Steve’s second example, and may not agree
that Condorcet, properly implemented, passes Steve’s test.  Finally, I
do not look forward to responses telling a poster that he or she is out
of order for having the temerity to propose something with an
explanation that is not “solid” or with a criterion that is not worthy
of “respect,” rather than simply addressing the posting on its merits
(IMHO people with something useful to offer may already have been
deterred from posting on this list by the tone of some of the
responses.)

In lieu of any statement about what “should not be posted”, I would
suggest an item in the FAQ that explains in neutral terms what format
and what type of information is helpful to readers when one posts a new
system or variant, and that goes on to indicate that because that S//C
[EM] was chosen by vote of the members of this list, posters should be
prepared to compare the results of their systems to those of S//C[EM] in
certain examples and to justify any differences.  I believe it should be
made clear that failing Steve’s first test poses a much more fundamental
issue -- i.e., what justifies rejecting the Condorcet criterion -- and
that example 2, if given at all, relates to a claimed advantage of a
particular Condorcet version.

As to sharing the burden, I have been critical of methods like IRO, and
Condorcet w/ Approval, where I thought that the responses of the
regulars left anything unsaid.  In general I find that others are so
quick and prolific in their criticism that one who cannot post daily
would only be redundant, or appear to be piling on, in criticizing
systems other than Smith//Condorcet [EM].    

> >raises the questions: (1) Why is truncation resistance more
> >important that resistance to order-reversal?
> -snip-
> 
> Because truncation will probably be a common occurrence when there
> are many candidates, even with "sincere" nonstrategically-minded
> voters.
> 
I am surprised by this explanation, because I thought truncation meant
withholding expression of  sincere preferences, and that the
reason Steve opposed the result in his second example was the incentive
it gave to A voters to truncate as strategy.  To say that an A victory
in  that example is intolerable even were we certain the voters were
entirely
sincere is another matter, and highly debatable.  If voters who cast
short ballots will most likely be sincere, this argues against Steve’s
criterion.  In that case it becomes more important to ensure that these
sincere voters are not penalized for not being devious enough to cast
insincere complete rankings.  But if A does not win in Steve’s second
example, the sincere A voters are penalized for this.

> >(2) Why is it critical to prevent a putatively organized and devious
> >group of plurality voters from achieving through truncation what
> >they could also achieve by insincerely dividing their second choices
> -snip-
> 
> Can we agree to make the following assumption?
> 
>     The level of "strategic sophistication" will be fairly even
>     among all the groups.
> 

I think that is very unlikely.  More likely there will be systemic bias:
some groups are highly organized and well-financed compared to others 
(I suspect that more extreme groups will be more disciplined).  
Differences in money and organization will affect the degree to which
strategic sophistication of leaders will be translated into false votes
by which their followers will improve their favorites' chances, even if
the followers do not themselves understand how the system works.  The
less organized and less doctrinaire voter more likely will vote
sincerely, perhaps only for one candidate if he knows nothing of the
others, if he considers them equally detestable, or if he naively
assumes (like a certain member of this list) that he thereby maximizes
the chances of this first choice.  This independent voter, by virtue of
his sincere short ballot, will have less effective voting power in
Condorcet [EM] than the member of an organized group who knows he should
cast an insincere long ballot.  (To the extent that latter voter knows
which way he should cast his insincere votes, he has an advantage even
in Condorcet methods that fail Steve’s second test, but it is a smaller
advantage).  Even among unorganized voters, there surely will be
systemic bias in strategic sophistication -- the classes with more
education and more leisure to concern themselves with the intricacies of
the system are more likely to vote strategically on their own.
But even if the assumption Steve proposes is made, it does not advance
his argument that truncation-resistance is so important as to be a
criterion.

> Truncation will occur even with low deviousness (and maybe
> especially with low deviousness), but massive reversal requires a
> highly devious group.

This does not make sense to me.  Truncation as offensive strategy
requires more, not less participation because each ballot is less
potent.  Order
reversal can succeed with only a minority of the A voters participating.
It does not seem more devious to withhold a true preference than to
reverse it, because in either case one either takes a conscious risk of
electing one's least favorite in order to enhance the chances of one's
favorite, or else one changes how one votes in order to follow strategy
directed by a political leader without understanding why. 
If a voter would have voted only for A without any strategy or
direction, then I can only conclude that he or she is indifferent among
the other candidates.  Indeed, this seems more certain for the A voter
than for those who did not got to the polls at all, because it is so
little trouble to express one's true preferences once in the voting
booth.

Perhaps one who expects that "truncation" by people who actually have
preferences will be widespread and will affect important pairwise races,
not just those involving irrelevant fringe candidates with no hope for
the Smith set, should support a version of Condorcet that would correct
for this phenomenon by counting these ballots as evenly split for
tiebreak purposes.  We have no legitimate basis for concluding that the
A voters actually preferred B more than C, or vice versa, so if we are
to try to give some effect to their unexpressed preferences (without
affecting the outcome of the B-C race with phantom votes), the best we
can do is assume they are equally AB and AC.(I cannot see what
“resistance” to nonstrategic truncation can mean, other than trying to
give effect to unexpressed preferences.)

>
>If the assumption above is correct, the
> reversal will be easily countered by one of the other similarly
> sophisticated groups.
>

But truncation could not be so countered? See below.

> >I submit that a system which [I meant “that” -- HT] reaches a different result from
> >Steve's second example if the "A" voters are divided into 23AB and
> >23AC creates a clear incentive to insincere voting.
> -snip-
> 
> The "largest loss" scores in Hugh's example are very close:
>     A=54, B=57, C=56
> A wins if the B and C voters roll over and play dead.  But the
> numbers are so close that a small defense is sufficient to counter
> the massive reversal.  And they're so close that the counter may
> make the reversal backfire by electing C.

A good reason why the BA voters might counter the “counter” (if it is
Ossipoff’s bitter prescription), by voting AB.  But the question here is
only whether truncation strategy is somehow more difficult to counter. 
See below. 
 My point about incentives for insincere voting did not relate to
reversal.  It is the sincerely indifferent A voter who has the clear
incentive to vote insincerely in a system such as I described (including
S//C [EM]).

> 
> Is it plausible the A voters will be able to successfully reverse
> without the B and/or C voters easily defending?  TR-2 guards against
> both innocent and devious truncation.  The other voters (a majority)
> can guard against, and maybe punish, devious reversal, just by making
> sure that B and/or C aren't both beaten by a majority.
> 

[It is not really the issue here, but the B voters have no real
"defense" in Condorcet, and those who prefer A to C would be
particularly irrational to use a strategy that would elect C to punish A
-- rather, all the B voters would want to convince the C voters that the
B voters would “cooperate” with the A strategy, i.e. vote sincerely, and
that therefore the C voters had better vote BC, or else A will win the
circular tie.  C’s “defense” is to throw in the towel and let B win. 
That prospect would not deter the A voters from offensive strategy.  If
C himself is unwilling to concede and asks the faithful to vote for him,
then A’s strategy looks promising -- if A has enough reliable
information about the distribution of true preferences among likely
voters.]

The point here is that what Steve says the B and C voters can do must be
at least
equally true if the A voters try a truncation strategy in a system, such
as Condorcet with a margin-of-defeat tiebreak, in which truncation by
voters with the true preference AB is equivalent to partial
order-reversal.  So whatever argument Steve can make about the
ineffectiveness of order-reversal undercuts his own argument about the
pernicious incentives allowed by any system that would elect A in his
second example.  However strong or weak those incentives are, they still
exist in Condorcet [EM].

I am puzzled by the notion of "guarding" against "innocent" truncation.
(Perhaps the system also should “guard” against complete abstention?)
If we assume application of Condorcet [EM] to Steve's second example,
then I think the phenomenon being described is nearly the opposite of
"guarding" -- it is really the exploitation of the A voters' innocence
about the features of the system, in order to deny them the victory they
would have gained, with zero risk, had they been organized or
well-advised. If they were really indifferent between B and C (which is
the only rational explanation for innocent truncation), then they should
have paired their votes or voted randomly for second place.
(Steve might argue that the A voters would not truncate in Condorcet
[EM] even if they were really indifferent, so I needn’t worry, but I
don’t think that is his argument, and if it were he might as well let
the A voters have the option to cast half-votes and remove the risk that
the B-C race will be decided by the deviation from 50% among the A
voters’ insincere second choices.)

 Steve, I understood your argument against A winning in your example 2
to be based on the incentive for truncation strategy by A voters who
really do have a second preference (i.e., B).  If your basis for
abhorring that result were instead something like the the so-called
"Majority Rule" standard (or criterion), then I presume you would not
implicitly have deemed potentially acceptable a system that would elect
C (with the largest majority against her) in your second example.  (Do
we at least agree, then, that given the Condorcet criterion, the goal of
limiting incentives to insincere voting is more important than the
“Majority Rule” criterion?)
But if incentive is the issue, what plausible set of expectations about
the votes of others could I have that would give me a rational
incentive, in Condorcet (margins-of-defeat), to truncate but not to
reverse order?

Finally, let me suggest that making Steve's second example a litmus test
(even with the reasonable exception), and implying that a “Condorcet”
system would not elect A (despite his large plurality and the weak
results of B and C), would unnecessarily detract from the much more
important Condorcet criterion and could put off those who otherwise
might support some version of Condorcet against the raft of inferior
alternatives.  


-- Hugh Tobin