[EM] Truncation

[Bart Ingles]

Adam Tarr wrote:
> 
> Joe Weinstein wrote:
> 
> >There is no point in invalidating or penalizing ballots of voters who have
> >reason to lack perfect information (especially when there is a gaggle of
> >mostly unknown candidates), or who do have (for their purposes) perfect
> >information but are simply trying to minimize time and effort and
> >confusion in marking their ballots.   Rather, when a given candidate has
> >not been explicitly marked, he can still be given a default evaluation.
> 
> I think virtually everyone agrees with this.  The debate is not really
> whether we ALLOW truncation in ballots.  The debate, rather, is what
> strategic impact truncation has in various voting systems, and what sort of
> incentives that gives to the voter.
> 
> Recently, there has been a revival of the debate about margins-based
> Condorcet completion methods versus winning votes-based Condorcet
> completion methods, with an eye towards the effects of truncation on
> each.  Specifically, there is the remarkable fact that a voter in a winning
> votes-based Condorcet voting system can NEVER be hurt by fully expressing
> their preferences.  There are cases where fully voting your preferences can
> fail to help you, but it can never actually hurt you.

Never is a strong word.  How about the following:

(projected vote percentages shown; assumed accurate to within +/- 5
percentage points)

45%   A  B  C
 5%   B  A  C
 5%   B  C  A
45%   C  B  A

If the A and C voters don't consider B a worthy compromise, it seems to
me that the A and C voters are both better off truncating, as this would
turn a certain loss for both A and C into a 50/50 chance of a win for
either A or C:

45%   A
 5%   B  A  C
 5%   B  C  A
45%   C

Since this doesn't involve defeat cycles, it makes no difference whether
the method uses winning votes or margins.


On the other hand, if only one side truncates, there is the potential
for a cycle, in which case if winning votes can guarantee a win for B
then the method at least avoids a prisoner's dilemma (is this the
case?).  Example:  Suppose one side truncates and the final result turns
out to be:

44%   A  B  C
 5%   B  A  C
 5%   B  C  A
45%   C

If I'm not mistaken, WV would elect B in this case, while margins would
pick A.  Margins seems to actually punish truncation in this case.  This
punishment then sets up the prisoner's dilemma, in which it doesn't pay
for either side to truncate unless both do.

But then I don't see truncation as necessarily a bad thing.  If
truncation can defeat a "hated middle" candidate, it addresses my main
misgiving about the Condorcet methods.

Bart Ingles



> This is not a distinction without a difference.  In every other ranked
> balloting method I am familiar with, the voter could potentially look at
> the results of an election and say, "If only I (and others like me) had
> just left some information off the bottom of our ballot, without changing
> the order of any candidates above that point, then I could have gotten a
> better result."  This is not the case in winning votes-based Condorcet
> methods, and that's an incredibly powerful statement.
> 
> One of Donald Davidson's favorite criticisms of non-IRV alternative voting
> methods is that, "your vote for your second choice can help defeat your
> first choice." (paraphrasing).  This is simply not true in winning
> votes-based Condorcet methods.  It is true, however, in margins-based
> Condorcet voting, or in Borda count, or in cardinal rankings, or in
> approval voting.  IRV itself is immune to this criticism, but in IRV your
> first place vote can help defeat your second place vote (and give the
> election to someone else altogether), which is not really any better.
> 
> So winning votes-based Condorcet voting's resistance to strategic
> truncation is essentially unparalleled in voting systems.  Blake has argued
> that this could encourage voters who sincerely have no preference among
> lower candidates to randomly rank those candidates on the bottom of their
> ballot, since it can't hurt them to do so.  This is of course true, but in
> my mind it is an extremely minor issue - we're talking about candidates who
> are so minor that the voter doesn't care enough to form any opinion on
> them.  If the voter is strategically aware of the advantage of full
> ranking, they are probably savvy enough to spend a few minutes reading
> basic candidate statements and picking some order to put the candidates
> in.  And in the end, doesn't it make sense to reward the voter who puts
> more information on their ballot rather than the voter who puts less?
> 
> There's no way to distinguish between the lazy voter and the sincerely
> indifferent voter, or between the informed voter and the haphazard
> voter.  But I'd rather put the haphazard voter on nearly the same ground as
> the informed voter than penalize the informed voter vis-a-vis the lazy
> voter.  Especially when doing otherwise gives rise to the strategically
> lazy voter, which is a FAR more dangerous development than the
> strategically haphazard voter.  This is not just a philosophical debate;
> I've shown examples in recent threads where margins-based Condorcet allows
> seemingly undemocratic results due to truncation.  I haven't seen any
> counter-examples where winning votes comes up with the undemocratic result
> due to its failure to penalize full preferences.
> 
> >Forest notes that the usual American academic grading system - which has
> >the advantage of being very familiar to almost all Americans - allows the
> >six grades A-E.  Typically,  grades A-D are degrees of definite pass,
> >grade F is definite fail, and grade E indicates that information is
> >incomplete to infer a definite pass or definite fail.
> >
> >Accordingly Forest proposes that if a given election is to be run so as to
> >allow voters to use at least four grades, then a good approach would be to
> >allow use precisely of the six academic grades, with ungraded candidates
> >being awarded the default grade E.
> >
> >This proposal makes excellent sense.  Four levels are surely enough to
> >distinguish substantially distinct degrees of active approval.  One level
> >suffices to express active disapproval.
> 
> At first I didn't like this idea, but its grown on me.  The simplicity to
> the voter of ABCD(E)F voting is worth it.  The voters who are interested
> and involved enough to actually need six distinct levels of approval are
> the same voters who will understand that the unmarked candidate will get
> the E grade.
> 
> I spent some time a few months back seeing if approval-completed Condorcet
> could be made to work using this sort of ballot, but in the end I realized
> that the only time approval completion worked like I thought it should was
> when the approval votes supported the sincere Condorcet winner.  When the
> approval votes did not do so, the system encouraged all sorts of strategic
> manipulations.  So I gave up on ACC, and I now hang my hat with
> winning-votes based Condorcet, which seems to be the system that is most
> resistant to strategic manipulation by a wide margin.
> 
> -Adam
> 
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