[EM] Advantages of CR style ballots

[Anthony Simmons]

Forest said (extracted from complete original message below):

>> Constraints tend to limit the information efficiency of
>> the ballot.

Here's another way of looking at the efficiency of the
ballot.  We don't want it to become too efficient because
ballots are very poor storage media.  Or put differently, an
election in the abstract (or in ATM-style voting machines)
can afford to ignore some of the mechanical considerations
that cause problems in elections.

I've worked at the polls quite a few times, and I've always
found it to provide a different perspective on the notion of
voting.  Most of that has been a shift in attitude, and
hardly something that would interest a group concerned with
election methods.  But this time I also worked at the
election board, processing absentee ballots (most of the
ballots in the area where I live are absentee), and there I
discovered some things that might bear directly on the choice
of election method.

While we look at the minutiae of mathematical criteria and
the influence of imperfect voters, and possibly even consider
software requirements, we tend to disregard such mechanical
problems as feeding paper ballots through a counter, and
reading imperfectly marked ballots (that bizarre -- and
avoidable -- Florida chad problem notwithstanding).

Here, in this part of Washington (Washington state -- it was
originally going to be called "Columbia", but it was thought
that might be confused with "District of Columbia") we use
optical scanners.  One marks a choice by connecting the two
ends of an arrow, so a valid mark is a line between two
fairly small points on the ballot.  Obviously, the ballots
have to be of good quality.  They are light card stock, with
matte coating.

A quick look at the machines shows that they use lasers.
There appear to be four lasers across, at the point where the
scanning actually occurs.  I think that means that the marks
must be restricted to four zones that run the length of the
ballot (top to bottom).  You can see how this would
complicate the use of any ranking method, in which the
candidates would be listed vertically, with a whole 2D array
of boxes next to them.  It would seem that the machines we
were using couldn't handle that arrangement.  I don't know
what they use in Australia or Ireland to count ballots, or in
other places that use rankings.  But the mechanical cost
would seem to depend on the choice of method, with rankings
being more expensive.  Just conjecture; I haven't looked into
this.

One problem we had to deal with was possible read errors
caused by spurious marks.  There might be a pencil spot, or
an incomplete erasure.  In general, marks, even faint marks
or smudges that obviously weren't votes were assumed to be a
problem, and the ballots had to be duplicated.  Duplicating a
ballot is an involved process; an identically marked ballot
has to be created, and you can imagine the amount of
procedural safeguard that is required.  For example,
possession of pencils is limited to pairs of workers; if you
get up and leave your partner at the table with ballots, you
take the pencil with you.  So duplication is a slow and
costly business.  And there are other similar processes, such
as examining ballots for possible problems, that are also
time-consuming.

Note that (1) Only smudges within an area where a line would
be a valid mark (a bit on the ballot, ignoring for now the
fact that only certain patterns of marks are valid) are
problems, so the number of places where such smudges might
occur -- and hence the number of problem marks -- can be
expected to be roughly proportional to the complexity (number
of bits).  Often, the smudges are caused by a pencil mark
offsetting from one part of the ballot to another because the
ballots are folded.  (2) These offset marks could be expected
to occur on the order of the square of complexity.  Clearly,
more complex ballots are going to demand more duplicating,
and the work of duplicating a single ballot increases with
complexity, so total duplicating work will be roughly
o(complexity^3).

Something to consider when choosing between a ranked election
method that uses arrays, and something like plurality,
approval or cumulative that requires only a single bit per
candidate.

Another consideration is:  Remember earlier discussions of
the usefulness of a "None of the above" option?  This was
mostly considered in terms of how to take into account that
voters are displeased with the choices, but there's another
way to look at it.  When checking ballots, we would sometimes
see a smudge that almost certainly was spurious, perhaps
caused by the opposite side of the ballot picking up ink off
a newspaper or some such.  Sometimes, that would be the only
mark for a group of candidates, and would have been a valid
vote if it were real, but in bad cases, it can be hard to
tell if it's a vote or not.  And sometimes there was a clear
vote, so the smudge could only be spurious.  The difference
in the two cases was that in the latter, any spurious mark
must produce an invalid ballot, while in the former, the
Hamming distance between valid ballots is one, so there is no
possibility of error checking.  In that case, a "None of the
above" option would guarantee a Hamming distance of two, so
any single error raises a flag.

I realize it's unrealistic to expect voters to compute cyclic
redundancy characters, but it should be possible to design a
system that would provide rudimentary parity checking.  IRV,
or any complete ranking, would do that automatically as long
as all candidates must be ranked.  Plurality does not.  Even
if voters were required to make exactly one mark (rather than
zero) or their votes won't count, how we know what to make of
a single faint mark?  Is it a vote, or is in an invalid
ballot (no marks) with a smudge?  Approval could be made to
comply with the simplest error checking by requiring a valid
ballot to have "yes" or "no" marked for every candidate.  I
suppose Plurality would also comply under the same
requirement.  However, we could expect the inevitable
confusion as voters find themselves faced with a task that
can only be reliably carried out by a pigeon after
substantial training.

I think that the incredibly poor mechanical qualities of
paper ballots need to be considered in any evaluation of
election methods.  To a rough approximation, it seems that
the more efficient the ballot, in the information-theoretic
sense, the less reliable it is going to be; sophisticated
error checking and correction are going to be hard to
incorporate into paper ballots.  Therefore, from a practical
perspective, perhaps it would be better, once again, to give
preference to methods that make it easy to identify errors.

By the way, I ran across the inevitable votes for the Mouse
and Duck, and it occured to me that people really do want the
ability to vote "None of the above", whether it has any
effect on the outcome or not.  Perhaps voting for Mickey
Mouse really does serve a purpose, and he should be entered
in every contest; he seems to have an important role to play
in world politics.



>> From: Forest Simmons <fsimmons at pcc.edu>
>> Subject: [EM] Advantages of CR style ballots

>> Joe Weinstein argues the advantages of unconstrained CR
>> style ballots below.  I would like to add my two bits
>> worth.

>> Most of the arguments against the use of CR ballots are
>> based on the misguided assumption that the only way to use
>> CR ballots is to give the win to the candidate with the
>> highest average rating.

>> That assumption is tantamount to believing that the only
>> way to use ranked ballots is to give the win to the
>> candidate with the highest average rank (the Borda
>> winner).

>> Note that CR ballots can be used for head-to-head
>> comparisons (generalizing Condorcet methods).

>> CR ballots can be used to find the candidate with the
>> highest median rating (generalizing Bucklin).

>> There are many other uses of CR ballots.  Lorrie Cranor
>> uses CR ballots as input for her Declared Strategy Voting
>> (DSV) methods.

>> All of these uses of unconstrained CR ballots allow the
>> voter more freedom of expression than the constrained
>> methods that use the same information capacity ballot.

>> Constraints tend to limit the information efficiency of
>> the ballot.

>> For example, the lone mark plurality ballot can be used
>> for Approval if the constraint is removed.

>> Another example:

>> Three bits of information are required to distinguish
>> among five candidates, so a ballot that allows the voter
>> to rank five candidates requires making at least a three
>> bit mark beside each candidate's name. Without the
>> constraint, the same ballot could be used to rate each
>> candidate on a scale of zero through seven.

>> More commonly five bit codes are used to rank five
>> candidates (five distinct bubbles to the right of each
>> candidate).  The same ballot could be used to rate each
>> candidate on a scale of zero to 31.

>> Furthermore, the lack of constraint makes it harder for a
>> voter to foul the ballot. In other words, a voter can
>> hardly violate non-existent constraints.  Which is harder
>> to mess up ... lone mark or Approval?  A lone mark voter
>> who doesn't notice the (rather ridiculous) "one mark only"
>> instruction can accidently foul his ballot if he likes two
>> of the candidates.

>> Forest