[Election-Methods] New improved fla for vote counts to be reported for auditing IRV elections

[Kathy Dopp]

On Sat, Aug 2, 2008 at 1:14 AM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> Kathy Dopp wrote:

>>
>> given:
>> R = the number of possible rankings or IRV rounds
>> N = the number of candidates in each election contest
>>
>> the total number of permutations and the number of vote counts which
>> must be publicly reported for EACH auditable unit is (drum roll):
>>
>> the sum from i = 0 to i = R-1 of N!/(i+N-R)!

Correction:
R= the number of permitted candidate rankings

*not* the number of IRV rounds.

>
> Well, any election method can be "parallelized" (in quote marks) with a
> superpolynomial amount of information when there are as many choices as
> candidates.

I am not certain what you mean. Precisely, any Ranked Choice ballot
has a number of possible permutations of all the candidates given by
the fla above; or a number of unique candidate rankings given by the
fla above.

> Since n! < n^n, it also reduces to a polynomial amount of
> information for a fixed number of choices or rankings (n for one, n*(n-1) =
> O(n^2) for two, and so on).
>
> Thus, if the activists claim that IRV escapes the problem if you do it in
> that way,

Not sure what you mean by "that way".

> you can say that that holds for absolutely every kind of ranked
> ballot method that exists - at least for the neutral ones, and election
> systems really should be neutral.

However, as you know, it is *not* true that the counting method is
complex or non-additive for each precinct with *any* counting method
for Ranked Choice ballots. The IRV method is, for instance, far more
complex than the approval or Borda methods where it is easy to audit
the accuracy of the machine counts *without* having to publicly report
all the tallies for all permutations of candidate orderings in order
to do valid partial post-election audits.

>
> Rated ballots with a granularity permitting k possible ratings for a single
> candidate would have complexity k for a single choice, k^2 for two, ..., k^n
> for a full preference ballot.

Yes. The ballots might be as complex but the counting method is not as
complex and doing partial post-election auditing does *not* require
keeping track of all the permutations of possible unique ballot
choices that voters can make.

>
> At some point, rated or ranked, it becomes easier to simply send every
> voter's preference. An interesting consequence of that would be that it'd be
> possible to "fingerprint" one's own vote to vote-buyers if there are a

Yes. That certainly might be possible because in most precincts, if
there were enough candidates, the number of voters would be far less
than the number of possible unique ballot ranking choices.

That is a disadvantage of any ranked choice voting ballot method - the
fact that post-election auditing on the individual ballot level is
probably not a good idea.  But auditing at the ballot level can be
problematic anyway due to ballot privacy concerns, even with a single
choice plurality ballot.

> sufficient number of choices, since one could use the extra information to
> make one's own ballot unique, and thus detectable - at least if the list of
> every voter's preference were to be made public afterwards.
>
> The activists may say that the ballot data can be transferred easily if one
> uses computerized means: a practical system would pick the lesser number of
> n! and (number of voters), so a strictly ranked Presidential election with
> full turnout (300 million voters) and 10 candidates, would need "only"
> ceil(lg(10!)) * 3e8 bits = 6.6e9 bits, which is slightly less than 787
> (binary) MB, enough to fit on a DVD.

How many ranked choices are you allowing each voter to make?  3?

>
> Still, that doesn't make the system any more summable, and like you say,
> when the "competitors" only have to ship 10^2 values (actually 10^2 - 10 =
> 90; Condorcet matrix with diagonal removed), 787 MB doesn't sound so
> impressive after all.

Well, I am worried less about the amount of disk space, although that
is very interesting that you can calculate that. I am more worried
about the confusion to the public who would like to achieve the goal
of publicly verifiable election outcome accuracy via post-election
manual audits to check the machine counted results.

In other words, election outcomes should be publicly verifiably
accurate in a way that is understandable/transparent to the public.
However, if the IRV folks can get election officials to instead do
publicly observable 100% manual counts of all IRV election contests,
that would work too.

However, I fail to see the need to use such a complex counting method
(IRV) that fails to even fully solve the spoiler problem it claims to
solve and which gives undesirable election outcomes some times, when
there are far simpler to count and audit election methods which seem
to fully solve the spoiler and other problems and give more
consistently desirable election outcomes.

Thanks for your input.

-- 

Kathy Dopp

The material expressed herein is the informed product of the author
Kathy Dopp's fact-finding and investigative efforts. Dopp is a
Mathematician, Expert in election audit mathematics and procedures; in
exit poll discrepancy analysis; and can be reached at

P.O. Box 680192
Park City, UT 84068
phone 435-658-4657

http://utahcountvotes.org
http://electionmathematics.org
http://electionarchive.org

History of Confidence Election Auditing Development & Overview of
Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf

Voters Have Reason to Worry
http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf

"Enlighten the people generally, and tyranny and oppressions of body
and mind will vanish like evil spirits at the dawn of day," wrote
Thomas Jefferson in 1816