IRV combinatorial pain

[Lucius Chiaraviglio]

In response to a message on another mailing list (peopl...@lists.riseup.net), I
put together lists of the tallies that would be needed for Instant Runoff Voting to avoid
centralized counting.

3 candidates: 16 tallies, for A>B>C, A>C>B, B>A>C, B>C>A, C>A>B, C>B>A,
A>B, A>C, B>A, B>C, C>A, C>B, A only, B only, C only, none (need count
of this to make sure that the ballots add up properly). Tallies like
A>B and A only include occurrences of people ranking like A>B>A, as well
as people only voting for 2 or 1 candidates.

4 candidates: 65 tallies (ouch), for A>B>C>D, A>B>D>C, A>C>B>D, A>C>D>B,
A>D>B>C, A>D>C>B, B>A>C>D, B>A>D>C, B>C>A>D, B>C>D>A, B>D>A>C, B>D>C>A,
C>A>B>D, C>A>D>B, C>B>A>D, C>B>D>A, C>D>A>B, C>D>B>A, D>A>B>C, D>A>C>B,
D>B>A>C, D>B>C>A, D>C>A>B, D>C>B>A, A>B>C, A>B>D, A>C>B, A>C>D, A>D>B,
A>D>C, B>A>C, B>A>D, B>C>A, B>C>D, B>D>A, B>D>C, C>A>B, C>A>D, C>B>A,
C>B>D, C>D>A, C>D>B, D>A>B, D>A>C, D>B>A, D>B>C, D>C>A, D>C>B, A>B, A>C,
A>D, B>A, B>C, B>D, C>A, C>B, C>D, D>A, D>B, D>C, A only, B only, C only,
D only, none.

4 candidates if you limit to 3 choices: 41 tallies, for A>B>C, A>B>D,
A>C>B, A>C>D, A>D>B, A>D>C, B>A>C, B>A>D, B>C>A, B>C>D, B>D>A, B>D>C,
C>A>B, C>A>D, C>B>A, C>B>D, C>D>A, C>D>B, D>A>B, D>A>C, D>B>A, D>B>C,
D>C>A, D>C>B, A>B, A>C, A>D, B>A, B>C, B>D, C>A, C>B, C>D, D>A, D>B,
D>C, A only, B only, C only, D only, none.

While the above is not impossible to do, it is definitely more work to
keep correct than just 1 tally for each candidate, and a lot more
chances to mess it up. For instance, even while trying really hard to
proofread the combinatorial aspects of this, I almost left out 4 of the
possible 4 rank combinations while putting together the 4 candidate
tally set above, and only realized my mistake shortly before sending
this out. It gets even worse if you have more than 4 candidates, even
if you limit to 3 choices for each voter.

The alternative is to transport all of the ballots to a central location
and count them there. While this is also possible, the logistics of
keeping all of the ballots secure during such an operation would be a
nightmare, even if done on a state-by-state basis as opposed to
nationwide.

--
Lucius Chiaraviglio | luc...@verizon.net (main)
| lchi...@gmail.com (photos)
| lchi...@yahoo.com (alternative)
| luc...@post.harvard.edu (fwd only)

[Kathy Dopp]

Thanks Lucius for yet another excellent post.

I also did some work this weekend to show how many tallies would be
needed for each polling location if there were three ballot positions
for voters to use and five, six, seven, eight, nine, or ten candidates
running. Also shown are how to obtain the actual 85 unique ballot
combinations for which tallies would be needed for the case of five
candidates running.

First the number of unique ballots with 5 to 10 candidates are:

5 candidates 85 = 5*4*3 + 5*4 + 5 tallies per precinct
6 candidates 156 tallies per precinct
7 candidates 259 tallies per precinct
8 candidates 400 tallies per precinct
9 candidates 585 tallies per precinct
10 candidates 820 tallies per precinct

Note this is in contrast to precinct-summable methods that can be
counted with a number of tallies equal to the number of candidates who
run for office for each precinct, or in the case of the Condorcet
method a number of tallies equal to the square of the number of
candidates who run for office - both numbers much much less than are
required for the complex IRV/STV counting methods. Most other
alternative proportional representation systems can be counted with a
far smaller number of tallies equal to the number of parties or
candidates running for office.

To give an example for the case of five candidates running for office
in an IRV/STV election:

A list of all the choices for 5 candidates A,B,C,D,E,F with 3
ballot positions, here are all the ones beginning with candidate A.
(where A B C means the voter prefers A over B and B over C)

A B C
A B D
A B E
A C B
A C D
A C E
A D B
A D C
A D E
A E B
A E C
A E D
A B
A C
A D
A E
A

There are 17 unique ballot choices beginning with candidate A, so for
all five candidates there is 5*17 = 85 unique ballot orderings with a
ballot that allows
for ranking up to 3 candidates.

Of course any ballot that limits the number of candidates that can be
ranked (as most US ballots do), prohibits voters from participating in
the final IRV/STV counting round.

In order not to prohibit voters from participating in the final
counting round, election officials would have to provide an unlimited
length ballot or limit the number of candidates who can run for office
to the number of ballot positions plus 1. In other words to avoid
involuntarily disenfranchising voters from participating in the final
counting round, at most 4 candidates would be able to run for office
in the case that there are three positions that voters can rank on the
ballot.

Cheers,

Kathy


>  Topic: IRV combinatorial pain
>
> Lucius Chiaraviglio <luc...@verizon.net> Nov 15 06:39PM -0600

--

Kathy Dopp

Town of Colonie, NY 12304
phone 518-952-4030
cell 518-505-0220

http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/

Realities Mar Instant Runoff Voting - 18 Flaws and 4 Benefits
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

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

Checking election outcome accuracy --- Post-election audit sampling
http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf

[Lucius Chiaraviglio]

Nov 15, 2009 11:49:29 PM, miketan...@gmail.com wrote:
> It seems to me that if those of you who believe in ballots being counted
> in the precincts actually got to where you had some jurisdictions in the
> country where that actually happens, then when folks like myself come
> in to take the elections to the next level, i.e., the eradication of plurality
> voting, then we'll have to do it in a way that respects your already
> implemented worthy accomplishment.
> [. . .]
> Which leads me to ask: Since we are so blasted far from
> accomplishing those those objectives, how can so many members of
> this group justify the tremendous expenditures of time and effort that
> are made to disparage IRV and those who promote it when there is so
> much in the way of "first things first" that has yet to be accomplished?

Because if IRV does anything with respect to getting the votes counted
fairly, it will get us FARTHER AWAY from that goal instead of closer, for
the reasons that I went into some detail about in my previous message.
In addition, while we clearly need to get rid of Plurality Voting, that DOES
NOT imply that IRV is an acceptable choice of replacement.

[Rob Richie]

Lucius makes this point: "In addition, while we clearly need to get rid of Plurality Voting, that DOES NOT imply that IRV is an acceptable choice of replacement."

When restricted to single winner reform (as we by definition are when looking at single winner executive office elections), this statement is easier to say than make real. See my discussion of why many people have concluded that instant runoff voting remains a good answer:
http://www.fairvote.org/blog/2009/10/single-winner-reform-and-why-fairvote-supports-instant-runoff-voting/

Another reasonable p;ossibility is traditional "vote once and come back again" majority runoffs, as done in French parliamentary elections. When done reasonably close together, as in France, it does create what amounts to a single "general election season", so doesn't completely exclude darkhorse candidates from the general election. As being considered in the US, however, it excludes such candidates from the whole general election season (Washington State eliminates all but two candidates in August, and California next year will vote on a similar system that would eliminate all but two candidates after June), and has impacts that must be measured on campaign financing and major disparities in turnout between rounds.

For those who push alternatives like approval voting and range voting, I think they need to test to the political waters more to understand why they have so rarely been adopted or even considered  (something I really hope is done so this debate becomes less theoretical, comparing a real alternative to a theoretical one). While these systems raise some election integrity concerns as well (chain of custody is important regardless, but particularly when someone can add a vote to someone's ballot without invalidating it), but their greater problem is violating basic principles of what many voters see as fair -- for example, a candidate could well lose who would have defeated the "winner" 55% to 45% under traditional "vote for one" rules, while indicating support for a lesser choice counts directly against your first choice.

Going outside of the boundaries of winner-take-all rules allows you to look a a broad range of proportional voting systems. Many of these systems can have simple "vote for one" formats or relatively simple variations on that. See:
http://www.mtholyoke.edu/acad/polit/damy/prlib.htm

As to precinct counting with IRV-type systems, Australia shows one approach you can do with hand-counted ballots -- it uses IRV for electing its house of representatives, and had a median average of seven candidates in each race in 2007, with many races decided based on instant runoffs. On election night, preliminary totals are provided from the precinct, and unofficial IRV tallies are done at the precinct based on those totals. Ballots then are centralized for the official count, but any variations in the tally of first choices  and rankings can be measured.

As to doing precinct sums, it would not be that hard to look at every ballot and record its preference order and have a sum of each possible combination -- it means examining each ballot and having more that one ballot-counter agree on what that combination is and record it. That can be compared to what was used to do the count at a central location to make sure the preference orders didn't change.

Rob

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[Mike Ridgway]

Lucius,

It seems to me that if those of you who believe in ballots being counted in the precincts actually got to where you had some jurisdictions in the country where that actually happens, then when folks like myself come in to take the elections to the next level, i.e., the eradication of plurality voting, then we'll have to do it in a way that respects your already implemented worthy accomplishment.

As it stands, though, we're not really close to large scale precinct based counting of ballots, and we're not really close to having secure chain of custody.

Which leads me to ask: Since we are so blasted far from accomplishing those those objectives, how can so many members of this group justify the tremendous expenditures of time and effort that are made to disparage IRV and those who promote it when there is so much in the way of "first things first" that has yet to be accomplished?

I mean really.  It seems that much more time was spent convincing voters to repeal IRV then convincing legislators or voters to mandate precinct-based election tabulation.

That all seemed like status quo to me.

Mike Ridgway

Some would say I was a lost man in a lost world
You could say I lost my faith in the people on TV
You could say I'd lost my belief in our politicians
They all seemed like game show hosts to me
-- Sting.  If I Ever Lose My Faith in You

"In the beginning of a change, the patriot is a scarce man, brave, hated and scorned. When his cause succeeds, however, the timid join him, for then it costs nothing to be a patriot." -- Mark Twain
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

[Mike Ridgway]

Thank goodness we have "parliamentary systems" as an acceptable alternative to both IRV and status quo Plurality Voting, since IRV and the Plurality Voting have now been so completely discredited by Kathy, Joyce and Lucius.

I can hear Americans taking to the streets now:

"No parliamentary systems!  No peace!"

Has kind of a powerful ring to it, doesn't it?

Now a movement needs more than street demonstrations.  We have to have a web site, too.

Since the bad guys grabbed "FairVote" before we could get to it, how about PSILoveYou.org?

Do I have a second?

Mike

"In the beginning of a change, the patriot is a scarce man, brave, hated and scorned. When his cause succeeds, however, the timid join him, for then it costs nothing to be a patriot." -- Mark Twain

On Mon, Nov 16, 2009 at 8:51 PM, Lucius Chiaraviglio <luc...@verizon.net> wrote:

Because if IRV does anything with respect to getting the votes counted
fairly, it will get us FARTHER AWAY from that goal instead of closer, for
the reasons that I went into some detail about in my previous message.
In addition, while we clearly need to get rid of Plurality Voting, that DOES
NOT imply that IRV is an acceptable choice of replacement.

--

Lucius Chiaraviglio | luc...@verizon.net (main)
                   | lchi...@gmail.com (photos)
                   | lchi...@yahoo.com (alternative)
                   | luc...@post.harvard.edu (fwd only)

--

[Lucius Chiaraviglio]

Nov 17, 2009 10:22:53 AM, miketan...@gmail.com wrote:
> Thank goodness we have "parliamentary systems" as an acceptable alternative to both
> IRV and status quo Plurality Voting, since IRV and the Plurality Voting have now been
> so completely discredited by Kathy, Joyce and Lucius.

Last time I checked, whether or not you have a parliamentary system is completely
independent of which voting system you use. For instance, some countries in Europe
use proportional representation, but the United Kingdom uses plurality voting to elect
its members of parliament. Interestingly, despite this similarity with the United States
in choice of voting, they still manage to have a third party that consistently wins some
seats (although a lot less than it should -- again, I do not deny that plurality voting is
bad).

> I can hear Americans taking to the streets now:
>
> "No parliamentary systems! No peace!"
>
> Has kind of a powerful ring to it, doesn't it?
>
> Now a movement needs more than street demonstrations. We have to have a web site, too.
>
> Since the bad guys grabbed "FairVote" before we could get to it, how about PSILoveYou.org?

Be careful what you wish for. If you actually manage to get a parliamentary system
instituted, this is no guarantee that the members of parliament will not be elected
by plurality voting (or some even worse corruption thereof, like the abomination we
call the Electoral College).