[EM] IRV counting with integers to handle multiple candidates at the same preference level

[Forest Simmons]

Here's how to make even IRV precinct summable in a practical way, even when
there are 135 candidates with 135 factorial permutations, and many more
when you take equal rankings an truncations into account:

Encode each ballot as a string, just as we do on EM list election profiles.
Add the ballot strings together algebraically as though each string were a
variable name. Algebra software easily adds these strings together
algebraically (as opposed to string concatenation) by collecting like terms
on the fly. The precinct sums are added together, as well, again by
collecting like terms. The coefficients of the collected terms tell how
many ballots in each faction, just as in our EM example profiles.

You don't need to initialize 135 factorial bins, when almost all of the
would end up empty, anyway!

El mié., 26 de ene. de 2022 5:46 p. m., Richard, the VoteFair guy <
electionmethods at votefair.org> escribió:

> I'd like to stop the misconception that IRV -- instant runoff voting,
> also called "single-winner ranked choice voting" -- cannot allow a voter
> to mark two or more candidates at the same preference level.
>
> In particular, it's ridiculous that the FairVote organization promotes
> the practice of tossing out a ballot when the counting reaches a
> preference level where the voter has marked more than one candidate.
>
> Although such shared preference levels are easy to handle using
> fractions or decimals, that violates the common legal requirement that
> votes be allocated to candidates in "whole" numbers.
>
> Instead it can be done using only integers.  It just involves
> "grouping."  Here's how:
>
> When there are two ballots that rank candidates A and B at the same
> preference level, one of the ballots is allocated to candidate A, and
> the other ballot is allocated to candidate B.
>
> When a third ballot with this preference is encountered, it's not yet
> allocated.  Then when the fourth arrives the third and fourth ballots
> (with this pattern) are allocated to the two candidates, with one ballot
> going to each candidate.
>
> When there are 379 ballots with this pattern, 378 will be allocated, and
> only one ballot will be uncounted.  That's much better than tossing out
> all 379 ballots.
>
> It's that simple.
>
> Writing the software is not difficult.  It just involves grouping
> equivalent ballots together.  This grouping must be done separately for
> each elimination round because the patterns change as candidates are
> eliminated.
>
> If anyone wants to know how the software can do this using only
> integers, and simple C-language-like statements, just ask.  I've
> implemented it in my vote-counting software on GitHub.
>
> The importance of this issue goes beyond a voter not having a preference
> between two (or more) candidates.
>
> Most of us voters want to be able to mark a strongly disliked candidate
> at the lowest preference level.  For example, imagine having 9
> candidates and 6 ranking levels and strongly disliking candidate "I":
>
> A > B > C+D > E > F+G+H > I
>
> Not being able to rank candidate "I" at the lowest preference level is
> unacceptable!  Yet that can't be done if IRV counting can't handle
> shared preference levels.
>
> (And having 9 preference levels for 9 candidates puts us on a slippery
> slope to how to handle the 135 candidates in the infamous California
> gubernatorial recall election.)
>
> Keep in mind that the number of viable candidates in elections will
> increase.  That's because vote splitting in general elections is what
> caused political parties to limit themselves to just one nominee from
> each party.  As more places adopt IRV and other better ranked-choice
> methods, vote splitting won't be an issue.
>
> There's yet another reason some political parties will need to offer a
> second candidate.  It defeats the election tactic named "blocking."
> That's the tactic of giving money to support a weaker candidate in a
> primary election so that it's easier to defeat that party during the
> general election.  A clear example happened in the 2008 U.S.
> presidential election when Hillary Clinton was blocked from reaching the
> general election partially because some Republicans gave money to Barack
> Obama based on their expectation that he could not possibly win the
> general election.
>
> Another reason for political parties offering a second nominee is that
> in a gerrymandered district (which applies to most U.S. federal and
> state districts) the winner's party is pre-determined, so offering just
> one nominee means the district's minority-party voters have no
> meaningful choice in the general election.
>
> (By the way, as pointed out in a recent article at the Center for
> Election Science, this is why extremist candidates are getting elected
> rather easily under our single-nominee election system.  They can get
> elected with plurality support from less than half the dominant-party
> voters, who themselves only need to be around 55 or 60 percent of the
> district's voters.  The single-nominee rule means the extremist
> candidate is virtually unopposed in the general election.)
>
> (Of course defeating these tactics won't come from political parties,
> and certainly won't come from government initiatives.  Yet ways to
> defeat these unfair political-manipulation tactics are waiting to be
> adopted.)
>
> (BTW, tiny parties, with fewer than, say 15 percent of the voters
> registered in that party, would only get one nominee.  Or they would be
> allowed a second nominee when a big party fails to offer a second nominee.)
>
> So, the increase in the number of party nominees, and hopefully an
> increase in opposition parties, will increase the number of candidates.
> This means the places that get stuck with IRV (in spite of much better
> methods), should not also be stuck with ranking each candidate at a
> different preference level.
>
> Of course the FairVote organization avoids this fairer approach because
> they're trying to use IRV as a stepping-stone to STV, and STV becomes
> complex when voters mark ballots this way.  But it's time to reject the
> unfairness of tossing out IRV ballots just because counting those
> ballots under STV would become complex.
>
> (Also, there are better STV-like methods that don't have the limitations
> of STV.)
>
> Now that discussions of IRV are increasing because of the proposed
> "Forward Party" endorsing "ranked choice voting," those of us who
> understand the math behind vote counting need to make it clear that IRV
> does not have the shared-ranking limitation that FairVote imposes in
> their certified software.
>
> Probably all of you who write messages on this forum already understand
> this concept.
>
> Yet I'm hoping that those who only read this forum's messages will
> understand that FairVote's claims (on their website and elsewhere) that
> IRV ("single-winner RCV") cannot handle a voter marking more than one
> candidate at the same preference level is a request to drink their
> Kool-Aid, not an actual limitation in IRV.
>
> Richard Fobes
> The VoteFair guy
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220126/9cd33b14/attachment-0001.html>