Bottom Two Runoff (Condorcet IRV hybrid)
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@jack-waugh It pretty easy to analyze how IRV and BTR work with a simple 3-candidate cycle that's like Rock-Paper-Scissors. Since this defeat line is circular we can assign whatever label to the candidate that has the most first-choice votes, say "Rock".
So it's Rock > Scissors > Paper > Rock ...
Now in the semifinal round, it's either
- Rock
- Paper
- Scissors
or it's
- Rock
- Scissors
- Paper
in the ranking of first-choice votes.
In the IRV case, Paper wins the first scenario and Rock wins the second. It's inconsistent.
In the BTR case, Scissors and Paper have a runoff, Paper loses and is eliminated, then Rock always beats Scissors in the final round.
For the 99.9999% of the cases (that either have a Condorcet winner or a simple Rock-Paper-Scissors cycle), the result with BTR is the same as using "straight-ahead" Condorcet and explicitly using plurality as the "completion method" for how to elect a candidate if there is no Condorcet winner. Then it really is a question of which has simpler language? BTR-IRV or simple Condorcet with an explicit completion method for the contingency that there is no Condorcet winner.
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@rob said in Bottom Two Runoff (Condorcet IRV hybrid):
Unlike IRV though, in almost every election, you can give results immediately with precinct sums (which would be pairwise matrix data, i.e. (N*N-1)/2 discrete integer values).
Two little mistakes. First, you need to either add a pair of parenths or you need to move one. And you're off by a factor of 2.
N*(N-1)/2 is the number of pairings of N candidates. For each pair, there are 2 numbers.
So, it's N(N-1) summable tallies that each polling place needs to publish at the end of the election day after the last voter has voted. Now, for the explicit Condorcet-plurality method, you would also need N tallies of first-choice votes for each candidate (to determine the plurality winner). Then it becomes simply N(N-1)+N tallies, which is N^2 tallies for each precinct to print. For 6 candidates, that's about 5 inches of paper tape to publish all of the tallies necessary to be fully precinct summable. For 7 candidates, it would be about 7 inches. Easily photographed with a smart phone.
For Hare IRV to be precinct-summable, you would have 205 numbers to publish for 5 candidates. Maybe 4 feet of paper tape. 1236 numbers for 6 candidates. Maybe 15 feet of paper tape to post at the poll entranceway.
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@rb-j said in Bottom Two Runoff (Condorcet IRV hybrid):
Two little mistakes. First, you need to either add a pair of parenths or you need to move one. And you're off by a factor of 2.
N*(N-1)/2 is the number of pairings of N candidates. For each pair, there are 2 numbers.Edited. Oops.
Just spent some hours last night writing a set of javascript classes that do pairwise matrices in a much more manageable way than stuff I've done before, so I shouldn't have made that mistake.
BTW, I'm planning on implementing BTR and straight-ahead Condorcet at the below Codepen as well as a few more. (along with pretty graphics). Do you know where I can find the the Burlington 2009 ballot data so I can test it on that?
(CodePen doesn't work great embedded here unfortunately, I kinda wish I could just post a link:)
https://codepen.io/karmatics/pen/poLPpzW -
@rob These algorithms are all almost trivial in Julia
unfortunately I don't know much JS -
@rob said in Bottom Two Runoff (Condorcet IRV hybrid):
I'm planning on implementing BTR and straight-ahead Condorcet at the below Codepen as well as a few more. (along with pretty graphics). Do you know where I can find the the Burlington 2009 ballot data so I can test it on that?
I can send you files, but I think you can get it from wayback:
https://web.archive.org/web/20090924005145/http://www.burlingtonvotes.org/20090303/
Specifically 2009 Burlington Mayor Final Piles Report.txt
and 2009 Burlington Mayor Detail Report.txt
I can send you my crappy MATLAB code that I used to parse the Final Piles text file.
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@andy-dienes They are certainly pretty simple in Javascript, but I did spend some time trying to make clean classes that would be flexible for a lot of things, not just tabulation itself. I like things that run in a browser, especially if it can be done in a coding playground like Codepen. It makes it so much easier to share.
Perfect example is the giant clusterf**k that was the vote for the domain of this forum. It was only like 12 people voting and we had to wait weeks for someone to deliver us the STAR voting results, which were completely wrong and started a big ugly situation. Sad that a group like this has so much trouble with a simple vote.
The harder part is integrating them into things that can visualize results and whatnot. (the graphical and interactive stuff being more my wheelhouse) I mean that isn't really hard hard, but no one has really done it well in my opinion. Or if they've done something, they do it in something that requires a ton of setup and downloading repos and such and they you can't even make it work in a web page.
My nephew (name Julian, coincidentally) is hardcore into Julia and sings its praises a lot.
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@rb-j said in Bottom Two Runoff (Condorcet IRV hybrid):
I can send you files, but I think you can get if from wayback:
Got it, perfect.... thanks!
For others interested, it is about 9000 lines that look like this (there's some extra fluff I removed):
C01,C03,C02
C01,C04
C01,C02,C04,C05,C03
C01,C02
C01,C02,C05,C04,C03
C01,C02
C01,C02
C01,C02,C04
C01,C02,C04,C05,C03
C01,C05,C04,C02
C01,C04,C02,C05
C01,C02,C04
C01,C02,C03,C04,C05
C01,C02,C04,C05,C03and where the candidates are defined as:
C01, "Bob Kiss"
C02, "Andy Montroll"
C03, "James Simpson"
C04, "Dan Smith"
C05, "Kurt Wright"
C06, "Write-in"I'll clean it up and have it in a codepen that others can play with. I think I can trim it down to about a tenth the size or less by combining duplicates, something like this:
bk: Bob Kiss
am: Andy Montroll
js: James Simpson
ds: Dan Smith
kw: Kurt Wright
x: (write in)345: bk>am>ds>kw
280: kw>bk>ds
120: ds>bketc
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it is about 9000 lines that look like this (there's some extra fluff I removed):
If you want results to be consistent with the City Clerk's report, you need to use the Kiss pile, the Wright pile, and the Exhausted ballot pile but remove the first four ballots from the Exhausted ballot pile. Those were never counted. You want exactly the same 8976 ballots that the City Clerk counted to at least one of those six candidates (counting Combined Write-In as one of the six).
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@andy-dienes said in Bottom Two Runoff (Condorcet IRV hybrid):
in Julia
Interesting, I hadn't made Julia's acquaintance. Once I finish my current project, I should probably be able to translate any working Julia code by hand into equivalent JS. It will help if it isn't using higher precision integers or floats than what can be represented in IEEE floating point. One of the readers of this forum said he is using the browser Waterfox Classic, which does not support JS' new long integers.
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@rb-j said in Bottom Two Runoff (Condorcet IRV hybrid):
If you want results to be consistent with the City Clerk's report,
Cool thanks I'll do that.
@jack-waugh said in Bottom Two Runoff (Condorcet IRV hybrid):
It will help if it isn't using higher precision integers or floats than what can be represented in IEEE floating point
I can't imagine floating point precision making a difference unless you are doing something really weird. I prefer avoid all floating point math in tabulation methods, or at the least define them in ways that floating point math isn't necessary. (javascript uses floating point even for operations that could be pure integer, such as counting, but I can't remember where it has ever been a problem in anything I've done except when converting a number to a human readable string)
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I have to say I am intrigued with the idea of marketing IRV Bottom-two Runoff. If it weren't for marketing concerns, I would want to perturb it further to make it balanced and pairwise additive, but that would throw away the possibility of getting IRV-Hare enthusiasts to accept it.
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@jack-waugh said in Bottom Two Runoff (Condorcet IRV hybrid):
I have to say I am intrigued with the idea of marketing IRV Bottom-two Runoff.
Awesome. Maybe all the time I've spent on this forum in the past week hasn't been entirely wasted.
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@rob, you said you think that whether equal ranking is permitted is an "implementation detail". But I wouldn't be surprised if RCV IRV Hare enthusiasts were to refuse to allow equal ranking. Anyway, they are refusing bottom-two runoff even without equal ranking, as the tweet I cite above argues against it and comes from whoever controls the Twitter account "fairvote".
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@jack-waugh I'm saying that, if equal ranking is allowed, it doesn't make it a different method. It is just one variation of the same method. Note that the Electowiki page for IRV mentions the possibility of equal ranking, and here is a (very short) discussion of equal rank IRV: https://www.reddit.com/r/EndFPTP/comments/dgzf5k/what_are_the_shortcomings_of_equalrank_irv/
I'm not speaking of the practical issue of whether Fairvote or RCV IRV Hare enthusiasts will allow it, whether voting machines can deal with it, whether it is allowed under some specific legislation, etc. That's a different issue.
I imagine the best way to handle equal rankings would be to count fractional votes. (I will need to implement it so I can process cardinal ballots as IRV-Hare and IRV-BTR)
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Untested, draft code for tallying RCV-IRV-B2R: tally.mjs
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@rob said in Bottom Two Runoff (Condorcet IRV hybrid):
I will need to implement it so I can process cardinal ballots as IRV-Hare and IRV-BTR
naive_strict_ranking.mjs is an untested draft for converting affinities (same form as so-called "cardinal" ballots) into ranking ballots. The assumption underlying my design of the code is that equal-ranking is forbidden except for the sludge at the bottom.
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For simulations and small elections in particular, it's in my opinion important to understand the corner cases that can arise in Bottom-Two Runoff, and decide how the outcome should be determined. One reason to think this way is to make sure that the tallying algorithm is deterministic. A deterministic algorithm will make all experiments repeatable, that are based on applying the algorithm to a given set of example data.
I posted an algorithm or two in here, but it or they were wrong.
