I’m working with some talented software developers to build an open source, multi-winner implementation of Ranked Pair/Tideman tailored toward budgeting to enable legislators to collectively and fairly rank their budget priorities to arrive at a democratic budget. As a former municipal legislator (Madison, WI) I discovered first-hand how dramatically typical budgeting processes can distort budgets and cause worthy initiatives to go unfunded. While building our open source software we quickly discovered the sort tie problem. I prefer Tideman/RP for public elections because it’s relatively conceptually simple compared to its criterion-meeting peers (I’m still a fan, Markus Schulze!). I can explain it to voters and politicians. However none of the Tideman tie-breaking procedures I’ve heard of meet that same criterion of explainability and grounding in democracy. I have a procedure that I believe meets those criteria, which I paraphrase as the “Lost worst: locked-in first” procedure. I like it, and I’d love to get feedback on it. I also imagine others have thought of it before so any research that’s been done would be helpful. Also the procedure wouldn’t work in every scenario so I proposed a secondary procedure that is less inspiring but still better than many alternatives (and also unlikely to work in every scenario). We’re working to have the software ready in the next couple months, so any feedback now would be greatly appreciated. And of course if anyone wants to contribute to the project we’re happy to work with other developers, designers, and mathematicians. Here’s a quick deck explaining the procedure: https://docs.google.com/presentation/d/1K6VWjMwscspFKRzc2h6YWfWEkqdnQgcLVyVXdTsEbkE/edit#slide=id.p Thanks in advance for your feedback! Cheers, Lucas -- Lucas Dailey blog: medium.com/@lucasdailey work: Product Manager | PropellerHealth.com <http://propellerhealth.com/>

I like it. It's clean and logical. Regarding the 2nd level tie-breaker: looks like you're using a median-rating type of method there? What about Majority Judgment? Frango ut patefaciam -- I break so that I may reveal On Sat, Jul 1, 2017 at 2:44 PM, Lucas Dailey <lucasdailey@gmail.com> wrote: > I’m working with some talented software developers to build an open > source, multi-winner implementation of Ranked Pair/Tideman tailored toward > budgeting to enable legislators to collectively and fairly rank their > budget priorities to arrive at a democratic budget. As a former municipal > legislator (Madison, WI) I discovered first-hand how dramatically typical > budgeting processes can distort budgets and cause worthy initiatives to go > unfunded. > > > > While building our open source software we quickly discovered the sort tie > problem. I prefer Tideman/RP for public elections because it’s relatively > conceptually simple compared to its criterion-meeting peers (I’m still a > fan, Markus Schulze!). I can explain it to voters and politicians. However > none of the Tideman tie-breaking procedures I’ve heard of meet that same > criterion of explainability and grounding in democracy. > > > > I have a procedure that I believe meets those criteria, which I paraphrase > as the “Lost worst: locked-in first” procedure. I like it, and I’d love to > get feedback on it. I also imagine others have thought of it before so any > research that’s been done would be helpful. Also the procedure wouldn’t > work in every scenario so I proposed a secondary procedure that is less > inspiring but still better than many alternatives (and also unlikely to > work in every scenario). > > > > We’re working to have the software ready in the next couple months, so any > feedback now would be greatly appreciated. And of course if anyone wants to > contribute to the project we’re happy to work with other developers, > designers, and mathematicians. > > > > Here’s a quick deck explaining the procedure: https://docs.google.com/ > presentation/d/1K6VWjMwscspFKRzc2h6YWfWEkqdnQ > gcLVyVXdTsEbkE/edit#slide=id.p > > > > Thanks in advance for your feedback! > > > > Cheers, > > Lucas > > -- > Lucas Dailey > blog: medium.com/@lucasdailey > work: Product Manager | PropellerHealth.com <http://propellerhealth.com/> > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >

On 07/01/2017 11:44 PM, Lucas Dailey wrote: > I’m working with some talented software developers to build an open > source, multi-winner implementation of Ranked Pair/Tideman tailored > toward budgeting to enable legislators to collectively and fairly rank > their budget priorities to arrive at a democratic budget. As a former > municipal legislator (Madison, WI) I discovered first-hand how > dramatically typical budgeting processes can distort budgets and cause > worthy initiatives to go unfunded. > > > > While building our open source software we quickly discovered the sort > tie problem. I prefer Tideman/RP for public elections because it’s > relatively conceptually simple compared to its criterion-meeting peers > (I’m still a fan, Markus Schulze!). I can explain it to voters and > politicians. However none of the Tideman tie-breaking procedures I’ve > heard of meet that same criterion of explainability and grounding in > democracy. > > > > I have a procedure that I believe meets those criteria, which I > paraphrase as the “Lost worst: locked-in first” procedure. I like it, > and I’d love to get feedback on it. I also imagine others have thought > of it before so any research that’s been done would be helpful. Also the > procedure wouldn’t work in every scenario so I proposed a secondary > procedure that is less inspiring but still better than many alternatives > (and also unlikely to work in every scenario). > > > > We’re working to have the software ready in the next couple months, so > any feedback now would be greatly appreciated. And of course if anyone > wants to contribute to the project we’re happy to work with other > developers, designers, and mathematicians. > > > > Here’s a quick deck explaining the procedure: > https://docs.google.com/presentation/d/1K6VWjMwscspFKRzc2h6YWfWEkqdnQgcLVyVXdTsEbkE/edit#slide=id.p From looking at it briefly, I suspect that the secondary tiebreak will fail clone independence. Consider a situation where A and B have the same average position (I assume by position, you mean rank, i.e. first place, second place, etc) so that you choose which is considered better by random choice. Suppose that the votes are set up so that the candidate you randomly choose will be the winner. Then suppose A is cloned into A1 and A2 so that everybody ranks A1 above A2. That may make A1's average position better than A's, and thus better than B's, making A1's win a certainty. Thus cloning A benefitted him. This is a very sketchy and quick argument; I haven't provided any actual scenario that exhibits the proprties I mentioned here. But it seems reasonable that cloning could affect the order of average positions for the different candidates.

On 07/01/2017 11:44 PM, Lucas Dailey wrote: >> I’m working with some talented software >> developers to build an open >> source, multi-winner implementation of >> Ranked Pair/Tideman tailored >> toward budgeting to enable legislators to >> collectively and fairly rank >> their budget priorities to arrive at a >> democratic budget. -snip- >> While building our open source software we >> quickly discovered the sort >> tie problem. I prefer Tideman/RP for >> public elections because it’s >> relatively conceptually simple compared to >> its criterion-meeting peers >> (I’m still a fan, Markus Schulze!). I can >> explain it to voters and >> politicians. However none of the Tideman >> tie-breaking procedures I’ve >> heard of meet that same criterion of >> explainability and grounding in >> democracy. >> >> I have a procedure that I believe meets >> those criteria, which I >> paraphrase as the “Lost worst: locked-in >> first” procedure. I like it, >> and I’d love to get feedback on it. I also >> imagine others have thought >> of it before so any research that’s been >> done would be helpful. Also the >> procedure wouldn’t work in every scenario >> so I proposed a secondary >> procedure that is less inspiring but still >> better than many alternatives >> (and also unlikely to work in every scenario). -snip- On 7/4/2017 7:40 PM, Kristofer Munsterhjelm replied: > From looking at it briefly, I suspect that > the secondary tiebreak will fail clone > independence. -snip- I would bet Kristofer is correct. It looks like the same problem with clones that Borda has, although Borda's problem is much more terrible because with Borda the problem isn't confined to tied scenarios. Consider an example: A large majority, say 66%, prefer X over Y. Given Borda, a person who prefers Y has an incentive to nominate extra alternatives that are similar to Y but slightly inferior. Then the votes would be something like: 66: X > Y > [some inferior clones of Y] 34: Y > [some inferior clones of Y] > X Let N denote the number of inferior clones. Y's Borda score is (66 x N) + (34 x N+1) = 100N + 34. X's Borda score is (66 x N+1) + (34 x 0) = 66N + 66. Y wins when 34N > 32. In other words, Y wins when N > 0. With Borda, a large majority can be overturned by simply nominating a similar alternative. Each faction has an incentive to nominate as many inferior clones of their preferred alternative as possible, like an arms race, which is farcical. Given Borda, the voters' preferences won't matter much; what matters is the number of inferior clones nominated, which is an even greater farce. (Call it a Type 2 farce.) Unfortunately, the incentive will exist even if clones only make a difference when tiebreaking same-size majorities, because the chance that such a tie will occur is greater than zero, and savvy nominators would know that nominating clones would help later in case of a tie and would never hurt. So, every faction would always have an incentive to nominate as many clones as possible. Thus Lucas' second tiebreak could make such farces commonplace. (But not the Type 2 kind.) Lucas is proposing his first tiebreak to reduce the need for another tiebreaking that he considers less democratic, which involves constructing a tiebreak ordering of the candidates by randomly picking one voter's order of preference (or more than one if the first one picked expresses indifference on the pairings relevant to the tiebreaking). In my webpages at http://alumnus.caltech.edu/~seppley/ I call the construction Random Voter Hierarchy, or RVH. Because there can be cases where Lucas' first and second tiebreaks both fail to resolve the ties, he presumably intends to use something like RVH anyway as a third tiebreak. (Note: RVH is a generalization of Tideman's Random Dictator tiebreak, generalized to handle the cases where votes may include indifference between some candidates. Random Dictator is insufficient because it's important to allow voters to express indifference, in order to satisfy Mike Ossipoff's "strong defensive strategy criterion," from which I derived the "minimal defense" criterion described in my webpages.) Clearly Lucas' system with RVH as its third tiebreak (or second, if he decides to eliminate his second tiebreak due to its clones nomination incentive) is more complex than simply using RVH, and I think that makes it harder to explain. Random Dictator sounds much less democratic than Random Chairperson, but they refer to the same idea. (That is, when a committee vote is tied, the tie is broken by the vote of the chairperson.) It might help if election reformers would use the latter name. Perhaps it would help change Lucas' opinion about the democratic-ness of tiebreak schemes he's been trying to avoid. The legislators who Lucas hopes to persuade already use voting methods that break ties using the preference of a single person, typically a chairperson, and I presume they don't believe it's undemocratic. I don't see why anyone should consider RVH less democratic than using the preferences of a chairperson. However, in the event that Lucas' legislators do consider randomness less democratic, my hunch is that they'd prefer to construct the tiebreak ordering using the preferences of a (non-random) seniority hierarchy (starting with the order of preference of the chairperson or "speaker of the house" or most senior member), and their familiarity with the concept may make it easier to explain to them than the tiebreak Lucas described. Assuming the voting method permits voters to express indifference, the minorities that oppose same-size majorities might not be the same size. So it's reasonable that the first tiebreak should instead compare the sizes of the opposing minorities, if it's desired to reduce the scenarios where randomness is a factor. (This is done by the Maximize Affirmed Majorities voting method, abbreviated MAM, which some people--but not me--call Ranked Pairs.) Example: 60 voters rank X over Y, 39 rank Y over X, and 1 ranks X=Y. 60 voters rank Z over W, and 40 rank W over Z. Because the 39 who oppose the X>Y majority are fewer than the 40 who oppose the Z>W majority, MAM gives the X>Y majority precedence over the Z>W majority. (Note: Another way to describe the sorting of all the majorities is to say that the primary sort key is size of majority, descending, and the secondary sort key is size of opposing minority, ascending. Given this notation, Lucas' first tiebreak would be the tertiary sort key, assuming he were to use opposing minorities as the secondary sort key.) I expect that much more common than scenarios with three same-size majorities (as in the example linked by Lucas) will be scenarios that have two same-size majorities. Here's a simple Rock-Paper-Scissors example: 55: R>S 51: S>P 51: P>R In this scenario, Lucas' first tiebreak would simply be the head-to-head pairing of the two pairlosers, P versus R, and the tiebreak ordering of candidates would be P>R. Since R is behind P in the tiebreak ordering, the primary tiebreak gives the P>R majority (which is "lost" by R) precedence over the S>P majority (which is "lost" by P). Thus, after R has been placed ahead of S in the order of finish due to the 55% majority, the P>R majority is considered and P is placed ahead of R in the order of finish. So P wins. It's been a long time since I looked at this scenario, but my recollection is that this tiebreak scheme has a significant negative consequence. Unfortunately I don't recall the details, and it's possible I'm mixing in a memory of a different tiebreak. (Somewhere among my old emails is a discussion I had with Mike Ossipoff about this tiebreak or something similar, in which we agreed there was a negative consequence. Maybe I'll find time to hunt for it, if it's important.) Lucas' example seems unclear about what his first tiebreak will do in the case where some of the same-size majorities have the same candidate as pairloser, like B in the following: ... 60: A>B 60: C>D 60: E>B ... I'll guess that Lucas would resolve the precedence of the A>B and E>B majorities by comparing their pairwinners, A&E. In other words, if E is ahead of A in the tiebreak ordering, then give the E>B majority precedence over the A>B majority. (That's what MAM does in such cases. When two same-size majorities' pairlosers are different candidates, MAM compares the two pairlosers' positions in the RVH tiebreak ordering. But when the two pairlosers are the same candidate, MAM compares the two pairwinners' positions in the RVH tiebreak ordering.) I should note, for the sake of anyone planning to implement Ranked Pairs, that there's an unnecessary flaw in the way Tideman & Zavist use Random Chairperson to break ties. The flaw is irrelevant if voters are forced to vote strict orders of preference (no indifferences) and/or if the voting method method pays attention to "pairwise margins of difference" instead of "sizes of majorities." But the flaw is a concern, since satisfaction of Mike Ossipoff's SDSC (a.k.a. minimal defense) requires allowing voters to express indifference and requires paying attention to sizes of majorities instead of margins of difference. (MAM does both and satisfies minimal defense, but Tideman-Zavist Ranked Pairs does neither and fails minimal defense.) Specifically, the Strong Pareto criterion is failed by the variation of Ranked Pairs that allows voters to express indifference and pays attention to majorities' sizes, if it uses Zavist's tiebreak scheme. (Strong Pareto: "If no voters rank x over y and at least one voter ranks y over x, then x must not finish ahead of y.") When I proved MAM completely satisfies Strong Pareto, I noticed the proof would not have worked if Zavist's scheme were used (unless I made a mistake). MAM tiebreaks same-size majorities by comparing the same-size majorities' pairlosers' positions in the tiebreak ordering (and when the pairlosers are the same candidate, it compares pairwinners' positions), whereas Zavist uses a mixture of pairwinners & pairlosers. Lucas apparently has an intuition for this already, since his first and second tiebreakers compare pairlosers' positions in tiebreaking orderings. (Equally good, I believe, would be to compare pairwinners' positions in the tiebreak ordering, instead of pairlosers' positions. For example, in the "two same-size majorities" example above, the pairwinners of the same-size majorities are S & P. If S is ahead of P in the tiebreak ordering, a pairwinners scheme would give precedence to the majority in which S is pairwinner (the S>P majority) over the majority in which P is the pairwinner (the P>R majority). As I wrote above, MAM's tiebreak compares pairlosers, so MAM compares the positions of the pairlosers P & R in the RVH ordering, and if P is behind R then MAM gives precedence to the majority in which P is pairloser. When I defined MAM about 15 years ago, based on conversations in the EM maillist I believed pairwise defeats were more significant than pairwise wins. I later decided they're equally significant and the choice to compare pairlosers is arbitrary. By then I'd already defined MAM and already constructed a large number of proofs and documents, and I know no compelling reason to change MAM's tiebreaker to use pairwinners. I think the choice between pairwinners or pairlosers is just a matter of taste.) I agree with Lucas that Ranked Pairs and MAM are simpler to explain than Schulze' method. MAM also satisfies some criteria that Schulze's method fails: Local IIA, Multiwinner Resolvability, Immunity from Majority Complaints, and Immunity from 2nd Place Complaints. Also, since Markus doesn't specify a tiebreaker in his Wikipedia page (the last time I looked, which was several years ago), it means Schulze's method doesn't clearly satisfy several other criteria, such as Independence of Clones. An free online engine to tally elections using MAM is available for groups to use (or for anyone to experiment with): http://MAM.hostei.com/ To use it, a group's secretary types or pastes their votes into the box, and then clicks the button underneath. Perhaps I can find some time to help Lucas' team develop their software, or help minimize the jargon when they pitch it to legislators and other groups, if he'd like me to consult. Cheers, Steve