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    Posts made by Casimir

    • RE: ABC voting and BTR-Score are the single best methods by VSE I've ever seen.

      @isocratia
      Good question. According to Electowiki:

      Methods that pass dominant mutual third burial resistance [DMTBR] provide no incentive to bury under a dark horse.

      Following the argument here it is clear that BTR-score fails DMTBR

      In election (A) and (B) A wins. In (D) the winner is C, but in (E) the winner is A again. (I assumed score from 0 to 2.)

      where A is the CW, and so (E)->(D) is a DMTBR failure.

      But this does not exclude the possibilty that the score part reduces the strategic incentive to bury.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: ABC voting and BTR-Score are the single best methods by VSE I've ever seen.

      @ex-dente-leonem
      I wanted to create some figures for an article on MARS voting that I plan to write, but fail to run vse-sim. Is it okay for you when use your results?

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: Nonmonotonic methods are unconstitutional in Germany?

      @cfrank
      I was using "expected" as from the view of the law makers. If it was a known issues while the law was made, then it has been accepted as part of the law. If it turns out that a law exhibits the problem contrary to expectation, then it's a problem.

      The report says in the summary (starting at page 135):

      Die integrierte Stichwahl ist anfällig für einen paradoxen Sondereffekt, der Monotonieversagen genannt wird. Nicht ausgeschlossen ist nämlich, dass ein Wähler zwar für seinen bevorzugten Kandidaten stimmt, ihm aber noch mehr genützt hätte, wenn er ein ganz bestimmtes alternatives Stimmverhalten gezeigt hätte. Dieser Effekt muss sich anhand von Maßstäben beurteilen lassen, die das BVerfG für die Verfassungsmäßigkeit eines ähnlichen Paradoxes, nämlich des sog. negativen Stimmgewichts, aufgestellt hat. Dieses Paradox besteht darin, dass ein Zuwachs an Zweitstimmen für eine Partei dazu führen kann, dass dieselbe Partei gerade dadurch Mandate verliert. Das BVerfG hält dies für verfassungswidrig, es sei denn, der Effekt ist dem Wahlsystemtyp eigen und lässt sich deshalb nur durch dessen vollständigen Wechsel vermeiden. So verhält es sich hier: Der Gesetzgeber müsste auf die integrierte Stichwahl ganz verzichten, wenn er die Anfälligkeit für Monotonieversagen vermeiden wollte. Daher ist die integrierte Stichwahl mit den Maßstäben des BVerfG vereinbar.

      Die integrierte Stichwahl ist auch mit dem Grundsatz der Unmittelbarkeit der Wahl vereinbar. Das BVerfG entnimmt ihm, für Wähler müsse vorhersehbar sein, wie sich die eigene Stimmabgabe auf den (Miss-)Erfolg der Kandidaten auswirken könne. Das ist bei integrierten Stichwahlen nicht in jeder Hinsicht der Fall, weil infolge der Anfälligkeit für Monotonieversagen für die Wähler nicht immer vorhersehbar ist, ob mit Blick auf das Endergebnis der Wahl paradoxerweise nicht ein ganz bestimmtes alternatives Stimmverhalten für den gewünschten Kandidaten günstiger wäre. Ein Verstoß gegen den Grundsatz der Unmittelbarkeit folgt daraus jedoch nicht, denn auch hier wirkt sich verfassungsrechtlich aus, dass die Anfälligkeit für Monotonieversagen innerhalb des Wahlsystemtyps nicht zu vermeiden ist.

      In English (I highlighted the important part):

      The instant runoff election is susceptible to a paradoxical special effect known as monotonicity failure. It is possible that a voter, even though they vote for their preferred candidate, could have actually benefited their candidate more by choosing a completely different voting behavior. This effect must be assessed using the criteria established by the Federal Constitutional Court (BVerfG) for the constitutionality of a similar paradox, namely the so-called negative voting weight ["negatives Stimmgewicht"]. This paradox occurs when an increase in second votes for a party can lead to that party losing seats as a result. The BVerfG considers this to be unconstitutional unless the effect is inherent to the type of electoral system and can therefore only be avoided by completely changing the system. This is the case here: the legislature would have to abandon the integrated runoff election entirely if it wanted to avoid susceptibility to monotonicity failure. Therefore, the integrated runoff election is compatible with the standards of the BVerfG.

      The instant runoff election is also compatible with the principle of directness in elections. The Federal Constitutional Court (BVerfG) interprets this principle to mean that voters must be able to foresee how their vote will affect the (success or failure) of the candidates. This is not always the case with integrated runoff elections because, due to the susceptibility to monotonicity failure, it is not always predictable for voters whether, paradoxically, a completely different voting behavior might be more favorable for the desired candidate with regard to the final election result. However, this does not constitute a violation of the principle of directness, as the susceptibility to monotonicity failure cannot be avoided within this type of electoral system.

      I'm neither defending this view, nor IRV. But apparently, according to this report, IRV is constitutional. The GG intentionally puts almost no constraints on the voting system and therefore does not go into the weeds of voting theory.

      posted in Voting Methods
      C
      Casimir
    • RE: Nonmonotonic methods are unconstitutional in Germany?

      @isocratia
      Not exactly.
      Article 38 of the GG (the constitution) says: "Members of the German Bundestag shall be elected in general, direct, free, equal and secret elections."
      The important part is the "direct". Which is interpreted in the way that votes have to translate to outcomes in a transparent and unaltered way. e.g. no electoral college.
      There was a ruling in a special case where non-monotonicity was the issue, but in this case the non-monotonicity came about through an unusual situation and was not expected. That means, the way the electoral law was intended and how it functioned where in conflict.
      There was a recent report where they looked at the question if IRV would be constitutional and concluded that it would, making the argument that when non-monotonicity is expected and accepted, then it's okay (or something like that).

      posted in Voting Methods
      C
      Casimir
    • RE: BTR-score

      @jack-waugh
      For the purpose of the article it was more than needed. The requirement of allowing equal ratings/ranks already covers many cases. I'm unsure if it is really "too restrictive", but I also can't tell at the moment if it is necessary as a minimum requirement.

      @GregW
      That's good. You may even remove the "Hiveism substack" in the text and just keep the foot note if this makes it more readable.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: ABC voting and BTR-Score are the single best methods by VSE I've ever seen.

      @ex-dente-leonem said in ABC voting and BTR-Score are the single best methods by VSE I've ever seen.:

      🙂 Have I got great news for you...

      Thank you very much. That's even better than I expected.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      @cfrank
      That's the issue that prompted me to think about related methods like BTR-score. Later however, I came across a good argument that convinced me this isn't so much of a problem. STAR becomes like score with strategic nomination, but that is the expected behavior. The main election is the score part, the runoff is there as a safe-guard and to make it compliant with laws that require a majority. Basically, the difference between score and STAR isn't that big, but practically it's easier to get STAR implemented. In the VSE simulation by John Huang, they even perform the same under "honest" and "two-sided strategic" assumptions.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: ABC voting and BTR-Score are the single best methods by VSE I've ever seen.

      I have to admit that I'm confused by the results. I did expect BTR-score to perform well, but I also thought that the difference to Smith//score would be to small to measure. I wonder why there is such a big difference.

      Also, when looking at viability-aware, STAR performs a lot better, which is also surprising. Is it that it better utilizes the score part and therefor gets the "best of both worlds"? I don't know.

      How long does it take for you to run those simulations?

      If it's not too much work, could you try out MARS? It's basically like BTR-score, but each round does not only compare votes, but votes+scores (both measured in % of maximum possible). Previously I thought that that would be even better than BTR-score (on the cost of being complicated), but now I'm no longer sure.

      One thing to be cautious of is that these results present very small differences in a high range. It might be that the choice of model has too much of an influence to make decisive claims.

      ABC is a good idea and I think could be really a viable method when fleshed out. Most importantly I think there may be more intuitive ways to preset it. Maybe something in between scores and approval, like "ABC-123" where letter ratings count as 0 and numbers as scores.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      @jack-waugh
      Balance is one feature that the four methods share, but as a general minimal requirement for me to support a voting system it's to restrictive. It might exclude methods that are reasonable. On the other hand, it does even include some that are not so good in my opinion. A for-or-against variant of plurality, where you can either vote for only one, or against only one candidate, would still pass balance, but would be hardly better than plain plurality.
      There has been a quite elaborate discussion about this on /r/endfptp which convinced me to remove that paragraph.

      @cfrank
      Thanks for the feedback. I will add that to the article.
      What is your reason against STAR?

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      @jack-waugh
      It might still be too complex for voters without prior education. As someone immersed in these discussions, it is easy to loose sight of how little people know about voting and how many conceptual steps people have to take before understanding the method. I've argued here that it might be more useful to promote a spectrum of compatible methods (approval, score, STAR and BTR-score in this case).

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      Here are all the permutation of a 4-cycle:

       C[A]BD    B[A]CD
       C[A]DB    B[A]DC
       [A]CBD    [A]BCD
       [A]CDB    [A]BDC
       [A]DCB    [A]DBC
      
       C[B]AD    [D]CAB
       C[B]DA    [D]CBA
       [B]CAD    [D]ACB
       [B]CDA    [D]ABC
       [B]DAC    [D]BCA
       [B]DCA    [D]BAC
      
       [C]DBA    [C]DAB
      

      Out of these there are six cases where the second highest candidate wins.

       C[A]BD    B[A]CD    C[B]AD 
       C[A]DB    B[A]DC    C[B]DA
      

      For this to be a problem there should exist an alternative where the first and second placed candidates swap, but the new second place wins. But looking at the options above, there is non where C wins in second place. Also, for the B first cases, swapping B and A still leaves A winning. So, at least in a 4-cycle, this is not an issue.

      As for FB, it fails the same way as this example with for example candidates ordered form high to low score as D A B C.

      All that said, I'm mostly concerned with practicality. For me the purpose of BTR-score is to be an as-simple-as-possible Condorcet method. Any way to make it compliant with more criteria would also make it more complex. It's good to know what properties it has, but I have no strict requirements. If it is non-monotonic in some rare cases, so be it - as long as it has no overt issues like Copeland does.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      I'm not sure I understand the question. In which case would it be beneficial to have your favorite placed second by score?

      posted in New Voting Methods and Variations
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      Casimir
    • RE: BTR-score

      @chocopi said in BTR-score:

      In this new ordering, Paper Jr. takes out Rock early, preventing Rock from taking out Scissors. Now Scissors wins.

      This is, of course, an extremely specific scenario--and a good illustration of why focusing on absolute criteria is misleading. No one should care that something like BTR or Stable Voting are non-monotonic one-in-a-gazillion elections.

      Thank you. I missed that case. In the list I provided this corresponds to [B]CAD turning to B[A]CD.

      @gregw said in BTR-score:

      Smith-Score would be ok but re-normalization would need to be explained.

      There might be a misunderstanding. The normalization of ballots is an assumptions of voter behavior, not part of the method. Smith//plurality misses that paragraph because it uses a ranked ballot instead of rated like Smith//score.

      @cfrank said in BTR-score:

      @casimir you indicated that the second-highest score winner in the cycle will be elected in a 4-cycle. This means that lowering the score of a candidate can cause them to win in such a case, which practically speaking is a very rare case.

      Take a look at the list I provided. It has some cases where the second highest candidate wins, but no case where lowering the score of a candidate causes them to win instead of someone else. Likewise, raising someones score won't cause them to loose. The case that @chocopi pointed out is one where changing the order of the other candidates causes someone to loose. It's weird, but it's no reason to not give your favorite candidate full support (except for the favorite betrayal case, which comes with being a Condorcet method).

      Because I'm from Germany, monotonicity is somewhat relevant, but it's not that all non-monotonic methods are banned.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: score interval: score with additional protection against the chicken dilemma

      As far as I can tell it's not additive, because it depends on how candidates compare on each ballot. Balance may be possible, but I have to check in detail. Casting a complementary ballot in the first round (which is possible) may inhibit the ability to cast a complementary ballot in the second round.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      I don't see how changing the score causes a monotonicity failure.

      For a cycle A > B > C > D > A, A > C, B > D (it helps to draw a picture) there are 24 ways candidates can be ordered by score (from high to low, winner in [brackets]) :

      C[A]BD    B[A]CD
      C[A]DB    B[A]DC
      [A]CBD    [A]BCD
      [A]CDB    [A]BDC
      [A]DCB    [A]DBC
      
      C[B]AD    [D]CAB
      C[B]DA    [D]CBA
      [B]CAD    [D]ACB
      [B]CDA    [D]ABC
      [B]DAC    [D]BCA
      [B]DCA    [D]BAC
      
      [C]DBA    [C]DAB
      

      The first three blocks have the cases where the second highest scored candidate wins, with alternations. This shows that raising a winning candidate in score will still result in that candidate winning. Also, changing the ordering of non-winning candidates doesn't affect the outcome. As far as I have checked, changing pairwise preference between non-winners also does not change the winner. Please tell me when I am missing something.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: score interval: score with additional protection against the chicken dilemma

      @jack-waugh What do you mean by "additiv" and "balanced"?

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: score interval: score with additional protection against the chicken dilemma

      Most likely, yes. The ideas here are a theoretical exploration.

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: BTR-score

      BTR stands for Bottom-Two-Runoff, like in BTR-IRV. I did an edit on the first post, fixed the typo.

      With no need for a matrix, I mean we only have to compare a few pairs, not all possible pairings (N instead of N²). In practice may still be useful to use a runoff matrix "behind the scenes".

      posted in New Voting Methods and Variations
      C
      Casimir
    • RE: MDD//Score

      Since it seems to be based on MDDA, it considers defeats by a majority of all voters.

      posted in Single-winner
      C
      Casimir
    • BTR-score

      The motivation for BTR-score (Bottom-Two-Runoff with score) is that it is a Condorcet method that is easy to explain and count, while avoiding obvious problems like e.g. Copeland has.

      1. Score candidates on a scale from 0 to 5.
      2. Order the candidates from highest to lowest score.
      3. Compare the lowest two candidates by pairwise preference. Eliminate the looser. Repeat.
      4. Elect the last remaining candidate.

      This always elects a candidate from the Smith-set. For cycles with 3 candidates, it always elects the score winner from within the cycle. In a 4-way cycle it becomes more complicated, but elects the score winner from within the cycle in 18 of 24 possible permutations. In the remaining 6 it elects the candidate with the second highest score from within the cycle. This means, in most (practically almost all?) cases it gives the same results as Smith//score.

      Note that in describing the method there is no need to explain what a Condorcet winner or Smith-set is and no need for a pairwise matrix. It also reduces the inferential steps needed when you already explained STAR voting. This means, in terms of voting advocacy, you can explain score, then STAR as "score with runoff" and BRT-score as "STAR but for all candidates".

      posted in New Voting Methods and Variations
      C
      Casimir