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B Instant Runoff Voting and How Safe Movies Win

  1. Jan 18, 2018 #1

    jedishrfu

    Staff: Mentor

    There are many ways to tally voting, one such scheme is Instant Runoff Voting where you are allowed to choose your top 3 favorites. However, this scheme can lead to mediocre choices when applied to Academy Award movie wins:

     
  2. jcsd
  3. Jan 18, 2018 #2

    Buzz Bloom

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    Hi jedishrfu:

    I think the word "mediocre" is a very misleading and biased word choice.

    In the ordinary use of Instant Runoff Voting (IRV) the goal is to avoid the election of a candidate that does not represent a majority of the votes cast. I gather from the explanation given in the included video that IRV is not actually used, but that some modified form is used in which the voter casts only three ordered choices. It is not clear what the goal of this method of voting is intended to achieve, but if the number of candidates is much greater than three, a winner is again not likely to be the desired choice of a majority. I am guessing that the process achieves a winner with a larger base of support than the method used previously, rather than a more intense level of individual support by fewer supporters. If this is correct, then it makes sense that the film industry would prefer it's Oscar choices to better match what most movie goers would want to see.

    Regards,
    Buzz
     
  4. Jan 18, 2018 #3

    jedishrfu

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    I quoting the view in the video where "safe" movies win over edgier movies.
     
  5. Jan 18, 2018 #4

    Buzz Bloom

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    Hi jedishrfu:

    I must have missed the oral statement in the video that used "mediocre". If the word was used in the video, I still find it to be a misleading and biased word choice.

    From
    http://www.dictionary.com/browse/mediocre
    adjective
    1. of only ordinary or moderate quality; neither good nor bad; barely adequate:
    The car gets only mediocre mileage, but it's fun to drive.
    2. not satisfactory; poor; inferior:
    Mediocre construction makes that building dangerous.​

    The bias of "mediocre" is that the user of the word prefers edgier movies to safe movies, and "mediocre" is pejorative.

    Regards,
    Buzz
     
  6. Jan 18, 2018 #5

    jedishrfu

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    Okay I changed the thread title to "Safe" to be safe.
     
  7. Jan 18, 2018 #6

    mfb

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    The perfect voting system cannot exist - Arrow's impossibility theorem - at least not if you just ask for an order of preference. There are many systems and good arguments for most of them.
     
  8. Jan 19, 2018 #7

    Buzz Bloom

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    Hi mfb:

    Thank you for the link about Arrow's impossibility theorem. I will have to spend some time to fully understand its implications. In particular the reference to the Cardinal Voting exception will also need some study.

    What is fascinating is that theorem also seems to (if I understand it) apply to an ordinary runoff system in which following an election in which there is no majority, the two candidates who had the highest number of votes have another opportunity to get a majority of votes from a second vote. I have not yet fully understood why this fails to work when the first election has only three candidates, except for the case where many voters whose first choice is eliminated have no interest in voting in the runoff. That means that there is no single candidate of the three who is acceptable to a majority of the voters. Perhaps a system might work in which it is determined by the first election with may candidates that none of the candidates in this election are acceptable to a majority of the voters, and that this result would require that a second election be run with entirely new candidates in which none of the candidates in the first election are included. I have not yet studied the theorem sufficiently to determine if this also violates the Arrow's theorem, except for he possibility when there is no possible candidate that is acceptable to a majority of voters.

    ADDED
    I am still not sure I understand the theorem, but the following quote from the Wikipedia article seems clear enough.
    We are searching for a ranked voting electoral system, called a social welfare function (preference aggregation rule), which transforms the set of preferences (profile of preferences) into a single global societal preference order.​
    This seems to assume that the purpose of an election is to determine "a single global societal preference order". But that is an unreasonable assumption about the goal of an election. Why is it not sufficient for an election to choose a candidate that is acceptable to a majority, and that among those candidates who are acceptable to a majority, it elects the one with the most votes when the fewest candidates with the least votes are eliminated?

    Regards,
    Buzz
     
    Last edited: Jan 19, 2018
  9. Jan 19, 2018 #8

    mfb

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    Let 40% favor A>B>C, let 35% favor C>B>A, 25% B>A>C.
    The first round gives 40% A, 35% C, 25% B and B is eliminated. The second round gives 65% A, 35% C and A wins.

    If C wouldn't have participated, B would have gotten 60% in the first round and would have won.
    A third candidate turned the outcome between A and B.

    While my numbers are not very realistic, the situation itself is very realistic. The recent French election was an example. There were two different right-wing candidates, one moderate candidate and one left-wing candidate, all with roughly similar poll results. The moderate candidate was the only one many would have preferred over other candidates, but he could have gotten kicked out in the first round. He stayed in, and won the second round with a clear victory over one of the right-wing candidates.

    Edit: Simplified the example a bit.
     
    Last edited: Jan 19, 2018
  10. Jan 19, 2018 #9

    Buzz Bloom

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    Hi mfb:

    Thanks for the excellent example. It shows that the way IRV is normally used is flawed. One has to assume that a voter may give no preference at all to a candidate that is unacceptable. Therefore, the votes should show acceptability is: 100% B, 65% A. 35% C. Instead of eliminating B, C should be eliminated, and B would be the winner with 60% of the runoff vote.. Note also, if the original votes are:
    40% A=1, B=2, C=blank
    35% C=1, B= blank, A=blank
    25% B=1, A = 2, C = blank​
    65% find A acceptable, 65% find B acceptable, and 60% find C acceptable, so C is eliminated again, but A wins the runoff . This seems to me to be the "right" result for this election. This might be made clearer it we give party associations for A, B, and C as follows:
    A = extreme liberal, B = moderate liberal, and C = conservative.​
    Thus there are 35% who are conservatives and who find either form of liberal unacceptable, but among the liberal voters who find both liberals acceptable, the majority prefer the extreme liberal.

    Regards,
    Buzz.
     
  11. Jan 19, 2018 #10

    mfb

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    You can find counterexamples for that as well. You don't even have to find numbers (although they are useful to see what is going on). The theorem guarantees that there is always a counterexample.

    If we always eliminate the candidate who is ranked third by most:
    Let 40% favor A>B>C, let 35% favor C>B>A, 25% C>A>B.
    While C gets 60% of the votes we eliminate C, afterwards A wins. Without B C would just win.

    If we only do that if no one gets an absolute majority:
    Let 40% favor A>B>C, let 20% favor C>B>A, 25% C>A>B, 15% B>C>A
    Again C is eliminated (45% of the first choice votes, but 40% hate C, compared to 35% who hate A), afterwards A wins. Without B, C would have won 60% of the votes and would have won.
     
  12. Jan 19, 2018 #11

    Buzz Bloom

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    Hi mfb:

    Another collection of good examples. You seem to have a knack for them.

    You have convinced my that my suggestion does not work either.

    Regards,
    Buzz
     
  13. Jan 19, 2018 #12

    jedishrfu

    Staff: Mentor

    To expand on the fairness in voting, here's an article on redistricting:

    https://priceonomics.com/algorithm-the-unfairness-of-gerrymandering/

    and how it can skew elections in favor of one party over another.

    I remember there was some work done on making this into a mathematical framework suitable for courts to decide if a redistricting plan would take away voting rights from some groups.

    https://www.quantamagazine.org/the-mathematics-behind-gerrymandering-20170404/

    I know in Austin Texas, they redistricted several congressional districts to favor Republican candidates and to unseat Congressman Lloyd Doggett.

    https://www.texastribune.org/2012/02/28/court-delivers-election-maps-texas-house-congress/

    https://www.texastribune.org/2017/08/15/federal-court-invalidates-part-texas-congressional-map/
     
  14. Jan 20, 2018 #13

    Buzz Bloom

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    I am hoping someone can offer me some advice.

    I would like to program a Monti-Carlo simulation to evaluate different rules for choosing an IRV candidate to eliminate on each round. To do this I need to define a rule that identifies a simulation run as OK or a failure. I find the rules of the Arrow assumptions too strict, so I will need to weaken them somewhat.

    There is also an issue of whether some of the permutations of the ordering of preferences by voters can be eliminated as generally unrealistic. I am thinking that it is reasonable to assume that the candidates may be structured into distinct political groups, and there may be multiple candidates within each group ordered between extreme and moderate. This will place some restrictions on plausible voting ordering.

    The final step of assigning a random distribution of number of voters to the remaining permutations will be straight forward.

    Regards,
    Buzz
     
  15. Jan 20, 2018 #14

    Buzz Bloom

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    Hi @mfb:
    I have taken a closer look at your first example in post # 8, and the "odd result" now doesn't look to me so odd.

    What happens in an ordinary election with 3 candidates and no runoffs? Frequently two candidates have somewhat similar politics, say A and B, but both want to run, and by so doing they split the majority who would have voted for either A or B if the other was absent. In this case the minority candidate C wins. In such an election, the majority of voters, which are those who don't like C, have a dilemma. They have to guess whether voting for the A or B candidate, which they much prefer to C, will allow C to win. The runoff result where A wins will always be a better result to the majority than that.

    In your example, if C is absent B wins, which shows that C's running has influenced the election such that a majority of the voters preferring C are prevented from getting their second choice B. That doesn't seem to me like a very terrible result, as compared with the no runoff election. Also note that if in the example the 35% relationship were modified to C>A>B, then A would win whether C ran or not.

    Regards,
    Buzz
     
  16. Jan 20, 2018 #15

    mfb

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    Consider the French election as real life example how it could have gone wrong (lead to a candidate the majority hates).

    An alternative is a single voting round and then a coalition between parties, as it is done in various countries.
     
  17. Jan 20, 2018 #16

    Buzz Bloom

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    Hi mfb:

    Could you make up some plausible 4 candidate ordered preferences that would demonstrate what might have happened if the French elections used IRV?

    Regards,
    Buzz
     
  18. Jan 20, 2018 #17

    mfb

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    The French election does use it. Here is its Wikipedia page.

    The relevant candidates:
    A) Emmanuel Macron, moderate
    B) Marine Le Pen, right-wing
    C) François Fillon, conservative/right-wing
    D) Jean-Luc Mélenchon, left

    All of them had about 20% in polls (the rest was distributed over many minor candidates). The voters for B didn't like C and hated D, the voters for C didn't like B and hated D, and the voters for D hated B and C. Macron (A) was the only one seen as acceptable by the majority.

    What actually happened: In the first round A got 24%, B 21%, C 20%, D 20%. A and B went into the second round, A won clearly with 66% and large support from the population.

    What could have happened with slightly changed numbers: Distribute 3% of the votes from A over the other candidates, now A has 21%, B 22%, C 22%, D 20%. Now the second round is between two right-wing candidates. 44% of the voters can keep voting for their favorite candidate, the rest hates both option. The president will be elected with something like 1/3 support from the population and 2/3 will hate the president.

    An alternative: Distribute 4% of the votes from A over the other candidates, now A has 20%, B 21%, C 22%, D 22%. Instead of A and B, we now have C and D in the second round. Again 44% of the voters can keep voting for their candidate, some voters for B will vote for C, and the rest has no candidate they feel confident to vote for. Again the president will be elected with something like 1/3 support from the population and 2/3 will hate the president.
     
  19. Jan 20, 2018 #18

    jedishrfu

    Staff: Mentor

    A lot of this analysis reminds me of a game theory problem where a husband and wife go camping at some national park. The husband likes to camp on the mountains and the wife likes to camp in the valleys.

    The game is played with husband choosing the latitude and the wife choosing the longitude. As you can imagine neither gets their favorite choice and it’s hard to figure who will really win the game. Basically, a two-person election with multiple candidates along the lines selected.
     
    Last edited: Jan 21, 2018
  20. Jan 21, 2018 #19

    Buzz Bloom

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    Hi @mfb:

    The French election did not use IRV. The ordinary runoff the of election the French used is generally an improvement of no runoff, since a no runoff election, which is used in the US, frequently results in a minority winner, while the ordinary runoff more rarely does so.

    Based on the data in your post and the Wikipedia article, it is likely that using IRV would have been elected Macron even with the voting modifications you gave in your example. Based on your modified results example data, the IRV would be something like the following. (I had to make up some numbers, based on preferences described your post, since neither you nor Wikipedia provided them.) I omitted Cheminade since he had only 0.18%.
    (A) Macron, (B) Le Pen, (C) Fillon, (D) Mélenchon, (E) Hamon, (F) Dupont-Aigan, (G) Lasalle, (H) PouTou, (I) Asselineau, (J) Arthau
    20% A>B
    21% B>C
    11% C>A>B
    11% C>B>A
    22% D>A
    6% E>B>A
    5% F>B>A
    1% G>C>A
    1% H>C>A
    1% I>C>A
    1% J>C>A

    The rules for eliminating candidates are as follows.

    Step 1: Add the votes for each candidate for all ballots that include the candidate as an acceptable choice. The results:
    100% A
    63% B
    58% C
    22% D
    6% E
    5% F
    1% G
    1% H
    1% I
    1% J
    Eliminate all candidates with less than 50+%. That leaves only A, B, and C. Distribute the highest acceptable choice among remaining candidates. This gives the result:
    42% A>B
    32% B>C
    13% C>A>B
    13% C>B>A
    Note that it is possible with IRV that no candidate has greater than 50% acceptability. I have not seen any clear rules about what should happen in such cases. One possibility I find reasonable is to elect the candidate with the greatest acceptability, rather than the most top preference votes, but many people might reject that as not reasonable. Another possibility is that an entirely new collection of candidates should be selected for a new election.

    Step 2: Eliminate the candidate with the fewest votes, C, and redistribute the ballots for that candidate to the remaining candidate with the highest preference. (This step is repeated until a candidate has greater than 50% of the votes.) This results in the following:
    55% A>B
    45% B>C
    A wins. Note however, if all voters who preferred C had B as the second choice, B would have won. This shows that a candidate which fewer voters find acceptable can still win if they have at least 50+% of acceptability.

    Although you have shown in your examples that it is possible for IRV to have a "bad" result, at least the results are not as bad as no runoff or ordinary runoff which methods can elect a candidate who has less than 50% acceptability.

    Regards,
    Buzz
     
    Last edited: Jan 21, 2018
  21. Jan 21, 2018 #20

    StoneTemplePython

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    This seems to be going off topic, and is wrong. In the US if no candidate has a majority of electoral college votes, then congress votes in the next president. It is simply a different non-comparable system.

    - - - -
    edit: I poked around and it seems that I was focusing on majority win voting while there are plurality win voting structures as well, and the run-off structuring can vary quite a bit. Most run-offs that I've read about in international politics, e.g. Peru's 2016 election, seem to be designed to deal with the case when there is no majority winner in round one (i.e. something different than the US setup), but it seems this musn't always be the case.

    The issue that I tried to highlight is that you cannot have a minority winner in the US by construction. (The fact that it is done via electoral college and not popular vote further muddies the waters and makes the comparison inappropriate in my view.)

    Stepping back a bit, I am getting a feeling that there could be an interesting insights piece on Arrow's impossibility theorem lurking under here...
     
    Last edited: Jan 21, 2018
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