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Pre-Proposal: Would you like to be able to vote with number?

Discussion in 'Pre + Budget Proposal Discussions' started by demo, Jun 2, 2016.

?

Would you like to be able to cast votes using numbers and extract the results as an average?

  1. yes

    15.8%
  2. no

    73.7%
  3. other

    7.0%
  4. yes, but only for the median average

    3.5%
  1. GrandMasterDash

    GrandMasterDash Well-known Member
    Masternode Owner/Operator

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    It's not a 400 vote gap. If someone only gets 100 NO's then they only need 100 x 1.1 Yes's to win.
     
  2. demo

    demo Well-known Member

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    I dont understand what you have just said...
     
  3. Kevin Stalker

    Kevin Stalker Member

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    Thats not what i am seeing. Here is an example:

    PROPOSAL “A_DASH_BRANED_ATM_IN_SOUTH_JERSEY_USA“ (ACTIVE)
    Votes: 399 Yes / 81 No / 11 Abstain
    Will be funded: No. This proposal needs additional 83 Yes votes to become funded.

    This proposal - copied from the masternode voting page right now, has generally good support, but won't get funding unless a lot more masternodes get involved. If masternodes get more lazy in the future it seems to me it will become hard to spend our budget. I'm quite new to it, so maybe the more experienced guys here can put me right?
     
  4. Kevin Stalker

    Kevin Stalker Member

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    Yes - ok. I use words like "good proposal" flippantly as if the term is valid. If we define a good proposal as one which has the majority of votes, however, it makes more sense. The obvious way to do this is to simply demand 51% majority. Why not just do that?
     
  5. UdjinM6

    UdjinM6 Official Dash Dev
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    Not sure I understand - majority of what? 51% of total number of masternodes - 2000+? Or 51% of votes for specific proposal - like 11 YES vs 5 NO?
    The gap is here to asure somewhat overwhelming support and avoid situations in which controversial proposals could be funded.
     
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  6. GrandMasterDash

    GrandMasterDash Well-known Member
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    Then I don't know, someone needs to explain it to me / us again.
     
  7. Kevin Stalker

    Kevin Stalker Member

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    i suggest we go for a percentage of the actual votes cast. Make it 60% if you like. But lets face it, a proposal that gets funded due due slightly more than half the votes, but which you think is not "good" is not very harmful overall. The dash would otherwise be not created anyway, so its not a lot lost.
     
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  8. demo

    demo Well-known Member

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    <vote history>
    Would you like to be able to cast votes using numbers and extract the results as an average?
    *yes 4 vote(s) 10.8%
    no 30 vote(s) 81.1%
    other 3 vote(s) 8.1%
    </vote history>
     
  9. demo

    demo Well-known Member

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    What do you mean by "if you like". This is not an accurate wording.
    Could you please explain in details what is your proposed selection process?
    Does your proposed selection process respects itself?
    How does your proposed selection process compares with the alternative ones?
     
    #69 demo, Mar 26, 2017
    Last edited: Mar 26, 2017
  10. Kevin Stalker

    Kevin Stalker Member

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    Its a very simple change. Currently a proposal needs to get a majority of 10% of the total number of masternodes in existence in order to be funded. This is risky because of possible masternode apathy. I am saying proposals get funded if they have more than 60% of the total Yes/No vote count (excluding abstains). Everything else stays the same as it is now.
     
  11. demo

    demo Well-known Member

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    So a proposal gets funded if it has (for example) just 2 YES and 1 NO ? Regardless of the total number of the masternodes?
    This is what you are proposing?
    If you allow reversible transactions, then I could find a reason to your proposal. Otherwise your proposal seems absurd.
     
    #71 demo, Mar 26, 2017
    Last edited: Mar 26, 2017
  12. Kevin Stalker

    Kevin Stalker Member

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    Thats correct, in theory, but of course that would never happen. You are suggesting that it is possible that there could be a proposal that would be so banal that out of 4000 masternodes only 3 could be bothered to express an opinion. If that ever happens we will have a lot more problems than just the unnecessary funding of a project.
     
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  13. demo

    demo Well-known Member

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    Of course it may happen a few masternodes to be able to express their opinion, especially if the proposal enters the budget system exactly 72 hours before the budget finalization. Accept it : Your proposed selection process, as long as the reversible transactions are not allowed, is considered as a stupid one and will cause chaos.

    Additionaly, your proposed selection process has another important deficiency. It forces the participation, and refuses the right of abstention which is a very important right in the voting procedure. It is a total nuisance to force the voters to vote for whatever stupid proposal someone may think. The voters should have the right to abstain and that way protect themselves from troll proposals. But of course in some circumstances the community may want to diminish the abstention, and in those specific cases your proposed selection process may fit well.
     
    #73 demo, Mar 26, 2017
    Last edited: Mar 26, 2017
  14. Kevin Stalker

    Kevin Stalker Member

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    Abstaining is the same as not voting. There is no other way to count it. We clearly need a cutoff date for proposals, after which they go into the following month. Don't we have that?
     
  15. demo

    demo Well-known Member

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    We dont need a cutoff date for proposals, if reversible transactions are implemented.
     
    #75 demo, Mar 26, 2017
    Last edited: Mar 28, 2017
  16. demo

    demo Well-known Member

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    When we spot the masternodes among those who voted here, the result is
    Masters: yes/no/other=0/6/1
    Slaves: yes/no/other=4/26/2

    <vote history> <-- why vote history is usefull?
    Would you like to be able to cast votes using numbers and extract the results as an average?
    *yes 4 vote(s) 10.3%

    no 32 vote(s) 82.1%

    other 3 vote(s) 7.7%


    </vote history>
     
    #76 demo, Mar 28, 2017
    Last edited: Mar 28, 2017
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  17. demo

    demo Well-known Member

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    The third vote arrived a long time ago, and I havent yet started hacking the code.
    I think I will be judged guilty of not keeping my promises.:oops::(:oops:o_O:eek::confused::rolleyes:

    <vote history> <-- why vote history is usefull?
    Would you like to be able to cast votes using numbers and extract the results as an average?
    *yes 5 vote(s) 12.5%
    no 32 vote(s) 80.0%
    other 3 vote(s) 7.5%
    <vote history>
     
    #77 demo, Apr 23, 2017
    Last edited: Apr 23, 2017
  18. solarguy

    solarguy Active Member

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    If you insult me long enough, perhaps I will like you and your proposals more. Or perhaps not...
     
  19. demo

    demo Well-known Member

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    The truth is not an insult. It is a help.
     
  20. Pietro Speroni

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    Hello,
    sorry if I arrive late. I just set up my masternode, and I am still having trouble with it. I am also writing a book on eDemocracy, and have been working on eDemocracy for several years now (at least from 2009 nearly full time, and interested from 2005). I am a mathematician interested in voting theory, I am actually writing a book on eDemocracy right now (you can find it and support me on Patreon).

    The idea of voting with a number is the proposal I wanted to make, so well done in beating me on time on this. But it is very important that this is done well. And to do well you should not take the average, but the median.

    I saw other people have suggested the median before but not everybody was able to defend it properly. So please let me do it for them.

    The median, respect to the average have several qualities.

    You know what a Condorcet Winner is? Basically when you have several options, the Condorcet winner is the proposal that wins all pair wise comparisons. In other words, if you have n proposals of which you are going to implement only one, given two proposals a, and b, a pairwise comparison between a and b measures how many people would prefer a to b and how many people would prefer b to a. A Condorcet winner is a proposal that is preferred respect to ALL other proposals. Not always there exist a Condorcet Winner. There are some loops where the majority of people prefer A to B, B to C and C to A. Which is weird at the beginning.

    Now, there is a theorem, theorem of Black, or of the median voter, that in simple terms says:
    If:
    H.1) you need to decide a number
    H.2) the number is on a one dimensional space
    H.3) every person have their favourite number and how much they like the results goes down as you go away from that number

    In other words if it is unidimensional single peaked.

    THEN:

    T.1) there exist a Condorcet winner among all the numbers,
    T.2) if everybody votes for their peak, the median will be a Condorcet winner among all the numbers voted.

    T.1 is already a really good result. There exist a condorcet winner, wow!, we have a solution. We don't need to find compromises where no majority likes. But the really good thing is T.2 that it is possible to calculate this number without having to ask everybody to vote with their whole spectrum (how much they like each possible number).

    This is amazing. Now, the average does not have this property, and it does not have this property for some very clear reasons. The average is subject to strategic voting. Let me explain, if everybody has voted, and only I need to vote, and I know how everybody have voted I can pretty much manipulate the result by voting something very extreme. Suppose that we need to decide how much each proposal should cost. Now it is 5 dash, some people are proposing 1 dash, other 0.1 and so on. Suppose that you want a result being 2.3 dash, and the actual average is 2.1 dash, and 4235 nodes have already voted. Now you are the last one, you can pretty much calculate a number such that the resulting average is exactly 2.3. And if you are allowed to vote negative numbers you can also do the same trick going down.

    Notice that this does not happen if you use the median.

    So, great idea, congratulations. But make it the median, not the average.
    Pietro Speroni

    P.S. I am tempted to upload the file of the chapter of my book on this topic. But I just arrived and I am not sure how this would be taken :).
     
    #80 Pietro Speroni, Apr 25, 2017
    Last edited: Apr 25, 2017
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  21. demo

    demo Well-known Member

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    Yes of course, but I consider strategic voting to be an advantage, not a disadvantage. It is very important to know what the other have voted, and to adapt to their votes, this is what the games theory states. You are trying to somehow "hide" this property, by introducing the median average, but this is wrong, because you accustom that way the voters not to watch of what the others have voted. In the system I have in my mind there is no one that votes the last. The polls are permanent and the voters can change their vote whenever they wish. So in general there is strategic voting, but no one is the last one who decides. This is valid for most of the governance decisions, which dont need to have a deadline. But of course there are some few cases where decisions need to have deadlines. In that case the strategic voting requires for the smart voters to vote the last minute, in order to be able to see what the other voters voted.

    It is obvious that H.3 does not complies to the games theory, presupposes the total absence of strategic voting, thus it is a wrong premise. Do you know what a conditional vote is? The conditional vote is the correct premise.

    We can solve the problem the mean average has with the people who cast very high number votes in order to screw the average. Excommunicate them! I really believe that the mean average is the best selection process, if it is combined with a threat of excommunication for those who are far away from the average. So you allow the freedom of choice, but you maintain the excommunication/ostracism threat for the individuals who constantly vote outrageous (of course the individuals who vote outrageous can protect their privacy, if a proof of individuality scheme is used) Excommunication/ostracism in the sense that they lose their voting rights, not their money. I am a proponent of the temporary excommunication/ostracism, which means that if the ones who vote outrageous change the voting that has been judged by the whole community as such, then they should automatically gain their voting rights again. The number voting has sense within some bounds , although @GrandMasterDash claims that the mean average is the cause of the bounds problem. And I claim that nature is always bounded, with the speed of light being the upper bound.

    Of course excommunication/ostracism is always a very bad thing, thats why I am trying to solve that problem by introducing my mode average variation 2 selection process which is a combination of the mean average and the mode average.
     
    #81 demo, Apr 25, 2017
    Last edited: Apr 25, 2017
  22. demo

    demo Well-known Member

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    Please do it. How this would be taken? I dont think it would be taken as a bad move. You are helping the community that way.

    <vote history> <-- why vote history is usefull?
    Would you like to be able to cast votes using numbers and extract the results as an average?
    yes 5 vote(s) 10.9%
    no 37 vote(s) 80.4%
    other 4 vote(s) 8.7%
    </vote history>
     
    #82 demo, Apr 25, 2017
    Last edited: Apr 25, 2017
  23. demo

    demo Well-known Member

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    The median average is also prone to strategic voting.
    People who own more than one votes, in case of polarization they can simply remove one of their votes and thus become the median who decides.
     
  24. TroyDASH

    TroyDASH Well-known Member
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    It doesn't matter so much which vote is the median if those same votes would not change the final outcome by much if they existed or not. Mode on the other hand, if you have the highest frequency then none of what anybody else voted is factored in at all.
     
  25. Pietro Speroni

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    Hello everybody, thanks for your replies. I would like to clarify a few things.

    When we speak about polarisation there are two situation we are speaking, the first is when the people are polarised, and the second is when they are not polarised but our voting system forces them to polarise their vote.

    So to understand well the situation we need to distinguish between what people want, and what they vote to achieve what they want. The way you represent what someone want is either through ordering the possibilities: proposal A before proposal B, before proposal D before proposal C. (which can and is usually more briefly expressed as: A > B > D > C). Or { A: 10, B: 8, C: 4, D:6}. The second possibility gives us more information and in fact when you use it in voting you tend to have some extra properties (*). So there are more situations which map onto the same ranking. Also a person which desired { A: 10, B: 8, C: 1, D:6} would have been represented as A > B > D > C. But this is a way in which we represent what people want.

    Then there is a way in which they vote.

    In voting theory it is considered a big property the non manipulability. In other words the fact that you obtain your maximum outcome by voting in a way that simply represent your situation, desires. This because you want to lower the work done by the voters in trying to achieve their result, lower their computational time, make sure that the result represents well what people want, and avoid that smarter people have a different weight than people who are either dumber or believe that they should vote in a certain way for ethical reasons.

    A very different point of view is the one from game theorists. In game theory you want to raise your outcome, if necessary at the expenses of others. And you see this as inevitable. So people in game theory will see the fact that a game is more complex as a feature, not a bug. Especially if they think they can then manipulate or play the game at their advantage. Maybe because they are better players.

    So do Voting Theory and Game Theory have nothing in common. And in particular how come one theory sees something as a feature and another as a bug. This is obviously very confusing. The idea in Game Theory is that after everybody plays and keep changing their move in response to what other people play, the result is a Nash Equilibrium. A situation where no one can obtain a higher yield by changing their vote. Does a Nash Equilibrium always exist? Well, no. For example in an infinite set of possibilities it does not always exist a Nash equilibrium.

    Example of two people showing how voting gets polarised
    Let's make an example, we have two people Anna and Ben. Anna has as desired outcomes 0. With 0 Anna gets as outcome 1. And then we can imagine her outcome to go down linearly as y=-|x|+1. Ben instead has as desired outcome 1. With 1 Ben gets as outcome 1. And then we can imagine his outcome to go down linearly as y=-|x-1|+1.

    So Anna starts and votes 0, average (and the median) 0.
    Then Ben votes 2. And now the average and the median is 1.
    Then Anna Switches her vote and votes -2, now the average is 0.
    Ben switches into 3. Anna switches into -3. Ben switches into 4, Anna into -4, Ben into 5, and so on.

    This is a situation where is we assume that they can vote any number they never reach an agreement. In fact they polarise more and more. But it is not their position which gets polarised, it is how they represent it. If you let it run it does not reach a Nash equilibrium, but Anna will tend to vote to -infinity, and Ben to +infinity. If you impose a time when the vote will end, the last person who manages to get his vote in will get their whole outcome and the other will get nothing. If you impose a random time when the voting randomly closes, the result will randomly be a very polarised position between an Anna who was driven to vote a value much lower than what she wants, and a Ben that voted a value much higher than he wants. But the result is not an average between the two. It is randomly either one or the other.

    Example of three people showing how voting gets polarised with the average and not with the median
    In this case sing the median would not change nothing. But let us take a case of three people. Anna, Ben and Carl. With desires Anna: 0, Ben: 1, Carl: 2. Now the average would have to be 1. And so the Median. But if you let people change their vote, the guys on the average will get crazy and polarised, while the people at the median will just remain as they are.

    Average:
    Anna: 0
    Ben: 2
    Carl: 2
    Anna: -4
    Ben: 5
    Carl: 8
    Anna: -13
    and then it goes crazy

    Median:
    Anna: 0
    Ben: 2
    Carl: 2
    Anna: 0
    Ben: 1
    Carl: 2
    Anna: 0
    Ben: 1
    Carl: 2
    Stabilised with winner 1, which is also the Condorcet winner among 0, 1 and 2.

    Problems with excomunication
    Now, you might say, I will excommunicate anyone that votes to manipulate a result. But this is the whole point of strategic voting, and game theory. If you do not want this, then just don't use a tool that permits it. Either people can change their vote, and however they vote is ok. Or they cannot change their vote. In both cases the average does a poor job.

    When the average does a good job
    You know when does the average does a good job? When people don't know that an average is being taken, and they cannot change their vote, and they cannot communicate to each other. THEN it is a good idea. Because then it represents the wisdom of the crowds. Example (taken from the first paper on the wisdom of the crowds), suppose you all need to guess something. Number of beans in a bucket, hight of a building, value of bitcoin in 10 days. And participating in the game will cost you x, but whoever guesses better will win much more than. This is a prediction market. Now you will put your number, and that's it. Provided people did not influence each other (so delete the bitcoin example), the average tends to be as close to the actual result as the best expert. But also the median tends to have this property. But if you say to people that you want your average to be the result, now they will vote with that in mind, and vote differently. This is why, for example, in Amazon votes of 5 stars and 1 star are more common that 2 stars and 4 stars. It is not that books are so polarised, but it is that people try to manipulate the result with their vote.

    Iterative voting leads to Condorcet Winner
    Lastly in some cases iterative voting permits to reach the Condorcet winner with more probability (notice how in the case I made Ben changing vote was important even in the median example. With more voters this is not the case. But in the cases when iterative voting is important you need to be able to vote again and again with no threat of excomunications. And in those cases the voting system is not one that would naturally find the Condorcet winner. We have the luck to have this property with the median. So it is like having for free, naturally, the wisdom of the crowds on a silver plate. And this is, by the way, what have been advertised for Dash: voting to obtain the wisdom of the crowds.
    Notice that the wisdom of the crowds is a very precise concept, and not all forms of voting has it. In other words, if you are trying to predict something, not in all forms of voting the result approximate the result as well as the top expert. This is why we need to use the median.

    Thanks for your attention.
    I now will go back and retire to my cave to keep on writing my book.

    * Range Voting (which uses the average) and Majority Judgment (which uses the median) posses the Independence of Irrelevant Alternative property and are not subject to the Theorem of Arrow.
     
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  26. demo

    demo Well-known Member

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    There is no infinitive. In practice almost everything is bounded.
    So you can simulate all kind of votes with a vote from -1 to 1 and let the people vote all the decimals inbetween.
    And then transform 1 to the upper bound, and -1 to the lower.
    Most of the cases , you can find the bounds.
    Even the time can be bounded, you can set as the max time the average life expectancy.

    And I think it is a bad practice for the selection process to be hardcoded.
    This is against the freedom of choice. The community must be able to choose and change the selection processes.
    It is a bad thing a minority to impose their favorite selection process to the others, and to the next generations. This is what is happening to the dash governance system.

    Here is the system I propose, in brief.
     
    #86 demo, Apr 26, 2017
    Last edited: Apr 27, 2017
  27. demo

    demo Well-known Member

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    Imagine this polarized set of votes. 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9
    The median is 2.
    Someone who has a lot of votes, he keeps two of his votes and cast them the last minute.
    0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9
    Now the median is 8.
    In a polarized set of votes, the one who has a lot of votes can manipulate the result whithin the bounds of the polarization.
    This cannot be done in the mean average.
    <vote history>
    Would you like to be able to cast votes using numbers and extract the results as an average?
    * yes 6 vote(s) 12.5%
    no 38 vote(s) 79.2%
    other 4 vote(s) 8.3%
    </vote history>
     
    #87 demo, Apr 27, 2017
    Last edited: Apr 27, 2017
  28. Pietro Speroni

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    I appreciate you coming around to realise that vote manipulability is a real issue and we need to avoid it. The problem is that with the average you just need a single person voting 125. But of course people with multiple votes can make their vote stick out less. But here are a few points about your counterexample

    you always have counterexamples
    Yes, absolutely. One of the thing that you notice when you study Voting Theory is that if you take pretty much any two voting system you can always design a problem ad-hoc that will come up with different result for the different voting systems. And always some special cases where it makes more sense one voting system respect to the other. There are books written just with the list of those counterexamples, and the geometry of the various voting system.

    Here is another counterexample I placed in my book if you are interested (conflict of interest warning, the link goes to a Patreon page from where you can support me... not on Dash unfortunately).

    if the group is naturally polarised the median gives the power to the bigger group
    So, yes, if you have a group that is naturally very polarised and that do not spread through the whole length of the space, then as soon as one of those poles reaches more than 50% of the votes they immediately have the winner. The other group can do anything they want, but they are, de facto, a minority. And thus counts nothing. We said the winner is the Condorcet Winner, and if more than 50% of the people vote for one candidate over all others, that is the Condorcet winner by definition. No other questions needed or asked.

    And if the two poles are exactly of the same strength, and if the median voter realises that they are the "weighting needle" (translated from the Italian, ago della bilancia, meaning the person in the center that chooses where a situation goes) now that person has a huge power. But this is ok because it is a very rare situation, And it is very difficult for a person to design such situation. Most of the time the situation is not naturally polarised and if it is polarised the two poles do not have exactly to the last vote the same weight.

    LATE EDIT: The study of the relative power of the various groups in decisions is something very much studied. I also have a chapter in my book about it (the one on Banzhaf Power Index), but it is not ready for public consumption (the chapter, not the studies :) ).

    The problem with people having multiple votes
    Then there is the problem of people having extra weight. And I think here you struck (finally I must say :) ), on a real limit which is in Dash. All the experiments that are done with "The wisdom of the crowds" are done with a situation where each person has only one vote. And there is also a paper showing how as soon as people can influence each other, the result goes astray. Having multiple votes is the ultimate form of influence. One person literally controls more than one vote.

    So, yes, this is not a good idea if you are trying to extract the wisdom of the crowd (an approximation of what an expert in that would say, without knowing who to ask to, and when many "experts" tell you different things). And absolutely yes, if you have more votes to play with you can manipulate the median. Basically the median looses its great properties that it had respect to the average. If someone controls two votes, now the result is within an error of 2 people from the median voter. If someone controls n votes, you know the right answer is within n from the median voter. Make n big enough and the vote is irrelevant. If n > 50% you can avoid voting, and just ask this person, and the result will be irrelevant. The only thing you can say on the other side is that a person that has more votes has a bigger incentive to see this project succeed, so they will make more research. But there are wonderful examples of situations in history where this was not enough

    The Comparison with Prediction Markets
    The only thing I can think of, is that in Prediction Markets you have the possibility to have "voters" (people that bet, "bettors" ?) that have different weight. And the person receiving the bets must adjust the weights so that both sides have equal value. Only in this way they do not lose money. And where they stand at the end is the best prediction of the outcome.This is very much like a system where people use the median. It is also like a system where people use the average... if they care more about their personal turnout and not about the collective result. It has been shown that prediction market are on average a good way of predicting the outcome (reference available)

    Differences with a Prediction Market
    But here we have a system where people care about the collective result (they don't gain something by being right against everybody else), and where some people have more weight than others. hmmm. Not necessarily a recipe for success. And the reason why it took me so long to invest in Dash, and the reason why if this shortcoming does not get addressed I might look for alternatives. I do have a suggestion that I will present in the next days. I don't expect the suggestion to pass, but it is something that will given an economic incentive to people to keep all their dash together. Thus exchanging the bigger weight in the online senate with some extra Dash.

    So, to summarise:
    The median does not have strategic voting.
    the average has strategic voting.
    Iterative Strategic voting polarises the votes if you use the average but not the median.
    If the system is naturally polarised, the median just gives the result to the biggest block (if two poles). In that case, sometimes it is better the average but this case is rare and then you are better off using a different form of voting.
    People having multiple votes can make the result less precise.
    Partially the fact of having a bigger stake makes this less a problem, but it is still a problem.
    This is not a Prediction Market.
     
    #88 Pietro Speroni, Apr 27, 2017
    Last edited: Apr 27, 2017
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  29. demo

    demo Well-known Member

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    The important thing is that no one can vote outside the bounds.
    Everything in nature is bounded.
    So a single person may vote 125, or he may vote 1125 but he cannot vote outside the bounds, because this vote will be irrational.
    Voting outside the bounds is a mathematical assumption. In practice such a situation does not exist, and everything is bounded.
    The only thing that has no bounds is the time, but even in that case we can solve this problem by defining as maximum time the life expectancy.
     
  30. Pietro Speroni

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    Look, Amazon evaluations of books is bounded (1 to 5 stars) this does not stop people from trying to manipulate the result by polarising. And they end up voting 1 and 5 stars, more than 2 and 4. You add a bound, now someone must decide what are the bounds of the vote (so more complexity), and you get people all divided between the one that are voting for the max and those that are voting for the min. No one achieve its aim, and the result is NOT comparable to what any expert would give you. Which is what the wisdom of the crowd should be able to give you.

    Said that, enough with this discussion. I am leaving this thread. You really should get the hint from what the people have been telling you. Your proposal was voted no by a huge number of people. MAYBE if you change it with the median it might get more yes. Personally I am starting to suspect you are not really interested in finding the best solution, but in just keep the discussion rolling. So I am quitting it.
     
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