A system to blow your mind

Just come across this as a voting system – and have severe brain-ache. It does however appear to have something going for it when it comes to wanting to vote for or against candidates or indeed for or against “the system”.

It’s called chiralkine logic.

Paraphrasing their website, In a chiralkine electoral system the process seems to be:

The voter can choose between four possible responses to each candidate:

  1. Vote positively (1, 0) meaning the voter wants the candidate
  2. Vote negatively (0, 1) meaning the voter would not want the candidate
  3. Vote actively indifferent (1, 1) meaning the voter is so indifferent as between (1, 0) and (0, 1), that they want no one to be elected (i.e. “none of the above”)
  4. Vote passively indifferent (0, 0) meaning the voter is indifferent as between (1, 0) and  (0, 1), but would accept someone being elected with a minority of the vote.

The counting system is even more mind-bending:

The votes can be processed by the following steps:

  1. The votes for (1, 0) and (0, 1) are paired and cancelled, leaving a remainder of (1, 0) or (0, 1) votes. This is the residual antisymmetric (odd) component of the vote.
  2. The votes for (1, 1) and (0, 0) are paired and cancelled, leaving a remainder of (1, 1) or (0, 0) votes. This is the residual symmetric (even) component of the vote.
    1. If the remainder for (1, 1) or (0, 0) votes is for (0, 0), the result is the remainder of (1, 0) or (0, 1) votes.
    2. If the remainder for (1, 1) or (0, 0) votes is for (1, 1), the remainder of (1, 0) or (0, 1) votes is paired and cancelled with the remainder of votes for (1, 1), leaving a remainder for (1, 0), (0, 1) or (1, 1). This is the result. Thus, if the remainder is (1, 1), the election is rejected.

I suggest that all those who claimed that AV was “too complicated” should be forced to attend a seminar on chiralkine voting!

I think I can see what the system is trying to achieve – allowing you to vote for or against each candidate and expressing a circumstance where you would want a “none of the above” victory (and presumably a new election – possibly with new candidates), but it fails on the transparency test both at the voting and the counting stage.

If I have understood this wrong and you can explain it better please (1, 0) post a comment.

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  • Martin A Hay  On 27 August 2013 at 6:30 pm

    This might help. Think: raise your left hand only means go left; raise your right hand only means go right; raise both hands means go up, and do no raise either hand means go down. You have four choices. With a normal voting system, you can raise your left hand up (for), your right hand up (against) or just not show up. If you do not show up in a normal vote, there are no consequences. Whatever you do, the result will be a left or right victory. If you do not show up in a chiralkine vote, it will affect the outcome of the vote. This is because for and against abstentions are tallied against each other. People in power would be well advised to trial candidates in primaries, or test out support for questions in sample votes, prior to having everyone vote. If not, they risk having all their candidates or their questions rejected.

    Power lies in the hands of those who select candidates or pose questions, such as referendum questions. If you want people to reengage with the democratic process, you need them to see that they can use their vote to challenge the status quo. If not, they either become apathetic or take to the streets.

  • enfranchiseme2  On 27 August 2013 at 6:38 pm

    Martin, thanks for the above – situation a little less murky!

    Given the forthcoming Scottish Independence Referendum could you illustrate how a “chiralkine” referendum might work? Perhaps walk through a few scenarios based on an electorate of say only six people (so we can see what is happening)?

  • Martin A Hay  On 27 August 2013 at 10:56 pm

    The United Kingdom has lived at peace with itself as a state for hundreds of years. One reason for this could be that the question of whether or not it should be divided has not been raised. The planned referendum does not offer voters the opportunity to reject the question.

    Voters could be asked to vote:-

    For independence, not against (1,0)
    Not for independence, against (0,1)
    Not for independence, not against independence (0,0) – indifferent to outcome
    For independence, against independence (1,1) – reject the question.

    With six people, the electorate is small.

    You could imagine all six voting (1,0), which leads to independence

    You could imagine all six voting (0,1), which leads to a rejection of independence

    You could imagine 5 voting (0,0) and 1 voting for (1,0), which leads to independence (majority 1)

    You could imagine 5 voting (0,0) and 1 voting (0,1), which leads to a rejection of independence

    You could imagine 6 voting (1,1) which leads to a rejection of the question. Really, what this is signalling is that the electorate’s view is not represented by political establishment (the two sides taken together). The electorate does not view the issue in the same way as the politicians.

    You could imagine 3 voting (1,0), 1 voting (0,0) and 2 voting (1,1). In this case a majority of 1 voted (1,1) as compared with (0,0). A majority of 3 voted (1,0) as compared with (0,1). 1 majority for (1,1) is 2 less than the majority for (1,0) over (0,1), so the vote is for independence. (A vote for (0,0) is equivalent to a vote for (1,0) and for (0,1) at the same time).

    If the group of politicians in power (the group of people appearing to act as antagonists of one another, but actually acting in concert to offer the electorate just two alternatives) was representative of the electorate, a majority of people would vote for or against independence.

    Some questions are best left unasked.

  • enfranchiseme2  On 27 August 2013 at 11:32 pm

    Thanks, so to check that I have understood the last scenario:

    Conventional Votes
    3 voting (1,0) – For Independence
    0 voting (0,1) – Against Independence
    3 Majority for Independence

    “Abstention” Votes
    2 voting (1,1) – accepting the question
    1 voting (0,0) – rejecting the question
    1 Majority for accepting the question

    3 Majority for Independence
    1 Majority for accepting the question
    2 Majority of Conventional Majority over Abstention Majority

    So as the weight of votes for independence exceeds the weight of abstentions (which accept the question), the Conventional Result stands.

    Conventional Votes
    2 voting (1,0) – For Independence
    0 voting (0,1) – Against Independence
    2 Majority for Independence

    “Abstention” Votes
    3 voting (1,1) – accepting the question
    1 voting (0,0) – rejecting the question
    2 Majority for accepting the question

    2 Majority for Independence
    2 Majority for accepting the question
    0 Majority of Conventional Majority over Abstention Majority

    So the abstentions “win”? Which presumably means we do not get Scottish independence, but the idea is not rejected, so politically the door remains open for another vote in the near future?

  • Martin A Hay  On 28 August 2013 at 9:08 am

    I have actually defined (1,1) as reject the question. It does not matter how we define (0,0) and (1,1) as long as we apply the definition consistently. There is nothing in a vote for (1,1) or (0,0) that signals any preference as between (1,0) and (0,1).

    When you have a tie, you are in a state of indecision. Sometimes that can be a good thing. A leader might remain in this state for some time until the leader can decide whether or not to launch an attack on Syria. The leader may try to break the tie by reframing the question: by looking for more options.

    Voting is all about decision making. I imagine that the neurons in our brains act like voters in a chiralkine system. Eventually a large majority of neurons is all firing one way, and so a decision emerges in the conscious mind. The brain is able to simultaneously weigh moving the body left, right, up, down, forwards and backwards in response to an opportunity or threat (e.g. a lion jumping out from behind a bush). It is not restricted to just two options.

    We need our democracy to work like a brain, where each voter is like a neuron contributing to our collective decision. If you are stuck in a go left or right paradigm, you cannot get to a decision to climb up into a tree when a lion appears.

  • enfranchiseme2  On 28 August 2013 at 7:30 pm

    “We need our democracy to work like a brain”
    Have you come across the work of Stafford Beer – Managerial Cybernetics and the Viable Systems Model?
    When I was a post-grad I was told studying this would be far more mind expanding than any substance you could buy in the city! It was (not that I tried the substances).

  • Martin A Hay  On 28 August 2013 at 8:33 pm

    Interesting. Have you seen this?
    Notice how the subject controls the quadcopter by imagining left and/or right movement.

  • enfranchiseme2  On 28 August 2013 at 9:11 pm

    Let’s push this to the next stage to test to see if my original post was right.

    Can you demonstrate a few election scenarios – say where 10 voters are trying to elect a single representative from three candidates. Presumably against each candidate’s name on the ballot paper is a box for “yes” and a box for “no”. Then what?

  • Martin A Hay  On 28 August 2013 at 9:59 pm

    There are three candidates: A, B and C, and 10 voters
    A vote for one candidate (1,0) is also treated as a vote against the other two candidates (0,1)
    A vote (0,0) is for all candidates
    A vote (1,1) is against all candidates.

    The candidate with the most votes wins unless the majority for the candidate is less than the majority for (1,1) over (0,0).

    A typical turnout in a UK general election is now only about 60%.
    In the event that A wins 4 votes, B wins 1 vote and C wins 1 vote, A with a majority of 3 will win unless all 4 of the symmetric votes are (1,1). In that case, it would be as if 4 have voted for A and 6 against.

    If each candidate wins 2 votes, there is a tie, but also potentially a majority for (1,1) over (0,0). More people can have voted against each candidate than for each candidate.

  • enfranchiseme2  On 28 August 2013 at 11:24 pm


    A vote (0,0) is for all candidates (i.e. you don’t mind who represents you)
    A vote (1,1) is against all candidates. (i.e. “none of the above” – a 1,1 majority would mean no one is elected – which could lead to a later by-election)

    However, the logic of how I had read it (to offer the electorate a means to reflect subtleties of opinion) was that you could, for instance, fill in a ballot paper as follows:

    Candidate A – Yes (1.0)
    Candidate B – Yes (you are genuinely indifferent between A and B)
    Then for Candidate C you could vote a variety of ways
    i) Candidate C – Yes (you find all candidates equally acceptable)
    ii) Candidate C – No (0,1)
    iii) Candidate C (0,0)
    iv) Candidate C (1,1)
    Presumably each of ii, iii, & iv have subtle differences – mainly focused around what happens if neither Candidate A nor Candidate B get a conventional majority. Or is this level of complexity not allowed?

  • Martin A Hay  On 30 August 2013 at 8:32 am

    Sorry for the delayed response, but I was tied up yesterday.

    I have not yet worked through the maths at the level of complexity you are thinking in, but had identified it as a project that needs to be done.

    When you are using number pairs like (1,0), you are actually working in complex numbers. These complex numbers do not add and negate like integers. For does not mean the same as not against.

  • Martin A Hay  On 31 August 2013 at 10:31 am

    I think that the UK parliamentary vote on military action in Syria illustrates what I am trying to get across. At the time of the vote (MP’s views might change), parliament voted against military action. The outcome of the vote gives no indication as to whether MPs want to consider a different course of action or take no action. The main party leaders have indicated that they think that a different course of action needs to be identified. If a parliamentary vote allowed MP’s to vote (0,0) or (1,1) then perhaps the public would have been able to see more clearly what the attitudes of their MP’s actually are, and perhaps a few more MP’s would have shown up for the vote.

    • enfranchiseme2  On 31 August 2013 at 12:28 pm

      Listening to the results of that debate, similar thoughts crossed my mind. What is not understood is that MPs have a variety of ways to abstain.

      • – They can stay away
      • – They can sit in the chamber (0,0?)
      • – They can vote in both lobbies (1.1?)

      “One Tory, Tim Loughton (Worthing East and Shoreham), and one Lib Dem, Paul Burstow (Sutton and Cheam) voted in both lobbies, a technical abstention”BBC News website 30 August 2013 Syria vote: Which Tory and Lib Dem MPs rebelled? EDIT: (Looking at Hansard I see they seem to be listed as making up the vote; so in theory you could have everyone (except the Speaker) vote twice and get a vote 649 Ayes and 649 Noes!)

  • Martin A Hay  On 31 August 2013 at 2:00 pm

    Yes, MP’s can already vote (1,1) by passing through both lobbies, but this action does not contribute to the overall outcome. It should.

    The three number (+1, -1, abstain) system is reflected in the layout of the house. A circular layout combined with electronic voting from the seats rather than passing through lobbies would be more representative.

    • enfranchiseme2  On 31 August 2013 at 6:06 pm

      It seems that “double voting to abstain” is deprecated by the House (see BBC Website: Yes but, no but… MPs who vote both ways), but is quite common. Unfortunately.such abstentions get confused with MPs who accidentally “voted through the wrong lobby” and vote through the other one to partially “undo” their mistake. The article also mentions people voting to get the quorum.

      It does seem as if there is a need for greater nuances in Westminster Divisions.
      For and Against is reasonably clear (assuming not voting just to make up quorum), but as someone who is represented I would like to understand how my MP voted. He could be:

      • – Absent/Non Voting because he is “paired”; so he is voting for or against but knows his vote is netted off against someone else – usually for his convenience, sometimes for valid personal reasons (e.g. In hospital with a sick child)
      • – Absent/Abstained because he could not be bothered to be there
      • – Absent/Abstained because he wanted to oppose the whips but did not have the balls to obviously do so.
      • – Absent because the whips knew he would rebel so got him out of the way.
      • – Present/Abstained because he could not make up his mind
      • – Present/Abstained because he wanted to half-oppose the whips
      • – Double Voted because he wanted to sit on the fence
      • – Double Voted because he went through the wrong lobby and self corrected
      • – Double Voted because he opposed the whips and was then whipped through the other lobby.
      • – Some form of abstention because he did not think the question should be put (although I think there is a procedural motion to try and achieve this)

      I quite like “walking through the lobbies”; electronic voting with everyone having a defined seat gives a different feel to the chamber (although some change would be welcome). Any electronic system would have to be multi-directional; would chiralkine be sufficient to cover the majority of the above – particularly if absent voting was allowed (which is a substantial change and puts more power in the hands of the whips).

  • Martin A Hay  On 31 August 2013 at 9:38 pm

    It should surely be possible for MP’s to vote securely from anywhere where there is a phone signal or internet connection. If secure communication were not possible, the military could not operate. We already operate our bank accounts in this way. Shareholders vote in this way.

    Given the technology now available, it would appear timely to consider a wholesale review of the UK’s voting/decision making processes.

    I would very much like to see studies conducted on whether chiralkine voting can provide the basis for an effective decision making process that everyone knows they should participate in.

    At present, my focus is on building a prototype for a chiralkine trading system. I am trying to get it coded.

  • Martin A. Hay  On 23 February 2014 at 4:49 pm

    I have refined my understanding of chiralkine voting, and updated our website with a specific example. I think that every person needs to be given two kinds of vote, which I call a right vote and a left mirror vote. The maths is more difficult to follow than with conventional voting, but I think it will be possible to code the new system for electronic voting. Exactly the same system could be used to effect exchange without using money (an imaginary store of value) and for taxation to enable the provision of public services.

  • Martin A. Hay  On 5 September 2014 at 5:00 pm

    A first prototype for a chiralkine voting system has now been coded and is available for inspection on request.

  • Martin A. Hay  On 16 June 2016 at 2:46 pm

    Our website http://www.chiralkine.com has been updated. We are running two votes at the moment, one on the EU referendum and one on the US presidential election. Please have a go: http://chiral.campaign.gets.cc/campaign/brexit.cshtm
    Hopefully the explanation given will be clear. Please let us have any suggestions for improvements!

    • enfranchiseme  On 16 June 2016 at 4:03 pm

      Essentially these two examples are the same (two options). It would have been useful to see a Libertarian on the US ballot and possibly some further options on the EU ballot:
      – stay with Cameron’s pathetic “renegotiated relationship”
      – stay with pre-renegotiation status quo (reject Cameron’s negotiation but stay)
      – leave (whatever)
      – move to negotiating a Lisbon 50 exit and then bring back to a referendum.

  • Martin A. Hay  On 16 June 2016 at 4:15 pm

    On a superficial look, it appears that there are only two options, but the system allows voters to say different things when looking at them from each side (like and dislike). There are actually six options: four being different kinds of abstention. If enough people make use of the abstention votes, the question posed by the referendum needs to be reformulated. Repeated use of the system with different questions will achieve what you have suggested, and I agree is highly desirable.

  • Bemused  On 19 June 2016 at 5:52 pm

    The “School” result just leaves me bemused. “Right” and “Left” ballot arr presumably not “political” sides, but what does it mean? Who won and how/why?

  • Martin A. Hay  On 19 June 2016 at 8:09 pm

    The right vote is taken when voters consider options from the viewpoint of what they like the most. The left vote is taken from the viewpoint of what they dislike the most. So the students were narrowly for conservative over labour, but they were against nationalist parties. Fear of the SNP entering into coalition with Labour may have influenced many to vote conservative in the general election. The chiralkine vote actually picked this up.

    Try one of the campaigns I have given links to above. This will help you see how it works. The code links to my website (see link at top left), which gives an example of how a vote is analysed.

    This is an extremely powerful tool for getting a 3D image of what people in a group like and dislike.

  • Bemused  On 19 June 2016 at 8:38 pm

    So who won:
    – Conservatives as Most Liked (56-2=54) or
    – Lib Dems as Least Disliked (1-0=1)? (or is there an apathy threshold that disqualifies them?)

  • Martin A. Hay  On 19 June 2016 at 8:55 pm

    It is up to a society to decide how it interprets the results of any vote. Football works the same way: the winner of a league can change depending on how points are awarded for “draws” and “wins”.

    In the real general election, the conservatives won and the libdems were wiped out. They did not polarize the electorate.

    I would say that the best candidate is one that scores highest on the right vote and also very low on the left vote.

    If you look at this small vote in India, you can see that Apple have optimized on both sides. http://chiral.campaign.gets.cc/campaign/mobile-customer-in-india.cshtm

    What would have been interesting and worrying in the general election would have been if the majority against the conservatives was larger that the majority for them. This could have lead to an unstable state. It is what happened, I think, in Ukraine and in Egypt (Morsi – Brotherhood). It is always a risk when many parties are contesting an election.

  • Bemused  On 19 June 2016 at 10:41 pm

    What would have been interesting and worrying in the general election would have been if the majority against the conservatives was larger that the majority for them.

    vote for the Conservatives 37% of those voting (24% of electorate)
    vote against the Conservatives (all the others) 67% of those voting

  • Martin A. Hay  On 20 June 2016 at 6:31 am

    No. That is thinking based on the principle of a balance (-1+1 = 0 = +1 -1). It is the thinking of George Bush – if you are not for me, you are against me.
    A chiralkine system works on the principle of order (handedness), not a balance. Just because you are most for any other party does not mean that you reject all others. If you are a Labour supporter, you may accept a Conservative or Libdem government, but not a far right or far left one.

    An easy way to understand this is to think about the sides of the face. You have a left eye and a right eye, yes? The left eye is on the left side of the face and the right eye is on the right side of the face, yes? So, is there any area of your face that is not on the left or the right? So, do you have a nose? You can switch between thinking left and right and front and back. There are not just two mutually exclusive options. To go back to George Bush, if you are not with him, it does not mean you are against him.

  • Martin Hay  On 25 June 2016 at 8:28 am

    If a chiralkine voting system had been used to pose the Brexit referendum question, either by the UK government or the EU, then everyone would have been requested to indicate their preference as between remain and leave. This would have signalled what would happen in a straight binary choice. However, using a chiralkine system voters could have rejected both options, providing the UK government or EU with a warning and an opportunity to provide different options around which voters could come together. Our flawed binary voting system has split our nation down the middle. The technology we are using to take decisions is not working. It is unnecessarily divisive.

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