In this article a collection of discussions regarding the fact that someone has put forward the hypothesis that The Perfect Choice could disprove Arrow’s Impossibility Theorem.
It would be a really important thing if this were the case, which is why we are looking for mathematicians who want to investigate this and produce a report to be peer-reviewed. Reward is negotiated, fresh minds are preferred, open to new things, even non-professionals, perhaps students, who could also propose a thesis on this method in comparison with other methods of collective choice.
Links with sources at the bottom of the article.
A.B: “OPEN” MESSAGE TO EMANUELE NUSCA
Emanuele, while I try to look for someone to compare The Perfect Choice with Arrow, I personally have come to the conclusion that dual voting will never be able to represent the real preferences of the electorate, despite being a good “simple and practical” solution, … and much better than single voting.
If we take for example 9 candidates — A, B, C, D, E, F, G, H and J — and model voters’ preferences with 100 positive points and 100 negative points to be freely distributed, for example +40 respectively , +30, +20, +10, 0, -10, -20, -30, -40 for voter able to grasp everything “in between”.
If, for example, all the voters wanted to vote for 4 candidates each, with +51, +49, -49, -51, distributing the 51 among different candidates, but concentrating the 49 on a few, it is evident that some candidate he could, by adding the +49 concentrated by everyone on him, add up to many more preferences than other candidates who each get a few “scattered” +51s.
That is, if there were 8 voters, each inclined to give one of the candidates, C excluded, +51, but ready to give +49 all together to C, all the “first choice” candidates would add only +51, while C as ” everyone’s second choice” would add 49 * 8 = 392!
With in the Perfect Choice, all but C would add up to 1, and there would be a similar dispersion of the -1s, without the “widespread second preference” for C emerging in any way.
All this does not take anything away from the practicality and usefulness of the dual vote, but it seems to me that it could undermine the basis of the term “perfect choice”, because having +100 and -100 points available would certainly be better than having only +1 and -1.
Emanuele Nusca: Thank you for explaining this point of view, which I have certainly been thinking about for some time.
First of all, I would like to remind you that “The Perfect Choice” is the name I gave to this method, which regardless of which one you wear, remains the same in substance.
However, the reasons for choosing the adjective “perfect” are multiple: the main one lies in the definition of this word which is also explained in the manual, not by chance
.. and it refers to the choice, which, when made, manifests itself through an action that in some way certifies it and therefore brings it to an end, that is, perfects it.
It can therefore be stated that every choice made is somehow perfect in itself and at that moment, precisely because it is the one that is made and not any other.
I make a further note: I would like the voting method to be considered during the examination phase, regardless of whether this is applied to the choice of a candidate for some office, because this is only one of its possible uses and a voting method must be chosen for its goodness with respect to the results it offers, regardless of the specific field in which it operates at a given moment. In fact, in the Perfect Choice manual , reference is made to generic options, while other voting methods are often described using the example of choosing a candidate and this can be in some way manipulative with respect to the judgment given to the system, or introduce unnecessary, indeed deplorable, bias.
Going back to math…
What you propose would be, if I understand correctly, a “Dual Ranked Vote, although you propose it in cents.
I’ll explain to you why for me the “dry” Dual Vote +1/-1 is in any case always preferable and desirable, compared to any other and therefore also to the hypothesis you make.
It has being understood that each voter has his own set of knowledge, tastes and needs on which he bases his own judgment which therefore determines his own unquestionable final vote, as required by any method, and that the options can certainly be placed in a individual satisfaction scale, it is not at all certain, indeed it is highly unlikely that the values assigned to the individual options, which are necessary to assume in order to order them, are equidistant from each other.
That is, to order options according to a preference and therefore on a certain scale (which is used for example in Condorcet and Shultze), whether it is dual or not, the voter must first judge all the proposals and assign a judgment to each proposal and then extract the ranking.
However, to rank order the options, you must first assign a single value to each option and these may not all be equally spaced apart.
An example could be that a voter, having to assign a value from 0 to 10 for each option, has these personal preferences: a 3, b 8, c 2, d 9, e 6, f 10, g 0, h 0, j 2.
So, if we translate this data into the ranked vote we already understand that we lose a big definition and insert a data that does not reflect the reality of the initial values!
That is, putting the proposals in order of preference does not provide data on the value distance they have from each other because if you look at the example I gave, the order would be: f (10), d (9), b (8), e (6), a (3), j-c (2), g-h (0), but the evaluation distances are not the same and there are also ties that would be changed in the ranked vote, because the real distances are: f >1> d >1> b >2> e >3> a >1> j =0= c >2> g =0= h.
A.B.: I don’t propose anything different from dual voting (which is simple and practical).
I say that when you say that some voting method “reflects the preferences of the electorate”, you have to be very careful what you mean. Because it might not be true.
E.N.: ok thanks, in fact I agree, which is why I am available to discuss any objections and explain the reasons for TPC!
I add further considerations: first of all we need to understand what ALL THE POSSIBLE OPTIONS are for a given problem which is the object of the choice and which can be presented by the group that chooses, before and regardless of the expression of the vote, because this will be a further investigation, which will be used to determine approval rankings.
That is, if the correct conditions for a collective choice are not created, it will not even be possible to arrive at a vote that makes sense and is successful.
That is, we must first of all be sure that THE OPTIONS ON THE VOTE ARE AN EXPRESSION OF THE ELECTORATE, to then understand how much and how they “weigh” and why one will be preferable by the group rather than another and how they are all arranged in relation to each other.
Furthermore, since the voter in the matter is an Earthly human being and no other, in practice, if there was only one voter in a vote, the final outcome would be the option he voted as the best as the winner, whatever method he uses, which is the one that will be realized, and would exclude all the others, and therefore the only thing envisaged by that option would materialize.
To explain it in other words, you cannot choose to go to more than one place at the same time by yourself, so for me it makes little sense to cast a multiple vote of any kind, in a vote, which is only necessary if there is disagreement in the group on the path that it must/wants to take.
Indicating your extremes of judgment with the Dual Vote therefore serves to define your ideal travel direction from A (-1, “where you come from”, “where you take energy from”) to B (+1, “where you goes”, “where the energy is placed”), which must be one and as precise as possible to be inserted within the pool of votes, which will then draw the overall figure, together with all the other votes.
Another conversation started by P.D., regarding ARROW’S THEORY.
P.D.: Arrow’s theorem is a mathematical demonstration of the impossibility of identifying the general interest of a community by taking the individual preferences of its members as a basis. In scientific terms, Arrow’s theorem demonstrates the intransitivity of collective choices even when individual preferences are transitive.
Intransitivity of collective choices
Voting order and final choice
Intransitivity of collective choices
Let’s take a practical example by taking a community of three people (A, B, C). We ask each person to reveal their individual preferences towards three choices X, Y, Z. Each of them orders their preferences in the following way:
Individual choice1. choice 2 choice 3
A
B Y > Z Z >
C Z > X X > Y Z > Y
Note: The > symbol means that the individual “prefers” one choice. For example, writing X > Y is equivalent to saying that the individual prefers X to Y.
As we can see in the table, individual preferences are transitive. In other words, if you prefer X to Y and Y to Z then you prefer The sum of transitive individual preferences determines intransitive collective preferences.
Voting order and final choice
The outcome of the final choice made by majority is therefore determined exclusively by the order of voting between the choices. Let’s take three practical examples:
If the community votes first between X and Y (choosing X) and then between X and Z, Z emerges as the final choice.
If the community votes first between X and Z (choosing Z) and then between Z and Y, Y emerges as the final choice.
If the community votes first between Y and Z (choosing Y) and then between Y and Z, X emerges as the final choice.
In conclusion, given the same individual preferences, the choice of voting order radically changes the result of the final vote (collective choice).
_
Emanuele Nusca: I think the only thing that Arrow demonstrates is that it is impossible to create the “perfect” system that he would like as such, on his own terms, which however DO NOT TAKE DUAL VOTING OPERATION INTO CONSIDERATION (they couldn’t at his time because TPC had not yet been conceived).
The problem, at this point, I believe is precisely the conditions he poses, in fact there are still many systems for making collective choices, which return complex figures in the results, but which in some way reflect the will of the choosing group.
That is, every voting system is actually an INSPECTION METHOD, that is, a tool used to carry out investigations, a tester of a collective orientation/taste/will.
However, as is logical to understand, each tester is the creator of the measurement, and each measurement also depends on the tester, which must be calibrated and which in any case can present different scales.
Even testers, and all tools in general, evolve over time and for me, the best voting system is currently The Perfect Choice with Dual Voting: The voter chooses 2 options: The best and the worst, which will respectively take + 1 and -1.
This reveals a very complex picture of results, but easily interpretable by everyone. Furthermore, if the group knows that it will have to express this type of dual preference, even the debate prior to the vote, the one where the problem is circumscribed and solutions are proposed, takes on a “new” turn, because we are aware of the fact that, after the vote, the “negative energy” intrinsic to every proposal will also be revealed, and not just the positive one or, the lack of this fundamental and opposite data to it, as always happens in a vote with only “positive” votes.
An example to understand that TPC “we want to see more” in the votes could be that of TV. In relatively few decades we have gone from a blurry black and white image to one that is almost more beautiful than the real one, full color, full HD and more. Surely with this technology we can see more and better and perceive details that were previously impossible to reproduce, although the sources of the images remain the same.
I could give the same example in the medical field: before the discovery of x-rays and all the inspection methods that were created, it’s not that we didn’t know that there were organs inside our body, but certainly many of their qualities and ways functioning or malfunctions could absolutely not be seen as we see them today with the new instruments!
Well, the same thing happens with TPC: the system REVEALS many aspects of the collective’s will that are simply impossible to reveal with other systems!
I would be really curious to know what Arrow would have thought of this system! 😉
In my opinion, in fact, one cannot fail to consider the soul, irrational part, always present in every earthling, which makes up the overall judgement, together with the rational one.
Another example I give, to understand the reason for the Dual Vow, is that of temperature and how it is known through the perceptions of the earthly, which are the basis from which we start to know and therefore compose any judgement.
We can understand the concept of temperature and consequently understand what is commonly identified as hot and cold, ONLY IF WE EXPERIENCE A CHANGE IN TEMPERATURE, therefore a change of state, from the one we are in to a new one, never experienced before.
If a Terrestrial were born and raised at a constant temperature, how would they know what a temperature change is?
How could you tell if you are okay or if you are feeling uncomfortable, hot or cold?
Only when he experiences a change in temperature can he understand what the temperature is and simultaneously identify hot and cold.
Ultimately we can carefully choose whether we like heat or cold more (therefore give a vote in a given circumstance) only when we have experienced both things in one passage.
Certainly when we opt for a political choice, which foresees that some or all of the options in play have never been tested or experienced before, we can only rely on forecasts, projections and analyzes to pre-judge them and assign them a possible vote, because we will have real knowledge of them only after having experienced them, however, even in this case the Dual Vote would be preferable, as the assignment of its negative part means that the voter also carefully examines the proposals that he perhaps does not know and tends to exclude default, because he already has his favorite to which to give consent, as very often happens.
P.B.: In my opinion, both Condorcet’s and Arrow’s theories are pure mathematical exercises that are of little use. Instead, the problem of democracy is poorly posed because it is based on the false idea that the community can formulate options on desires in holistic conditions of ophelimity.
(ofelimità s. f. [der. of the Greek ὠϕέλιμος “useful, advantageous”, der. of ὠϕελέω “to be useful, to benefit”]. – Term used, instead of utility, by the Italian economist and sociologist V. Pareto (1848- 1923), to designate the more or less intense sensation that an individual associates with the use or simple possession of an asset; it represents a purely subjective economic value (use value) which may not coincide with objective utility)
Emanuele Nusca: Why would it be a false idea? The Perfect Choice works precisely in this way: it encourages the community to formulate options on desires and will in holistic and ophelimity conditions, before voting.
The application of TPC, which is in fact a process that mostly takes place before the final voting phase, favors the community’s research work, but everything always depends on its will: if the latter does not want to operate in this way , there is no way to impose it, which is why there is no voting method or other tool that can change what the Earthling’s free will imposes.
The Terrestrials has the capacity to choose, albeit limited and almost certainly different from that of all his peers, and therefore to determine himself and therefore also to choose which method of choice to use.
How do you judge a method of choice if not through a method of judgment, however chosen arbitrarily by someone?
Is there a choice method to judge and choose the best among the choice methods that is not a choice method?
I doubt very much, but in this case we could make a vote between certain choice methods by repeating it with all the choice methods and where the options are the same choice methods, and compare the results provided by all the methods, to draw a study from it.
Not easy but absolutely doable.
…work in progress…
Arrow’s Theorem from Wikipedia:
https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem