The Uncertainty of the US Presidential Election

– Hungarian version –

The scientific dialogue. Through the analysis of the recent, embarrassingly dubious American elections, we prove that
the American people is just as much a victim of manipulation as the citizens living under dictatorship.
Using a mathematical model, the authors show that through simple media techniques one can easily manipulate
common consensus so that one reach the most favorable decisions with regard to the current situation.

“Nothing is good if there are victims.” - B

How the era of world powers has conclusively come to an end, and how near the time is when no small group of people will be able to determine the life, feelings and thoughts of others beyond its own competence, without the possibility of being punished.

Getting to Know the Problem

Dániel Erdély: Before all the fuss around the US presidential elections, I made a bet on the whole thing.

Gyula Fáy: And did you win that bet?

D: Yes, I did! And it’s certified by a notary public!

G: That’s great! Congratulations! And now what?

D: I’ve been invited to the US to tell them how I knew this.

G: So, really, how did you know?

D: I don’t really know . . .

G: Anticipation? Intuition?

D: Not really. I have a theory, which says an election which reacts with itself has necessarily to malfunction, but I can’t prove this.

G: So, you need proof?

D: Yes, I’d need that. I have to explain . . .

G: To whom?

D: I don’t know exactly. Maybe the press, maybe the politologists, sociologists.

G: Is this the order of importance?

D: Yes...

G: Will there be any poll-workers?

D: Maybe there will be.

G: So, now what?

D: It would be kind of you to help me. Last time we met you told me you had a good model.

G: Not me, Shannon!

D: Ok, then it’s Shannon.

G: And Moore.

D: And Moore. I didn’t really pay attention last time.
If I recall correctly, with that model we can identify the undecidable scenarios.

G: You remember that right.

D: Is this the so-called ‘Quorum-theory’? Where Shannon starts with a fault-tree?

G: No, no! Back at Shannon’s time, the fault-tree wasn’t invented yet.

D: Oops, sorry. The fault-tree was invented by you based on Shannon’s work.

G: Don’t be joke! The fault-tree was created by the Livermore atom-scientists, including Ede Teller, back in the 1950’s.
Then in 1965 the first public document was disclosed by Haasl, at a Boeing-conference.
In 1972, the fault-tree approach became a US engineering standard.

D: Engineering?

G: What do you mean by “engineering”?

D: I mean, not social.

G: So you’d need a social standard?

D: If you want, you can call the laws and the orders a social standard.

G: Sorry, you started it. But I hope we’ll get back to the laws and the orders at the end of this talk.

D: Ok, so what’s up with this fault-tree approach? If you didn’t invent it, what do you have to do with it?

G: I said that I connected the fault-tree method to Shannon’s Quorum-theory.

D: I see. And am I correct regarding that this would provide an answer to my problem?

G: Look, Daniel. Your problem is too unclear (of course it has to be)...

D: Okay, then serve me an “if-then” type answer.

G: Well, if the question is “Do I think that I can give you a mathematical model for specifying the relationship between the self-reflection and the undecidability of a voting” my answer is yes.

D: Good. Could you explain?

G: To whom?

D: What do you mean by “to whom”? A model doesn’t get created for “somebody”.
A model is a thesis, which can be proven by anyone in certain terms. Any specialist, that is.

G: Yes, but you told me you have to make a presentation at a conference, or something...

D: To whom I’ll be presenting and how, now that’s my problem. But first, let me understand the theory, please!

G: As you like it. So you say “yes” to my question, which asked you whether you’re willing to get acquainted with a mathematical model of vote-manipulation and undecidability.

D: Do I have any other choice?

G: I think not.

D: Then I’ll say “yes” for the second time.

G: Well, and then let’s get on with it!

D: Let’s start!

Chapter 1

The Quorum

D: What the heck does “quorum” mean?

G: Did you learn Latin?

D: Yeah, but it doesn’t make any sense as a relative pronoun.
“Qui, quae, quod”“this, that, and this” – doesn’t say very much to me.

G: If you look it up in the explanatory dictionary, you can find out that “quorum magna pars fuit” means
“I contributed to it too, I participated in it as well (i.e. I played a great role in it).”

D: Sorry, but even this “i.e.” stuff couldn’t clear it up a bit.

G: I’m gonna explain it to you.

D: Does it have anything to do with the election after all?

G: Sure it does! Listen. I’m rather telling you my own version, so as to avoid having the religion-historians sue me.
Imagine that there are twelve cardinals who are locked up in a room, and they aren’t allowed to come out or even get anything to eat until they elect the new pope from among themselves by simple majority.
Of course, every single person is allowed to vote for himself as well. Well then, if I was a cardinal and had spent a whole lifetime hoping to become the pope some day, it would be a dead sure thing that I’d cast my own vote for myself.
And if the others think in a way similar to mine, the election of the pope will never ever damn happen.

D: Jesus! They cannot come to a decision, you mean?

G: Absolutely.

D: The cardinals were manipulated, weren’t they?

G: I didn’t say that. I’m only trying to explain the etymology of the word “quorum”.

D: Oh yeah?

G: Of course, sooner or later the “habemus papam” stands forth . . .

D: . . . and the mist vanishes . . .

G: . . . and there has to be one among the starveling old cardinals who hasn’t voted for himself, but for someone else.
Now, this self-sacrifying man can just proudly tap himself on the back, mumbling “quorum magna pars fuit, quorum magna pars fuit, quorum magna pars fuit”.
In English: “What would all you guys do now if I don’t give in?”

D: I see.

G: And the word, having undergone several changes in meaning, of course, now means . . .

D: . . . the ability to make a decision.

G: So much about the meaning of the word “quorum”.

D: And there’s a Shanonnish theory about this concept?

G: Exactly!

D: Well, what?

Chapter 2

The Quorum and the Flashlight

G: Let’s take the flashlight!

D: The what?

G: The flashlight!

D: What do you mean by flashlight?

G: I’d like to present a model of the absolutely reliable system.

D: By the aid of a flashlight.

G: That’s right. Look at this figure (Fig. 1)

fig. 1.
Fig. 1

Demonstration of the Shannon-model of reliability-theory with a simple flashlight

You can see on the figure, that by closing the switch K the lamp L becomes lit. If K is closed p times during a definite time interval, L will be lit p times. Of course, all this is only true if the parts (the power-supply T, the lamp L, the switch K and the connecting wires) are functioning faultlessly, absolutely reliably.

D: All right, I understand that.

G: Let’s call it main-event, when the lamp is lit, and let’s indicate that with F.

D: Consequently, the main-event, namely that the lamp is lit, happens then, and only then, when switch K is closed.

G: In other words, the output frequency of the system equals its input frequency.

The graphical representation of function F(p) is a line (Fig. 2.) :

fig. 2.
Fig. 2

F: frequency of the main-event
p: input frequency

In reality, of course, all the four parts can be faulty (the lamp, the battery, the switch and the wires). Supposing that every part is faultless, except the switch, the behav-ior of the lamp can deviate from the ideal behavior in two ways according to the state of the switch. It can happen that the lamp is not lit when the switch is closed, due to the faulty contact. This is what we call a first-order fault.

On the other hand, the lamp can be lit even when the contact is open, because the switch is short-circuited. This is called a second-order fault.

D: For example, if sand gets in between the contacts, that’s a first-order fault?

G: Yes. We can call it an “S” fault, not necessarily because it can refer to “sand”, but because it can mean “shifting error” as well. If the contact is faulty, that’s a first-order fault.

D: . . . then the sand shifts the effect of the closed contact.

G: . . . and the lamp will light up less frequently than in the ideal case. Consequently, according to the theory the characteristic Shannon-curve will run under the ideal straight line in this case, approximately so (Fig. 3.):

fig. 3.
Fig. 3

D: Excuse me, but does this thing have anything to do with the election?

G: Yeah, sure!

D: What would represent a switch at an election, for example? The voting button in the Congress?

G: Of course. With the difference that in the Congress not one person pushes one button many times, but many persons one button once.

D: And is this the same thing?

G: Yeah, the same.

D: Hey, why would it be the same?

G: Because of the ergodyc theorem.

D: What the heck is that?

G: We don’t have the time. Look it up somewhere. You gotta take it from me now.

D: OK. And what’s the lamp? The display indicating the total number of votes?

G: Not exactly. To be more precise, the event that the results are being displayed on the display.

D: The results are being displayed on the display? Couldn’t you say it more properly? For instance, the display shows the results?

G: The display shows the results and the results are being displayed on the display right now. It’s not the same thing when I say “I caught a cold” or “I’m suffering from influenza”.

D: Because there’s a possibility that you got better in the meantime?

G: Yes, and I’m not suffering from the flu anymore.

D: Is being so precise really important?

G: Only if you want an exact model.

D: OK, then let me try it. In fact, the display should blink as many times as the “yes” button had been pushed, right?

G: Yeah, that’s right!

D: And what about those who didn’t vote?

G: They are out of the paradigm.

D: Out of the what?

G: Out of the sphere of action of the model.

D: That’s too bad.

G: Why? Would it be better if it would include those people too?

D: Would be good.

G: And that it would report what those people do instead of voting?

D: Would be good, too.

G: Anything else I can do for you, Mister?

D: Okay, okay.

G: Then let’s continue. If the contact is faulty and we’re handling a second order fault, then the lamp will light up more frequently than it normally would be expected, because not every opening of the contact will be successful. According to the theory, in this case the characteristic Shannon curve will run above the straight line, approximately so (Fig. 4.):

fig. 4.
Fig. 4

We can call this a “C” type error, which can refer to the word “coffee”, since when you pour coffee into your keyboard a short-circuit is generated, which has the same effect as if you pressed a key, but in reality you didn’t, of course. But “C” can mean too that coffee causes a false effect.

D: I’m really not a nitpicking person, but I simply can’t comprehend what on earth am I to do with the failure of the buttons in the Congress. I am completely aware of it without any kind of Quorum Theory that when the electronics responsible for counting votes has malfunctions, the Congress cannot possibly arrive at a decision, no matter whether the devices had been manipulated or not.

G: Are you crazy? I’m talking figuratively!

D: What do you mean figuratively?

G: Well, a key press in the Congress can be ineffectual not only when the electronics break down, but there can be some other reasons too.

D: For example?

G: What example? You think I’m a janitor?

D: No, of course not, but I think the main point is that due to certain circumstances some votes can become ineffectual, or can even cause quite the opposite effect and this may lead to fatal situations when a decision cannot be made. Isn’t that right?

G: Yeah, that’s right. In order to avoid misunderstandings, and the chance for them will only increase as we progress further, I repeat that, due to certain circumstances some votes can become ineffectual, or can even cause quite the opposite effect and this may lead to fatal situations when a decision cannot be made.

D: Thank God!

G: Why are you so happy now?

D: Because now you’re gonna tell me the causes why votes get “distorted” and then I will understand how inquorate situations are actually developed, right?

G: Hell, no!!!

D: What?

G: Look, if your aunt remits you a 100 HUF bill from Szeged, but the postman in Budapest hands you over two 50 HUF coins, will you go all the way back to Szeged just to find out in which village exactly did your auntie’s 100 HUF bill fall apart to two coins?

D: I also know this remarkable scene by George Marx, but I don’t see that it has got any connection to our story.

G: The connection is that you’ll never solve the secret of the two 50 HUF coins in this bloody life if you just keep strolling the countryside with your ingenious common sense. The real cause is somewhere hidden in the whole postal system, which is hard to comprehend, indeed. Scaring the hell out of the poor postman asking how did he dare not to give you the bill of your auntie wouldn’t help at all. He would only think you’re a complete idiot and would say that he could pay you in bills as well. And if you demanded the original bills, you’d find yourself in a totally absurd situation.

D: This is all very nice, but I just can’t see the analogy.

G: Do you admit that there should be some sort of cause that distorts the effect of votes?

D: Of course I do, I’m here for that exactly. And I’d like to know what these causes are.

G: Here’s the problem, you see. Don’t try to seek what these causes are but rather what sort of causes they are.

D: This sounds slightly stupid.

G: Then let me add something more, paraphrasing Eddington this time. The causes are knocking on our senses, and we cannot stick out our heads to see who’s knocking, but can only learn how they are knocking. I can call even Neumann and Russel for help if needed.

D: Couldn’t we stick to Shannon and Moore?

G: We could. Now comes the great idea. The first-order failure of contact K in the Shannon model can so be taken into consideration that we substitute contact K with two contacts K1 and K2 connected in series (Fig. 5):

fig. 5.
Fig. 5

In this case the lamp is lit then and only then, when both K1 and K2 are closed. If the frequencies of K1 and K2 are both p, their collective frequency is p.p, evidently. Thus the quorum function will be a simple quadratic equation (a parabola): F(p)=p2.

D: Now I understand figure 5! And of course we don’t even think about investigating why the hell switch K falls apart to K1 and K2.

G: Not at all!

The second-order failure of contact K in the Shannon model can so be taken into consideration that we substitute contact K with two contacts K1 and K2 connected in parallel (Fig. 6.).

fig. 6.
Fig. 6

In this case the lamp is lit only when K1 or K2 is closed. If the frequencies of K1 and K2 are both p, it can be proved that their collective frequency is p(2-p). Thus the quorum function is a quadratic equation again (parabola): F(p)=p(2-p).

If we increase the number of switches either in an entirely serial or parallel architecture, the characteristics of the curve don’t change but it only becomes more and more “sharp”.

D: I think I understand that too. What happens in a general case, by the way?

G: If there are switches connected both in series and in parallel, the characteristics of the quorum function can radically change.

D: How?

G: So, that perhaps there would be a point of intersection where the curve would cross the ideal straight line (Fig. 7).

fig. 7.
Fig. 7

D: Wow! What kind of circuit would that be?

G: This one. (Fig. 8)

fig. 8.
Fig. 8

D: So in this circuit K1 and K2 are connected in parallel, K3 and K4 as well, while K1, K2 and K3, K4 are connected in series.

G: Yes.

D: This point of intersection is exciting. What does it mean if we have it? Of course, I’m not asking what it means regarding the structure of the circuit, because that would be some sort of extraparadigmal strolling about a non-existing countryside, but I’d like to know what it reveals to us about the election itself.

G: Isn’t it obvious enough? The system behaves ideally in the point of intersection. This is a state where the system represents the votes exactly. The output frequency equals the input frequency.

D: Is it like some kind of a focal point?

G: Something like that.

D: When the president behaves like an ideal flashlight?

G: Yeah, but only when there’s a point of intersection, or a quorum, as we use it in the jargon.

D: And there’s not always a quorum, of course.

G: Only in that case.

D: Since they can manipulate it. The quorum, I mean.

G: Yes, but through the switching circuits.

D: What kind of switching circuits are you talking about?

G: The ones in the model!

D: Do they really exist?

G: Unfortunately, I don’t know what “really” means.

D: Really?

G: Really.

D: Well, but can I ask what this structure is like, or how could one learn what it’s like?

G: Yes, you can. Actually, you must ask this question by all means if you want to understand the undecidable situation.

D: Sure, I want to.

G: It’s very simple. You just have to model the circuit diagram of the president by the aid of the fault-tree method.

D: You’re kidding, aren’t you?

G: I have never been so earnest in my life.

D: And is the fault-tree method advanced enough for that?

G: Advanced enough! They’ve been using it for a quarter of a decade over there. Many fault-trees have been modeled, including atom reactors’, points’ and welding workers accidents’ fault-trees, namely their virtual and invisible circuit diagrams.

D: And if I get to know these things then I know everything about elections, decisions and quorums?

G: Everything that’s worth it.

Chapter 3
The Self-Reflexive Voting

D: What happens if the result of the voting affects itself, namely that during the election voters can find about the voting results.

G: Then we’re dealing with Heisenberg’s uncertainty relation. If you try to measure the temperature of a flea with a room-thermometer, the flea will take up the room’s temperature.

D: Well, and according to the model, is such a feedback possible that leads us to an undecidable situation? Of course I’m not talking about equal number of votes but a lack of a point of intersection.

G: Certainly! The model says that all you need to do is monitor the blinking of the lamp by means of a photocell, and then this signal can be fed back to any of the switches by inserting delay. Thus you can deactivate any switch you want. If you know well the structure of the switching circuit, you can practically do just what you want.

D: Can it be simulated with a computer?

G: Nothing is easier than that!

Error tree
by John0

Error is the occurrence of a certain undesired event. For instance, if we have a gas boiler in our cellar, we do not desire it to explode. Of course, this possibility was presumably taken into account at the time of production, so we do not really have to be afraid of such an event.

But how can we be sure of this?

For this, we must map the structure of the system (the gas boiler in this case).

We must enumerate what can go wrong, what can lead to an error. If we are to be very systematic, we must choose some method as the basis of our investigation. The error tree provides such a method. Using the error tree, we can analyze the reasons for an error, and we will eventually arrive at an elementary event or a set of such events which may cause an error.

Let us consider what this means in relation to the gas boiler. (The particular events are fictive examples.)

The boiler can explode if neither the electric controller, nor the safety valve works. The electric controller does not work if the main circuit is damaged, it malfunctions, or some important wires are damaged. Important wires are damaged if either the wires between the thermometer and the controller, or the wires between the controller and the heating apparatus (i.e. the switch-off circuits) suffer damage. These events can be further analyzed, but sooner or later we will come to an event which is no longer worth analyzing. Such an event is an atomic event. In our case, for example, it is an atomic event if the safety valve is out of order, since it is completely irrelevant to us whether it is so because the packing ring has become worn, or the spring has broken.

We have seen that we can break down complex events to elementary events, and thus construct a tree diagram, which we call the error tree. In the error tree, we can put together special sets using atomic events, and these sets will then constitute strong and weak points.

Weak elements are elements (or sets of elements) whose realization results in

a system error. For instance, in the above example, the safety valve and the controller unit together form a weak set of elements. If both malfunction simultaneously, the result is a catastrophe.

Strong elements are those whose protection precludes the malfunctioning of the system. Thus if a ‘perfect’ guard ensures that the safety valve always function properly, the security of the gas boiler will never be endangered.

But how is this all related to the presidential elections?

Not only can we draw up an error tree with regard to errors, but also to other events.

Let us take the following event: Bush will be elected President of the US. Let us construct the error tree. Bush will be elected President if the electors elect him. They can elect him if their majority vote for him. Their majority will vote for him if they

follow the traditions (they vote predictably, which is by no means their duty), and their majority is Republican. For their majority to be Republican, it is necessary that Bush win the elections in states where his victory can ensure this majority. (This could also be formalized, using a very complex ‘either … or’ structure based on victory in states A, C, E, F, G, H … Z.) What matters in the present situation is the branch showing those states in which the majority has voted for Bush, plus Florida. Going on, we can further analyze Florida. (We may be interested in a further analysis, but it might prove rather complicated.)

Weak elements: it is interesting to observe that a weak element in the system is the supposition that the electors vote predictably. If, for instance, the opposite comes true [i. e. Republican electors vote for the Democratic candidate – Translator’s note], this will have a catastrophic effect on the whole event investigated, that is, Bush will not be elected President. Obviously, there are several other weak sets of elements as well, but the one mentioned is a particularly intriguing one. We must consider whether we should not break down this weak element into its further constituents. It may be necessary.

I have realized something: in an undecidable situation, every decision is bad. (Though the degree of this ‘badness’ can vary–but this is already a different question.)

For example, you are driving a car, and two cars are coming towards you, the one overtaking the other. Moreover, near the edge of the road, there is a precipice. This might not be an undecidable situation, but if it is, every decision will be bad.

(Translator: Boldizsár Fejérvári)

© Dániel Erdély és Gyula Fáy
Option Laboratories, 1055 – Hungary, Budapest, Falk Miksa 12.
Phone: +36 1 3324 032, E-mail: info@option.hu
Ötlet / Idea:
4 November 2000; Kézirat / Manuscript: 12 November 2000
Elsõ angol nyelvû publikáció / First publication in English: 4 January 2001, Israel
Második kiadás/ Sencond edition 15 January 2001, Budapest–Árnyékkötõk/28.
További részletek és dokumentumok / More details and documents on the websites:
www.option.hu/edan and www.openmail.hu.