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Ordinal preferences are not real preferences

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Nathyn Posted: Thu, Dec 27 2007 9:46 AM

Just a thought I had. Ordinal preferences are not real preferences and I can demonstrate this praxeologically.

But first: I've heard this has been proven using behavioral economics and game theory. They have had experiments where they will give a person a choice between several sets of 2 options and the outcome is different depending on the order in which they've given the options.

As I said, this can be demonstrated praxeologically, however. Ask yourself: What do I want? If you're hungry and you want to eat, what you want to eat is not such because of what it isn't. In other words, you don't prefer pizza because it's better than tacos but not as good as ice cream. You prefer pizza solely because you prefer the quality of pizza. Preferences are not ordinal. They are dynamic.

This can also be demonstrated through multi-tiered elections. Support for candidates vary widely based upon who they run against. Ron Paul has little chance of being president because few Republicans are Libertarians. Few Americans in general are Libertarians, but ironically, in any general election, Ron Paul would win by a large margin. Similarly, Hillary Clinton has a good chance of winning the Democratic primaries, but she would struggle in a general election. Who becomes president, then, isn't exactly who people want most. They often have arbitrary preferences that are irrational because they are inconsistent with themselves.

As a result, if there is some kind of large inequality -- like high structural unemployment stemming from technological growth -- closing that inequality through government spending would not reduce individual utility.

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Kirznerian replied on Thu, Dec 27 2007 11:58 AM

 

Nathyn:

As a result, if there is some kind of large inequality -- like high structural unemployment stemming from technological growth -- closing that inequality through government spending would not reduce individual utility.

 

 

Do you mean that goverment spending can reduce unemployment?

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DBratton replied on Thu, Dec 27 2007 12:00 PM

Nathyn:
Just a thought I had. Ordinal preferences are not real preferences and I can demonstrate this praxeologically.
 

No you can't.

Nathyn:
But first: I've heard this has been proven using behavioral economics and game theory. They have had experiments where they will give a person a choice between several sets of 2 options and the outcome is different depending on the order in which they've given the options.

This just says that preferences are influenced by environmental factors. Has someone claimed otherwise?

Nathyn:
Preferences are not ordinal. They are dynamic.

Ordinal and dynamic are not exclusive domains. They are not even related. Preferences can change from minute to minute but at any point in time you still have a first preference. This is why preferences are only interesting for purposes of economic analysis after they have been demonstrated through action.

Nathyn:
This can also be demonstrated through multi-tiered elections. Support for candidates vary widely based upon who they run against. Ron Paul has little chance of being president because few Republicans are Libertarians. Few Americans in general are Libertarians, but ironically, in any general election, Ron Paul would win by a large margin. Similarly, Hillary Clinton has a good chance of winning the Democratic primaries, but she would struggle in a general election. Who becomes president, then, isn't exactly who people want most. They often have arbitrary preferences that are irrational because they are inconsistent with themselves.

This doesn't support you claim either. You seem to be assuming here that there is or should be one overarching set of preferences; but election are aggregations of individual preferences. It is perfectly possible to have a scenario in which Paul can beat Hillary, Hillary can beat Giuliani, and Guiliani can beat Paul. Some of the people who have Paul as their first choice have Giuliani as their second choice and some have Hillary as their second choice. This is not a problem in the theory of ordinal value. It is simply a characteristic of the way we conduct elections.

 

 

 

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Kirznerian replied on Thu, Dec 27 2007 12:02 PM

 

Preferences are not ordinal. They are dynamic.

 

 

No. Preferences are ordinal and dynamic. The problem is that the individual does not know his achievable preferences because he does not have full knowledge of all means available to satisfy all possible ends.

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Nathyn replied on Thu, Dec 27 2007 12:21 PM
Kirznerian:


 
Nathyn:


As a result, if there is some kind of large inequality -- like high structural unemployment stemming from technological growth -- closing that inequality through government spending would not reduce individual utility.

 


 

Do you mean that goverment spending can reduce unemployment?



I'm saying the government can address inefficiencies in the distribution of wealth, leading to higher utility overall.

Structural unemployment stemming from technological growth (lots of high-tech jobs, not enough high-tech workers) was just an example. It could be addressed through public education.

DBratton:

Ordinal and dynamic are not exclusive domains. They are not even related. Preferences can change from minute to minute but at any point in time you still have a first preference. This is why preferences are only interesting for purposes of economic analysis after they have been demonstrated through action.

If preferences change from moment to moment, people apparently aren't even certain about what they want. Kirznerian said this above, too.

If this is true, it doesn't make much sense to call contracts necessarily "fair," because if one person has greater information, he can be deceived.

DBratton:

This doesn't support you claim either. You seem to be assuming here that there is or should be one overarching set of preferences; but election are aggregations of individual preferences. It is perfectly possible to have a scenario in which Paul can beat Hillary, Hillary can beat Giuliani, and Guiliani can beat Paul. Some of the people who have Paul as their first choice have Giuliani as their second choice and some have Hillary as their second choice. This is not a problem in the theory of ordinal value. It is simply a characteristic of the way we conduct elections.

Based on what you just said, their preference can't be ordinal.

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macsnafu replied on Thu, Dec 27 2007 3:01 PM

If you want pizza, you want pizza instead of anything else you can think of.  How is that not ordinal?

And the point about elections is that the electoral system doesn't really gauge individual preferences, ordinal or otherwise, therefore it's pretty irrelevant to your argument.

 

 

 

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DBratton replied on Thu, Dec 27 2007 3:08 PM

Nathyn:
I'm saying the government can address inefficiencies in the distribution of wealth, leading to higher utility overall.

Structural unemployment stemming from technological growth (lots of high-tech jobs, not enough high-tech workers) was just an example. It could be addressed through public education.
 

Who gets to play god and decide whose choices are good and need to be subsidized versus whose choices are bad and need to be taxed? We had a shortage of programmers which we "addressed" with higher funding for computer science programs. Now we have a glut of programmers. 

Nathyn:
If preferences change from moment to moment, people apparently aren't even certain about what they want. Kirznerian said this above, too.

I don't think that follows, but in any case we aren't interested in what anyone wants from one moment to the next. We are interested in what they do. Praxeology is the study of action. 

Nathyn:
If this is true, it doesn't make much sense to call contracts necessarily "fair," because if one person has greater information, he can be deceived.

One person having more or different information than another does not make a contract unfair. If you buy my car I don't care what you can use it for as long as we agree on a price. And knowledge is often subjective anyway. What you know may lead you to a different value assessment than the same information would lead me. 

Nathyn:
Based on what you just said, their preference can't be ordinal.

Sure they can. Assume 300 voters distributed as follows: 

        #voters   First Choice  Second Choice
           10         guiliani          hillary
           90         guiliani          paul
           10         hillary           paul
           90         hillary           guiliani
           10         paul              guiliani
           90         paul              hillary

So in a match up between giuliani and hillary  10 of paul's     votes go to giuliani and 90 to hillary:  hillary  wins.
So in a match up between hillary  and paul     10 of giuliani's votes go to hillary  and 90 to paul:     paul     wins.
So in a match up between paul     and guiliani 10 of hillary's  votes go to paul     and 90 to Giuliani: guiliani wins.

I think you were initially assuming that everyone who has Giuliani as a first choice must also have the same second choice, but that's not true. And the diagram you made for your last post depicts three people in the race; but there will only be two and the votes from the eliminated candidates will be distributed between them.

 

 

 

 

 

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rjljr2 replied on Thu, Dec 27 2007 3:25 PM

 Be careful using elections as an example. There are many ways to combine preferences, and they all suffer from some kind of issue or another. Generally, Arrow's theorem tells us it is not really possible to combine preferences in a completely satisfactory way. For example, transitive preferences can be come nontransitive.  See for example:

http://www.colorado.edu/education/DMP/voting_b.html 

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I fail to see any novel argument here. Are you saying people can change their preferences, and thus prefer A to B at time 1 and then B to A at time 2? So? How does this make them 'irrational', as opposed to capable of changing their minds? This is a point Mises makes in Human Action anyway.

So long as fraud has not taken place, not having perfect information and then regretting a decision is too bad. Information is a commodity, to be produced, sold and utilised. Should you desire to avoid 'buyer's remorse' you purchase it. It is amusing how the government is always the proposed solution.

 

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Nathyn replied on Fri, Dec 28 2007 9:22 AM

Inquisitor:

So long as fraud has not taken place, not having perfect information and then regretting a decision is too bad. Information is a commodity, to be produced, sold and utilised. Should you desire to avoid 'buyer's remorse' you purchase it. It is amusing how the government is always the proposed solution.

 

Is there any practical limit on how much information can be purchased? I don't believe so.

 In other words, if we all had the equal ability to purchase perfect information, you're right. But we can't purchase perfect information and our ability to purchase information still doesn't create equal access to information because of inequalities of income. This unequal access to information makes the fairness of certain deals somewhat dubious (for example, con artists' tricks).

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Nathyn:
Kirznerian:


 
Nathyn:


As a result, if there is some kind of large inequality -- like high structural unemployment stemming from technological growth -- closing that inequality through government spending would not reduce individual utility.

 


 

Do you mean that goverment spending can reduce unemployment?



I'm saying the government can address inefficiencies in the distribution of wealth, leading to higher utility overall.

Structural unemployment stemming from technological growth (lots of high-tech jobs, not enough high-tech workers) was just an example. It could be addressed through public education.

 

 

Never heard about the impossibility of interpersonal utility comparisons?

 

Structural unemployment exists because the individuals do not know were the jobs are. State intervention in education will no change this, it will only result in waste of scarce resources.

 

Unemployment is a phenomenon of disequilibrium, in equilibrium there is not such thing. The problem is how the equilibrating forces emerge to create the movement from disequilibrium towards equilibrium. State intervention generally reduces the strength of equilibrating forces with means that unemployment will be higher with intervention than without intervention.

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Nathyn:

Is there any practical limit on how much information can be purchased? I don't believe so.

The practical limit is how much money and/or time of yours you're willing to devote to purchasing information.

In other words, if we all had the equal ability to purchase perfect information, you're right. But we can't purchase perfect information and our ability to purchase information still doesn't create equal access to information because of inequalities of income. This unequal access to information makes the fairness of certain deals somewhat dubious (for example, con artists' tricks).

No, I am right regardless. You do not need 'perfect' information (what is 'perfect' information anyway?) All that the seller is obligated to do is refrain from lying about their product, and not selling it on false pretenses. Only if they deliberately misinform has fraud been commited. From there on it is up to the buyer how much they want to know about the product. Companies and not-for-profit institutions exist that release information on and reviews of products; their services may be utilized.


 

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Nathyn:

Is there any practical limit on how much information can be purchased? I don't believe so.

 

 

Depends on the nature of this information. There exists knowledge that cannot be purchased, because this type of knowledge is knowledge of your state of knowledge regarding the meas/ends framework. It is knowledge of your ignorance: Subjective knowledge.

 

 

In other words, if we all had the equal ability to purchase perfect information, you're right. But we can't purchase perfect information and our ability to purchase information still doesn't create equal access to information because of inequalities of income. This unequal access to information makes the fairness of certain deals somewhat dubious (for example, con artists' tricks).

 

 

Do you mean that only with perfect information transactions would be fair?

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Nathyn replied on Fri, Dec 28 2007 10:17 AM

Kirznerian:

Do you mean that only with perfect information transactions would be fair?

 

No, that's an absurd simplification.

Only with perfect information would ALL transactions be GUARANTEED to  be fair. With imperfect information and an unequal distribution of information, some can take advantage of the ignorance of others.

And in any case, shifting ordinal preferences just don't make any sense. When I say they're irrational, here's what I mean: If I want a car today and I want truck tomorrow, then my work towards getting a car yesterday was counterproductive to my getting a truck today. If ordinal preferences shift like that, that certainly contradicts the Austrian theory about "time-preferences." If what I want from today or tomorrow can shift, there is no reason to assume a persisting preference for goods & services within a certain time frame.

Based on this claim, you couldn't even really make any assertions about utility at all, whether it's satisfied or not satisfied. You might think that's great  because it prevents us from saying the state "helps" anyone, but it equally creates the opposite ambiguity: if you can't make any assertions about utility, then you cannot claim the state "harms" anyone or that any resources are "wasted." In fact, you couldn't even develop economics suitable for business practices with that assumption.

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Kirznerian replied on Fri, Dec 28 2007 10:56 AM

Nathyn:

No, that's an absurd simplification.Only

with perfect information would ALL transactions be GUARANTEED to  be fair. With imperfect information and an unequal distribution of information, some can take advantage of the ignorance of others.

 

 

 

I would not say that some can take advantage of the ignorance of others. But simply that some do not know the consequences of the transaction, and do not know that they do not know that. Since they will only realize a transaction if both think that they will be better of. The problem is not on the fact of imperfect objective information, since if they know that they have imperfect information and the consequences of it, they will know if that transaction can have bad consequences, with means that they will be able to maximize their utility. The problem is having knowledge of the extend of uncertainty involved in action, not on pure objective uncertainty itself.

 

And in any case, shifting ordinal preferences just don't make any sense. When I say they're irrational, here's what I mean: If I want a car today and I want truck tomorrow, then my work towards getting a car yesterday was counterproductive to my getting a truck today. If ordinal preferences shift like that, that certainly contradicts the Austrian theory about "time-preferences." If what I want from today or tomorrow can shift, there is no reason to assume a persisting preference for goods & services within a certain time frame.

 

It is not that preferences change, in acting, the agent discovers their true preferences. They do not contradict Austrian theory, they ARE the CORE of austrian economics.

Intertemporal preferences is a concept about preference about some data. The data is assumed to be given.

I am talking about the procedure of discovering the data itself, and changing knowledge about preferences is about that. If you knew that you would want a truck in the future, you will work towards obtaining the truck, not the car.

 

Based on this claim, you couldn't even really make any assertions about utility at all, whether it's satisfied or not satisfied. You might think that's great  because it prevents us from saying the state "helps" anyone, but it equally creates the opposite ambiguity: if you can't make any assertions about utility, then you cannot claim the state "harms" anyone or that any resources are "wasted." In fact, you couldn't even develop economics suitable for business practices with that assumption.

 

 

If you understand what the discovery procedure means, you will understand that there is no problem with changing perceptions about the preferences. In fact, that these changing perceptions exist because the individual does not know exactly the ends/means framework of action.

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Kirznerian replied on Fri, Dec 28 2007 11:11 AM

Nathyn, if you want to have a good understanding of the nature of these problems, you need to read Hayek and Kirzner. This one hour interview with Kirzner explains many of these problems:

http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=978&Itemid=99999999 

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JAlanKatz replied on Sat, Dec 29 2007 1:42 AM

Nathyn:

But first: I've heard this has been proven using behavioral economics and game theory. They have had experiments where they will give a person a choice between several sets of 2 options and the outcome is different depending on the order in which they've given the options.

Which proves what?  First of all, the only way I can think of that this experiment would be carried out would be to present to some people the choices, first in one order, then in another.  So, right away we have a time difference - they preferred A at time 1, but B at time 2 - don't see the problem.  Next, sure the order in which the choices are given can influence the decision - so?  Also, within the experimental context I would guess that the person simply stated their preference verbally, rather than expressing it through action, so this isn't necessarily reliable since preference can only be reliably expressed in action.

 

Nathyn:
As I said, this can be demonstrated praxeologically, however. Ask yourself: What do I want? If you're hungry and you want to eat, what you want to eat is not such because of what it isn't. In other words, you don't prefer pizza because it's better than tacos but not as good as ice cream. You prefer pizza solely because you prefer the quality of pizza. Preferences are not ordinal. They are dynamic.

Dynamic would mean changing over time.  Ordinal properties can change over time.  Take 100 people and have them run a race - keep track of who comes in first, second, and so on.  Then have them run the race again, and again keep track of the order in which they arrive.  The listing of the results for the first race gives the order at time 1, the listing of results for the second race gives the order at time 2.  Each gives only ordinal properties, yet the outcome is dynamic - different at different times.  Now, the pizza example.  Naturally I don't prefer pizza because it's better than tacos but not as good as ice cream - in that case, and with all three available, I'd choose ice cream.  The point of ordinal preferences is just that, at a given time, a man ranks the attainable outcomes in order of preference, and chooses his favorite.  However, if you prefer A over B, and B over C, there's no precise way of saying which difference is greater, or how much each difference is.  This is the case with ordinal numbers - if a runner comes in first, and another comes in second, it doesn't follow that the second runner took twice as long as the first, even though 2 is twice 1.  Cardinals, on the other hand, do give that kind of ratio.  One uses cardinal numbers, for instance, by giving the time in seconds for each runner to end the race.  In that case, yes, a runner who has a score 1 did finish in half the time of a runner who has a score of 2. 

This is an application of set theory to the natural numbers.  In set theory, the set universe can be pictured to be shaped like a cone.  At the vertex of the cone is the empty set.  From the vertex, draw a straight line up through the center of the cone.  This line forms the class Ord of ordinals.  This line begins with the set 1, then the set 2, etc., finally reaching the set aleph-nought=omega-nought of all natural numbers.  It then goes on to omega-nought +1, omega-nought +2, and so on.  Eventually, it reaches omega-1, the set containing all natural numbers and all elements of sets formed by adding natural numbers to omega-nought.  Then we have omega-1+1, etc.  There are certain questions about all this, such as the continuum hypothesis, known to be independent of the axioms, and the question of indescribable sets, also independent.  Since the axiom of choice is independent, a precise definition of an ordinal also is lacking, since the only clear definition requires the axiom of choice to be true. For any set located within the cone, its order type is said to be the ordinal one attains by drawing a horizontal line from the set to the vertical line and finding the intersection point.  Among the ordinals, there are certain sets which are cardinals.  To be a cardinal, an ordinal must be strictly larger than any set below it - that is, there does not exist a function f with domain the cardinal and image any subset of the cardinal which is an isomorphism.  For example, omega-nought+1 is not a cardinal, since we have the function f from omega-nought+1 to omega-nought given by f(x)=x+1, x not equal to omega, and f(omega)=0, which is an isomorphism. 

What this definition gives us is that cardinals differ by size, while ordinals differ only by order type.  For example, consider the two sets just discussed:

omega: {0,1,2,3,...} and omega+1: {0,1,2,3...omega} clearly differ in how ordering works - the second has a largest element, while the first doesn't.  However, as just seen, they are the same size.

The natural numbers, it turns out, are all cardinals.  So each one can be treated as an ordinal or cardinal - that is, each has the properties of both.  This is where the discussion comes from, not some idea that ordinal preferences are fixed in time. 

Nathyn:
Support for candidates vary widely based upon who they run against. Ron Paul has little chance of being president because few Republicans are Libertarians. Few Americans in general are Libertarians, but ironically, in any general election, Ron Paul would win by a large margin. Similarly, Hillary Clinton has a good chance of winning the Democratic primaries, but she would struggle in a general election. Who becomes president, then, isn't exactly who people want most. They often have arbitrary preferences that are irrational because they are inconsistent with themselves.

Well, you only reach that conclusion through aggregating preferences, which is precisely one reason that we treat preferences as ordinal, not cardinal - because aggregation doesn't work.  This aggregation, though, wouldn't even work with cardinals, because it's sloppy aggregation.  Let's scale it down to a country with 100 people.  We have four candidates, A, B, C, and D.  A and B are from Party 1, C and D are from party 2.  Now, imagine the preferences are as follows.

Party 1 - 50 members

30 prefer A to B, and prefer B to C or D. (hence, prefer A over C or D, and there's nothing irrational in their preferences)

20 prefer B to A, and prefer A to C or D.

Then A wins the primary.

Party 2 - 50 members

30 prefer C to D, and prefer B to C, while preferring C over D over A.

20 prefer D to C, and prefer B to D, while preferring D over A over C.

Then C wins the primary.

General election:  will be A vs. C

We'll have all members of party 1 voting for A, and 20 members of party 2 also voting for A.  So A wins.

Now, look at B.  B lost the party 1 primary, yet would have easily won the general election.  This seems unfair.  Yet, if we rearrange the system so that B is guaranteed a win, we'll find other elements which point to unfairness.  This was proven by Arrow - given 5 reasonable criteria of fairness, no voting system can fulfill them all.  It has nothing to do with preferences, though, since there isn't a single person who holds any irrational preference schedule.  In fact, even if people did hold something appearing to be an irrational preference schedule, it wouldn't establish your point, since the primary election is held prior to the general election, and so is separated in time. 

Nathyn:
As a result, if there is some kind of large inequality -- like high structural unemployment stemming from technological growth -- closing that inequality through government spending would not reduce individual utility.

I don't see how this is supposed to follow from your premises.  If somehow you had shown that preferences aren't linearly ordered, which I think is what you meant to show, it isn't clear that this would follow as an immediate step, you'd seem to need some work to close the gap between that very abstract point and this very practical point.  Technological growth, unless it eliminates scarcity, also won't produce high structural unemployment in the absence of union laws or minimum wage - and if it eliminates scarcity, then the unemployment rate should be 100%.  I also don't know how you intend to eliminate unemployment through government spending, unless you mean hire people to do unneeded work on the government payroll.  Finally, how would you know that, in fact, the person you took the money from had such irrational preference schedules as to prefer having money stolen from him to spending it on what he wants?

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